diff --git a/src/ed25519/constants.rs b/src/ed25519/constants.rs new file mode 100644 index 0000000..139144b --- /dev/null +++ b/src/ed25519/constants.rs @@ -0,0 +1,1453 @@ +use ed25519::fe::{NUM_ELEMENT_LIMBS,Element,fe1,fe0}; +#[cfg(test)] +use ed25519::fe::test_from_bytes; + +pub struct Precomp { + pub yplusx: Element, + pub yminusx: Element, + pub xy2d: Element +} + +pub fn ge_precomp_0(h: &mut Precomp) +{ + fe1(&mut h.yplusx); + fe1(&mut h.yminusx); + fe0(&mut h.xy2d); +} + +impl Precomp +{ + pub fn new() -> Precomp + { + Precomp { + yplusx: [0; NUM_ELEMENT_LIMBS], + yminusx: [0; NUM_ELEMENT_LIMBS], + xy2d: [0; NUM_ELEMENT_LIMBS] + } + } + + #[cfg(test)] + pub fn load_test_value(xs: &[u8]) -> Precomp { + assert!(xs.len() == 160); + Precomp { + yplusx: test_from_bytes(&xs[0..40]), + yminusx: test_from_bytes(&xs[40..80]), + xy2d: test_from_bytes(&xs[80..]) + } + } +} + +/* k25519Precomp[i][j] = (j+1)*256^i*B */ +pub const K25519_PRECOMP: [[Precomp; 8]; 32] = [ + [ + Precomp { + yplusx: [25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605], + yminusx: [-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378], + xy2d: [-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546], + }, + Precomp { + yplusx: [-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303], + yminusx: [-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081], + xy2d: [26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697], + }, + Precomp { + yplusx: [15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024], + yminusx: [16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574], + xy2d: [30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357], + }, + Precomp { + yplusx: [-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540], + yminusx: [23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397], + xy2d: [7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325], + }, + Precomp { + yplusx: [10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380], + yminusx: [4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306], + xy2d: [19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942], + }, + Precomp { + yplusx: [-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777], + yminusx: [-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737], + xy2d: [-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652], + }, + Precomp { + yplusx: [5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766], + yminusx: [-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701], + xy2d: [28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300], + }, + Precomp { + yplusx: [14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726], + yminusx: [-7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955], + xy2d: [27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425], + }, + ], + [ + Precomp { + yplusx: [-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171], + yminusx: [27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510], + xy2d: [17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660], + }, + Precomp { + yplusx: [-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639], + yminusx: [29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963], + xy2d: [5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950], + }, + Precomp { + yplusx: [-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568], + yminusx: [12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335], + xy2d: [25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628], + }, + Precomp { + yplusx: [-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007], + yminusx: [-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772], + xy2d: [-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653], + }, + Precomp { + yplusx: [2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567], + yminusx: [13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686], + xy2d: [21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372], + }, + Precomp { + yplusx: [-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887], + yminusx: [-23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954], + xy2d: [-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953], + }, + Precomp { + yplusx: [24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833], + yminusx: [-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532], + xy2d: [-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876], + }, + Precomp { + yplusx: [2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268], + yminusx: [33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214], + xy2d: [1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038], + }, + ], + [ + Precomp { + yplusx: [6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800], + yminusx: [4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645], + xy2d: [-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664], + }, + Precomp { + yplusx: [1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933], + yminusx: [-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182], + xy2d: [-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222], + }, + Precomp { + yplusx: [-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991], + yminusx: [20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880], + xy2d: [9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092], + }, + Precomp { + yplusx: [-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295], + yminusx: [19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788], + xy2d: [8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553], + }, + Precomp { + yplusx: [-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026], + yminusx: [11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347], + xy2d: [-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033], + }, + Precomp { + yplusx: [-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395], + yminusx: [-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278], + xy2d: [1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890], + }, + Precomp { + yplusx: [32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995], + yminusx: [-30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596], + xy2d: [-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891], + }, + Precomp { + yplusx: [31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060], + yminusx: [11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608], + xy2d: [-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606], + }, + ], + [ + Precomp { + yplusx: [7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389], + yminusx: [-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016], + xy2d: [-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341], + }, + Precomp { + yplusx: [-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505], + yminusx: [14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553], + xy2d: [-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655], + }, + Precomp { + yplusx: [15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220], + yminusx: [12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631], + xy2d: [-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099], + }, + Precomp { + yplusx: [26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556], + yminusx: [14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749], + xy2d: [236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930], + }, + Precomp { + yplusx: [1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391], + yminusx: [5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253], + xy2d: [20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066], + }, + Precomp { + yplusx: [24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958], + yminusx: [-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082], + xy2d: [-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383], + }, + Precomp { + yplusx: [-30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521], + yminusx: [-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807], + xy2d: [23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948], + }, + Precomp { + yplusx: [9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134], + yminusx: [-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455], + xy2d: [27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629], + }, + ], + [ + Precomp { + yplusx: [-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069], + yminusx: [-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746], + xy2d: [24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919], + }, + Precomp { + yplusx: [11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837], + yminusx: [8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906], + xy2d: [-28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771], + }, + Precomp { + yplusx: [-25742899, -12566864, -15649966, -846607, -33026686, -796288, -33481822, 15824474, -604426, -9039817], + yminusx: [10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -4890037, 1657394, 3084098], + xy2d: [10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 31280319, 14396151, -30233575, 15272409], + }, + Precomp { + yplusx: [-12288309, 3169463, 28813183, 16658753, 25116432, -5630466, -25173957, -12636138, -25014757, 1950504], + yminusx: [-26180358, 9489187, 11053416, -14746161, -31053720, 5825630, -8384306, -8767532, 15341279, 8373727], + xy2d: [28685821, 7759505, -14378516, -12002860, -31971820, 4079242, 298136, -10232602, -2878207, 15190420], + }, + Precomp { + yplusx: [-32932876, 13806336, -14337485, -15794431, -24004620, 10940928, 8669718, 2742393, -26033313, -6875003], + yminusx: [-1580388, -11729417, -25979658, -11445023, -17411874, -10912854, 9291594, -16247779, -12154742, 6048605], + xy2d: [-30305315, 14843444, 1539301, 11864366, 20201677, 1900163, 13934231, 5128323, 11213262, 9168384], + }, + Precomp { + yplusx: [-26280513, 11007847, 19408960, -940758, -18592965, -4328580, -5088060, -11105150, 20470157, -16398701], + yminusx: [-23136053, 9282192, 14855179, -15390078, -7362815, -14408560, -22783952, 14461608, 14042978, 5230683], + xy2d: [29969567, -2741594, -16711867, -8552442, 9175486, -2468974, 21556951, 3506042, -5933891, -12449708], + }, + Precomp { + yplusx: [-3144746, 8744661, 19704003, 4581278, -20430686, 6830683, -21284170, 8971513, -28539189, 15326563], + yminusx: [-19464629, 10110288, -17262528, -3503892, -23500387, 1355669, -15523050, 15300988, -20514118, 9168260], + xy2d: [-5353335, 4488613, -23803248, 16314347, 7780487, -15638939, -28948358, 9601605, 33087103, -9011387], + }, + Precomp { + yplusx: [-19443170, -15512900, -20797467, -12445323, -29824447, 10229461, -27444329, -15000531, -5996870, 15664672], + yminusx: [23294591, -16632613, -22650781, -8470978, 27844204, 11461195, 13099750, -2460356, 18151676, 13417686], + xy2d: [-24722913, -4176517, -31150679, 5988919, -26858785, 6685065, 1661597, -12551441, 15271676, -15452665], + }, + ], + [ + Precomp { + yplusx: [11433042, -13228665, 8239631, -5279517, -1985436, -725718, -18698764, 2167544, -6921301, -13440182], + yminusx: [-31436171, 15575146, 30436815, 12192228, -22463353, 9395379, -9917708, -8638997, 12215110, 12028277], + xy2d: [14098400, 6555944, 23007258, 5757252, -15427832, -12950502, 30123440, 4617780, -16900089, -655628], + }, + Precomp { + yplusx: [-4026201, -15240835, 11893168, 13718664, -14809462, 1847385, -15819999, 10154009, 23973261, -12684474], + yminusx: [-26531820, -3695990, -1908898, 2534301, -31870557, -16550355, 18341390, -11419951, 32013174, -10103539], + xy2d: [-25479301, 10876443, -11771086, -14625140, -12369567, 1838104, 21911214, 6354752, 4425632, -837822], + }, + Precomp { + yplusx: [-10433389, -14612966, 22229858, -3091047, -13191166, 776729, -17415375, -12020462, 4725005, 14044970], + yminusx: [19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390, -1411784, -19522291, -16109756], + xy2d: [-24864089, 12986008, -10898878, -5558584, -11312371, -148526, 19541418, 8180106, 9282262, 10282508], + }, + Precomp { + yplusx: [-26205082, 4428547, -8661196, -13194263, 4098402, -14165257, 15522535, 8372215, 5542595, -10702683], + yminusx: [-10562541, 14895633, 26814552, -16673850, -17480754, -2489360, -2781891, 6993761, -18093885, 10114655], + xy2d: [-20107055, -929418, 31422704, 10427861, -7110749, 6150669, -29091755, -11529146, 25953725, -106158], + }, + Precomp { + yplusx: [-4234397, -8039292, -9119125, 3046000, 2101609, -12607294, 19390020, 6094296, -3315279, 12831125], + yminusx: [-15998678, 7578152, 5310217, 14408357, -33548620, -224739, 31575954, 6326196, 7381791, -2421839], + xy2d: [-20902779, 3296811, 24736065, -16328389, 18374254, 7318640, 6295303, 8082724, -15362489, 12339664], + }, + Precomp { + yplusx: [27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414, 15768922, 25091167, 14856294], + yminusx: [-18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300, -12695493, -22182473, -9012899], + xy2d: [-11423429, -5421590, 11632845, 3405020, 30536730, -11674039, -27260765, 13866390, 30146206, 9142070], + }, + Precomp { + yplusx: [3924129, -15307516, -13817122, -10054960, 12291820, -668366, -27702774, 9326384, -8237858, 4171294], + yminusx: [-15921940, 16037937, 6713787, 16606682, -21612135, 2790944, 26396185, 3731949, 345228, -5462949], + xy2d: [-21327538, 13448259, 25284571, 1143661, 20614966, -8849387, 2031539, -12391231, -16253183, -13582083], + }, + Precomp { + yplusx: [31016211, -16722429, 26371392, -14451233, -5027349, 14854137, 17477601, 3842657, 28012650, -16405420], + yminusx: [-5075835, 9368966, -8562079, -4600902, -15249953, 6970560, -9189873, 16292057, -8867157, 3507940], + xy2d: [29439664, 3537914, 23333589, 6997794, -17555561, -11018068, -15209202, -15051267, -9164929, 6580396], + }, + ], + [ + Precomp { + yplusx: [-12185861, -7679788, 16438269, 10826160, -8696817, -6235611, 17860444, -9273846, -2095802, 9304567], + yminusx: [20714564, -4336911, 29088195, 7406487, 11426967, -5095705, 14792667, -14608617, 5289421, -477127], + xy2d: [-16665533, -10650790, -6160345, -13305760, 9192020, -1802462, 17271490, 12349094, 26939669, -3752294], + }, + Precomp { + yplusx: [-12889898, 9373458, 31595848, 16374215, 21471720, 13221525, -27283495, -12348559, -3698806, 117887], + yminusx: [22263325, -6560050, 3984570, -11174646, -15114008, -566785, 28311253, 5358056, -23319780, 541964], + xy2d: [16259219, 3261970, 2309254, -15534474, -16885711, -4581916, 24134070, -16705829, -13337066, -13552195], + }, + Precomp { + yplusx: [9378160, -13140186, -22845982, -12745264, 28198281, -7244098, -2399684, -717351, 690426, 14876244], + yminusx: [24977353, -314384, -8223969, -13465086, 28432343, -1176353, -13068804, -12297348, -22380984, 6618999], + xy2d: [-1538174, 11685646, 12944378, 13682314, -24389511, -14413193, 8044829, -13817328, 32239829, -5652762], + }, + Precomp { + yplusx: [-18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647, -10350059, 32779359, 5095274], + yminusx: [-33008130, -5214506, -32264887, -3685216, 9460461, -9327423, -24601656, 14506724, 21639561, -2630236], + xy2d: [-16400943, -13112215, 25239338, 15531969, 3987758, -4499318, -1289502, -6863535, 17874574, 558605], + }, + Precomp { + yplusx: [-13600129, 10240081, 9171883, 16131053, -20869254, 9599700, 33499487, 5080151, 2085892, 5119761], + yminusx: [-22205145, -2519528, -16381601, 414691, -25019550, 2170430, 30634760, -8363614, -31999993, -5759884], + xy2d: [-6845704, 15791202, 8550074, -1312654, 29928809, -12092256, 27534430, -7192145, -22351378, 12961482], + }, + Precomp { + yplusx: [-24492060, -9570771, 10368194, 11582341, -23397293, -2245287, 16533930, 8206996, -30194652, -5159638], + yminusx: [-11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630, 7031275, 7589640, 8945490], + xy2d: [-32152748, 8917967, 6661220, -11677616, -1192060, -15793393, 7251489, -11182180, 24099109, -14456170], + }, + Precomp { + yplusx: [5019558, -7907470, 4244127, -14714356, -26933272, 6453165, -19118182, -13289025, -6231896, -10280736], + yminusx: [10853594, 10721687, 26480089, 5861829, -22995819, 1972175, -1866647, -10557898, -3363451, -6441124], + xy2d: [-17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661, -2008168, -13866408, 7421392], + }, + Precomp { + yplusx: [8139927, -6546497, 32257646, -5890546, 30375719, 1886181, -21175108, 15441252, 28826358, -4123029], + yminusx: [6267086, 9695052, 7709135, -16603597, -32869068, -1886135, 14795160, -7840124, 13746021, -1742048], + xy2d: [28584902, 7787108, -6732942, -15050729, 22846041, -7571236, -3181936, -363524, 4771362, -8419958], + }, + ], + [ + Precomp { + yplusx: [24949256, 6376279, -27466481, -8174608, -18646154, -9930606, 33543569, -12141695, 3569627, 11342593], + yminusx: [26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886, 4608608, 7325975, -14801071], + xy2d: [-11618399, -14554430, -24321212, 7655128, -1369274, 5214312, -27400540, 10258390, -17646694, -8186692], + }, + Precomp { + yplusx: [11431204, 15823007, 26570245, 14329124, 18029990, 4796082, -31446179, 15580664, 9280358, -3973687], + yminusx: [-160783, -10326257, -22855316, -4304997, -20861367, -13621002, -32810901, -11181622, -15545091, 4387441], + xy2d: [-20799378, 12194512, 3937617, -5805892, -27154820, 9340370, -24513992, 8548137, 20617071, -7482001], + }, + Precomp { + yplusx: [-938825, -3930586, -8714311, 16124718, 24603125, -6225393, -13775352, -11875822, 24345683, 10325460], + yminusx: [-19855277, -1568885, -22202708, 8714034, 14007766, 6928528, 16318175, -1010689, 4766743, 3552007], + xy2d: [-21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514, 14481909, 10988822, -3994762], + }, + Precomp { + yplusx: [15564307, -14311570, 3101243, 5684148, 30446780, -8051356, 12677127, -6505343, -8295852, 13296005], + yminusx: [-9442290, 6624296, -30298964, -11913677, -4670981, -2057379, 31521204, 9614054, -30000824, 12074674], + xy2d: [4771191, -135239, 14290749, -13089852, 27992298, 14998318, -1413936, -1556716, 29832613, -16391035], + }, + Precomp { + yplusx: [7064884, -7541174, -19161962, -5067537, -18891269, -2912736, 25825242, 5293297, -27122660, 13101590], + yminusx: [-2298563, 2439670, -7466610, 1719965, -27267541, -16328445, 32512469, -5317593, -30356070, -4190957], + xy2d: [-30006540, 10162316, -33180176, 3981723, -16482138, -13070044, 14413974, 9515896, 19568978, 9628812], + }, + Precomp { + yplusx: [33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894, -6106839, -6291786, 3437740], + yminusx: [-18978877, 3884493, 19469877, 12726490, 15913552, 13614290, -22961733, 70104, 7463304, 4176122], + xy2d: [-27124001, 10659917, 11482427, -16070381, 12771467, -6635117, -32719404, -5322751, 24216882, 5944158], + }, + Precomp { + yplusx: [8894125, 7450974, -2664149, -9765752, -28080517, -12389115, 19345746, 14680796, 11632993, 5847885], + yminusx: [26942781, -2315317, 9129564, -4906607, 26024105, 11769399, -11518837, 6367194, -9727230, 4782140], + xy2d: [19916461, -4828410, -22910704, -11414391, 25606324, -5972441, 33253853, 8220911, 6358847, -1873857], + }, + Precomp { + yplusx: [801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388, -4480480, -13538503, 1387155], + yminusx: [19646058, 5720633, -11416706, 12814209, 11607948, 12749789, 14147075, 15156355, -21866831, 11835260], + xy2d: [19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523, 15467869, -26560550, 5052483], + }, + ], + [ + Precomp { + yplusx: [-3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123, -12618185, 12228557, -7003677], + yminusx: [32944382, 14922211, -22844894, 5188528, 21913450, -8719943, 4001465, 13238564, -6114803, 8653815], + xy2d: [22865569, -4652735, 27603668, -12545395, 14348958, 8234005, 24808405, 5719875, 28483275, 2841751], + }, + Precomp { + yplusx: [-16420968, -1113305, -327719, -12107856, 21886282, -15552774, -1887966, -315658, 19932058, -12739203], + yminusx: [-11656086, 10087521, -8864888, -5536143, -19278573, -3055912, 3999228, 13239134, -4777469, -13910208], + xy2d: [1382174, -11694719, 17266790, 9194690, -13324356, 9720081, 20403944, 11284705, -14013818, 3093230], + }, + Precomp { + yplusx: [16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424, 16271225, -24049421, -6691850], + yminusx: [-21911077, -5927941, -4611316, -5560156, -31744103, -10785293, 24123614, 15193618, -21652117, -16739389], + xy2d: [-9935934, -4289447, -25279823, 4372842, 2087473, 10399484, 31870908, 14690798, 17361620, 11864968], + }, + Precomp { + yplusx: [-11307610, 6210372, 13206574, 5806320, -29017692, -13967200, -12331205, -7486601, -25578460, -16240689], + yminusx: [14668462, -12270235, 26039039, 15305210, 25515617, 4542480, 10453892, 6577524, 9145645, -6443880], + xy2d: [5974874, 3053895, -9433049, -10385191, -31865124, 3225009, -7972642, 3936128, -5652273, -3050304], + }, + Precomp { + yplusx: [30625386, -4729400, -25555961, -12792866, -20484575, 7695099, 17097188, -16303496, -27999779, 1803632], + yminusx: [-3553091, 9865099, -5228566, 4272701, -5673832, -16689700, 14911344, 12196514, -21405489, 7047412], + xy2d: [20093277, 9920966, -11138194, -5343857, 13161587, 12044805, -32856851, 4124601, -32343828, -10257566], + }, + Precomp { + yplusx: [-20788824, 14084654, -13531713, 7842147, 19119038, -13822605, 4752377, -8714640, -21679658, 2288038], + yminusx: [-26819236, -3283715, 29965059, 3039786, -14473765, 2540457, 29457502, 14625692, -24819617, 12570232], + xy2d: [-1063558, -11551823, 16920318, 12494842, 1278292, -5869109, -21159943, -3498680, -11974704, 4724943], + }, + Precomp { + yplusx: [17960970, -11775534, -4140968, -9702530, -8876562, -1410617, -12907383, -8659932, -29576300, 1903856], + yminusx: [23134274, -14279132, -10681997, -1611936, 20684485, 15770816, -12989750, 3190296, 26955097, 14109738], + xy2d: [15308788, 5320727, -30113809, -14318877, 22902008, 7767164, 29425325, -11277562, 31960942, 11934971], + }, + Precomp { + yplusx: [-27395711, 8435796, 4109644, 12222639, -24627868, 14818669, 20638173, 4875028, 10491392, 1379718], + yminusx: [-13159415, 9197841, 3875503, -8936108, -1383712, -5879801, 33518459, 16176658, 21432314, 12180697], + xy2d: [-11787308, 11500838, 13787581, -13832590, -22430679, 10140205, 1465425, 12689540, -10301319, -13872883], + }, + ], + [ + Precomp { + yplusx: [5414091, -15386041, -21007664, 9643570, 12834970, 1186149, -2622916, -1342231, 26128231, 6032912], + yminusx: [-26337395, -13766162, 32496025, -13653919, 17847801, -12669156, 3604025, 8316894, -25875034, -10437358], + xy2d: [3296484, 6223048, 24680646, -12246460, -23052020, 5903205, -8862297, -4639164, 12376617, 3188849], + }, + Precomp { + yplusx: [29190488, -14659046, 27549113, -1183516, 3520066, -10697301, 32049515, -7309113, -16109234, -9852307], + yminusx: [-14744486, -9309156, 735818, -598978, -20407687, -5057904, 25246078, -15795669, 18640741, -960977], + xy2d: [-6928835, -16430795, 10361374, 5642961, 4910474, 12345252, -31638386, -494430, 10530747, 1053335], + }, + Precomp { + yplusx: [-29265967, -14186805, -13538216, -12117373, -19457059, -10655384, -31462369, -2948985, 24018831, 15026644], + yminusx: [-22592535, -3145277, -2289276, 5953843, -13440189, 9425631, 25310643, 13003497, -2314791, -15145616], + xy2d: [-27419985, -603321, -8043984, -1669117, -26092265, 13987819, -27297622, 187899, -23166419, -2531735], + }, + Precomp { + yplusx: [-21744398, -13810475, 1844840, 5021428, -10434399, -15911473, 9716667, 16266922, -5070217, 726099], + yminusx: [29370922, -6053998, 7334071, -15342259, 9385287, 2247707, -13661962, -4839461, 30007388, -15823341], + xy2d: [-936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109, 730663, 9835848, 4555336], + }, + Precomp { + yplusx: [-23376435, 1410446, -22253753, -12899614, 30867635, 15826977, 17693930, 544696, -11985298, 12422646], + yminusx: [31117226, -12215734, -13502838, 6561947, -9876867, -12757670, -5118685, -4096706, 29120153, 13924425], + xy2d: [-17400879, -14233209, 19675799, -2734756, -11006962, -5858820, -9383939, -11317700, 7240931, -237388], + }, + Precomp { + yplusx: [-31361739, -11346780, -15007447, -5856218, -22453340, -12152771, 1222336, 4389483, 3293637, -15551743], + yminusx: [-16684801, -14444245, 11038544, 11054958, -13801175, -3338533, -24319580, 7733547, 12796905, -6335822], + xy2d: [-8759414, -10817836, -25418864, 10783769, -30615557, -9746811, -28253339, 3647836, 3222231, -11160462], + }, + Precomp { + yplusx: [18606113, 1693100, -25448386, -15170272, 4112353, 10045021, 23603893, -2048234, -7550776, 2484985], + yminusx: [9255317, -3131197, -12156162, -1004256, 13098013, -9214866, 16377220, -2102812, -19802075, -3034702], + xy2d: [-22729289, 7496160, -5742199, 11329249, 19991973, -3347502, -31718148, 9936966, -30097688, -10618797], + }, + Precomp { + yplusx: [21878590, -5001297, 4338336, 13643897, -3036865, 13160960, 19708896, 5415497, -7360503, -4109293], + yminusx: [27736861, 10103576, 12500508, 8502413, -3413016, -9633558, 10436918, -1550276, -23659143, -8132100], + xy2d: [19492550, -12104365, -29681976, -852630, -3208171, 12403437, 30066266, 8367329, 13243957, 8709688], + }, + ], + [ + Precomp { + yplusx: [12015105, 2801261, 28198131, 10151021, 24818120, -4743133, -11194191, -5645734, 5150968, 7274186], + yminusx: [2831366, -12492146, 1478975, 6122054, 23825128, -12733586, 31097299, 6083058, 31021603, -9793610], + xy2d: [-2529932, -2229646, 445613, 10720828, -13849527, -11505937, -23507731, 16354465, 15067285, -14147707], + }, + Precomp { + yplusx: [7840942, 14037873, -33364863, 15934016, -728213, -3642706, 21403988, 1057586, -19379462, -12403220], + yminusx: [915865, -16469274, 15608285, -8789130, -24357026, 6060030, -17371319, 8410997, -7220461, 16527025], + xy2d: [32922597, -556987, 20336074, -16184568, 10903705, -5384487, 16957574, 52992, 23834301, 6588044], + }, + Precomp { + yplusx: [32752030, 11232950, 3381995, -8714866, 22652988, -10744103, 17159699, 16689107, -20314580, -1305992], + yminusx: [-4689649, 9166776, -25710296, -10847306, 11576752, 12733943, 7924251, -2752281, 1976123, -7249027], + xy2d: [21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041, -3371252, 12331345, -8237197], + }, + Precomp { + yplusx: [8651614, -4477032, -16085636, -4996994, 13002507, 2950805, 29054427, -5106970, 10008136, -4667901], + yminusx: [31486080, 15114593, -14261250, 12951354, 14369431, -7387845, 16347321, -13662089, 8684155, -10532952], + xy2d: [19443825, 11385320, 24468943, -9659068, -23919258, 2187569, -26263207, -6086921, 31316348, 14219878], + }, + Precomp { + yplusx: [-28594490, 1193785, 32245219, 11392485, 31092169, 15722801, 27146014, 6992409, 29126555, 9207390], + yminusx: [32382935, 1110093, 18477781, 11028262, -27411763, -7548111, -4980517, 10843782, -7957600, -14435730], + xy2d: [2814918, 7836403, 27519878, -7868156, -20894015, -11553689, -21494559, 8550130, 28346258, 1994730], + }, + Precomp { + yplusx: [-19578299, 8085545, -14000519, -3948622, 2785838, -16231307, -19516951, 7174894, 22628102, 8115180], + yminusx: [-30405132, 955511, -11133838, -15078069, -32447087, -13278079, -25651578, 3317160, -9943017, 930272], + xy2d: [-15303681, -6833769, 28856490, 1357446, 23421993, 1057177, 24091212, -1388970, -22765376, -10650715], + }, + Precomp { + yplusx: [-22751231, -5303997, -12907607, -12768866, -15811511, -7797053, -14839018, -16554220, -1867018, 8398970], + yminusx: [-31969310, 2106403, -4736360, 1362501, 12813763, 16200670, 22981545, -6291273, 18009408, -15772772], + xy2d: [-17220923, -9545221, -27784654, 14166835, 29815394, 7444469, 29551787, -3727419, 19288549, 1325865], + }, + Precomp { + yplusx: [15100157, -15835752, -23923978, -1005098, -26450192, 15509408, 12376730, -3479146, 33166107, -8042750], + yminusx: [20909231, 13023121, -9209752, 16251778, -5778415, -8094914, 12412151, 10018715, 2213263, -13878373], + xy2d: [32529814, -11074689, 30361439, -16689753, -9135940, 1513226, 22922121, 6382134, -5766928, 8371348], + }, + ], + [ + Precomp { + yplusx: [9923462, 11271500, 12616794, 3544722, -29998368, -1721626, 12891687, -8193132, -26442943, 10486144], + yminusx: [-22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726, 2610596, -23921530, -11455195], + xy2d: [5408411, -1136691, -4969122, 10561668, 24145918, 14240566, 31319731, -4235541, 19985175, -3436086], + }, + Precomp { + yplusx: [-13994457, 16616821, 14549246, 3341099, 32155958, 13648976, -17577068, 8849297, 65030, 8370684], + yminusx: [-8320926, -12049626, 31204563, 5839400, -20627288, -1057277, -19442942, 6922164, 12743482, -9800518], + xy2d: [-2361371, 12678785, 28815050, 4759974, -23893047, 4884717, 23783145, 11038569, 18800704, 255233], + }, + Precomp { + yplusx: [-5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847, 9066957, 19258688, -14753793], + yminusx: [-2936654, -10827535, -10432089, 14516793, -3640786, 4372541, -31934921, 2209390, -1524053, 2055794], + xy2d: [580882, 16705327, 5468415, -2683018, -30926419, -14696000, -7203346, -8994389, -30021019, 7394435], + }, + Precomp { + yplusx: [23838809, 1822728, -15738443, 15242727, 8318092, -3733104, -21672180, -3492205, -4821741, 14799921], + yminusx: [13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804, 13496856, -9056018, 7402518], + xy2d: [2286874, -4435931, -20042458, -2008336, -13696227, 5038122, 11006906, -15760352, 8205061, 1607563], + }, + Precomp { + yplusx: [14414086, -8002132, 3331830, -3208217, 22249151, -5594188, 18364661, -2906958, 30019587, -9029278], + yminusx: [-27688051, 1585953, -10775053, 931069, -29120221, -11002319, -14410829, 12029093, 9944378, 8024], + xy2d: [4368715, -3709630, 29874200, -15022983, -20230386, -11410704, -16114594, -999085, -8142388, 5640030], + }, + Precomp { + yplusx: [10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887, -16694564, 15219798, -14327783], + yminusx: [27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605, -1173195, -18342183, 9742717], + xy2d: [6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614, 7406442, 12420155, 1994844], + }, + Precomp { + yplusx: [14012521, -5024720, -18384453, -9578469, -26485342, -3936439, -13033478, -10909803, 24319929, -6446333], + yminusx: [16412690, -4507367, 10772641, 15929391, -17068788, -4658621, 10555945, -10484049, -30102368, -4739048], + xy2d: [22397382, -7767684, -9293161, -12792868, 17166287, -9755136, -27333065, 6199366, 21880021, -12250760], + }, + Precomp { + yplusx: [-4283307, 5368523, -31117018, 8163389, -30323063, 3209128, 16557151, 8890729, 8840445, 4957760], + yminusx: [-15447727, 709327, -6919446, -10870178, -29777922, 6522332, -21720181, 12130072, -14796503, 5005757], + xy2d: [-2114751, -14308128, 23019042, 15765735, -25269683, 6002752, 10183197, -13239326, -16395286, -2176112], + }, + ], + [ + Precomp { + yplusx: [-19025756, 1632005, 13466291, -7995100, -23640451, 16573537, -32013908, -3057104, 22208662, 2000468], + yminusx: [3065073, -1412761, -25598674, -361432, -17683065, -5703415, -8164212, 11248527, -3691214, -7414184], + xy2d: [10379208, -6045554, 8877319, 1473647, -29291284, -12507580, 16690915, 2553332, -3132688, 16400289], + }, + Precomp { + yplusx: [15716668, 1254266, -18472690, 7446274, -8448918, 6344164, -22097271, -7285580, 26894937, 9132066], + yminusx: [24158887, 12938817, 11085297, -8177598, -28063478, -4457083, -30576463, 64452, -6817084, -2692882], + xy2d: [13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710, -3418511, -4688006, 2364226], + }, + Precomp { + yplusx: [16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024, -11697457, 15445875, -7798101], + yminusx: [29004207, -7867081, 28661402, -640412, -12794003, -7943086, 31863255, -4135540, -278050, -15759279], + xy2d: [-6122061, -14866665, -28614905, 14569919, -10857999, -3591829, 10343412, -6976290, -29828287, -10815811], + }, + Precomp { + yplusx: [27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636, 15372179, 17293797, 960709], + yminusx: [20263915, 11434237, -5765435, 11236810, 13505955, -10857102, -16111345, 6493122, -19384511, 7639714], + xy2d: [-2830798, -14839232, 25403038, -8215196, -8317012, -16173699, 18006287, -16043750, 29994677, -15808121], + }, + Precomp { + yplusx: [9769828, 5202651, -24157398, -13631392, -28051003, -11561624, -24613141, -13860782, -31184575, 709464], + yminusx: [12286395, 13076066, -21775189, -1176622, -25003198, 4057652, -32018128, -8890874, 16102007, 13205847], + xy2d: [13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170, 8525972, 10151379, 10394400], + }, + Precomp { + yplusx: [4024660, -16137551, 22436262, 12276534, -9099015, -2686099, 19698229, 11743039, -33302334, 8934414], + yminusx: [-15879800, -4525240, -8580747, -2934061, 14634845, -698278, -9449077, 3137094, -11536886, 11721158], + xy2d: [17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229, 8835153, -9205489, -1280045], + }, + Precomp { + yplusx: [-461409, -7830014, 20614118, 16688288, -7514766, -4807119, 22300304, 505429, 6108462, -6183415], + yminusx: [-5070281, 12367917, -30663534, 3234473, 32617080, -8422642, 29880583, -13483331, -26898490, -7867459], + xy2d: [-31975283, 5726539, 26934134, 10237677, -3173717, -605053, 24199304, 3795095, 7592688, -14992079], + }, + Precomp { + yplusx: [21594432, -14964228, 17466408, -4077222, 32537084, 2739898, 6407723, 12018833, -28256052, 4298412], + yminusx: [-20650503, -11961496, -27236275, 570498, 3767144, -1717540, 13891942, -1569194, 13717174, 10805743], + xy2d: [-14676630, -15644296, 15287174, 11927123, 24177847, -8175568, -796431, 14860609, -26938930, -5863836], + }, + ], + [ + Precomp { + yplusx: [12962541, 5311799, -10060768, 11658280, 18855286, -7954201, 13286263, -12808704, -4381056, 9882022], + yminusx: [18512079, 11319350, -20123124, 15090309, 18818594, 5271736, -22727904, 3666879, -23967430, -3299429], + xy2d: [-6789020, -3146043, 16192429, 13241070, 15898607, -14206114, -10084880, -6661110, -2403099, 5276065], + }, + Precomp { + yplusx: [30169808, -5317648, 26306206, -11750859, 27814964, 7069267, 7152851, 3684982, 1449224, 13082861], + yminusx: [10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382, 15056736, -21016438, -8202000], + xy2d: [-33150110, 3261608, 22745853, 7948688, 19370557, -15177665, -26171976, 6482814, -10300080, -11060101], + }, + Precomp { + yplusx: [32869458, -5408545, 25609743, 15678670, -10687769, -15471071, 26112421, 2521008, -22664288, 6904815], + yminusx: [29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737, 3841096, -29003639, -6657642], + xy2d: [10340844, -6630377, -18656632, -2278430, 12621151, -13339055, 30878497, -11824370, -25584551, 5181966], + }, + Precomp { + yplusx: [25940115, -12658025, 17324188, -10307374, -8671468, 15029094, 24396252, -16450922, -2322852, -12388574], + yminusx: [-21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390, 12641087, 20603771, -6561742], + xy2d: [-18882287, -11673380, 24849422, 11501709, 13161720, -4768874, 1925523, 11914390, 4662781, 7820689], + }, + Precomp { + yplusx: [12241050, -425982, 8132691, 9393934, 32846760, -1599620, 29749456, 12172924, 16136752, 15264020], + yminusx: [-10349955, -14680563, -8211979, 2330220, -17662549, -14545780, 10658213, 6671822, 19012087, 3772772], + xy2d: [3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732, -15762884, 20527771, 12988982], + }, + Precomp { + yplusx: [-14822485, -5797269, -3707987, 12689773, -898983, -10914866, -24183046, -10564943, 3299665, -12424953], + yminusx: [-16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197, 6461331, -25583147, 8991218], + xy2d: [-17226263, 1816362, -1673288, -6086439, 31783888, -8175991, -32948145, 7417950, -30242287, 1507265], + }, + Precomp { + yplusx: [29692663, 6829891, -10498800, 4334896, 20945975, -11906496, -28887608, 8209391, 14606362, -10647073], + yminusx: [-3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695, 9761487, 4170404, -2085325], + xy2d: [-11587470, 14855945, -4127778, -1531857, -26649089, 15084046, 22186522, 16002000, -14276837, -8400798], + }, + Precomp { + yplusx: [-4811456, 13761029, -31703877, -2483919, -3312471, 7869047, -7113572, -9620092, 13240845, 10965870], + yminusx: [-7742563, -8256762, -14768334, -13656260, -23232383, 12387166, 4498947, 14147411, 29514390, 4302863], + xy2d: [-13413405, -12407859, 20757302, -13801832, 14785143, 8976368, -5061276, -2144373, 17846988, -13971927], + }, + ], + [ + Precomp { + yplusx: [-2244452, -754728, -4597030, -1066309, -6247172, 1455299, -21647728, -9214789, -5222701, 12650267], + yminusx: [-9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813, 13770293, -19134326, 10958663], + xy2d: [22470984, 12369526, 23446014, -5441109, -21520802, -9698723, -11772496, -11574455, -25083830, 4271862], + }, + Precomp { + yplusx: [-25169565, -10053642, -19909332, 15361595, -5984358, 2159192, 75375, -4278529, -32526221, 8469673], + yminusx: [15854970, 4148314, -8893890, 7259002, 11666551, 13824734, -30531198, 2697372, 24154791, -9460943], + xy2d: [15446137, -15806644, 29759747, 14019369, 30811221, -9610191, -31582008, 12840104, 24913809, 9815020], + }, + Precomp { + yplusx: [-4709286, -5614269, -31841498, -12288893, -14443537, 10799414, -9103676, 13438769, 18735128, 9466238], + yminusx: [11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821, -10896103, -22728655, 16199064], + xy2d: [14576810, 379472, -26786533, -8317236, -29426508, -10812974, -102766, 1876699, 30801119, 2164795], + }, + Precomp { + yplusx: [15995086, 3199873, 13672555, 13712240, -19378835, -4647646, -13081610, -15496269, -13492807, 1268052], + yminusx: [-10290614, -3659039, -3286592, 10948818, 23037027, 3794475, -3470338, -12600221, -17055369, 3565904], + xy2d: [29210088, -9419337, -5919792, -4952785, 10834811, -13327726, -16512102, -10820713, -27162222, -14030531], + }, + Precomp { + yplusx: [-13161890, 15508588, 16663704, -8156150, -28349942, 9019123, -29183421, -3769423, 2244111, -14001979], + yminusx: [-5152875, -3800936, -9306475, -6071583, 16243069, 14684434, -25673088, -16180800, 13491506, 4641841], + xy2d: [10813417, 643330, -19188515, -728916, 30292062, -16600078, 27548447, -7721242, 14476989, -12767431], + }, + Precomp { + yplusx: [10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937, -1644259, -27912810, 12651324], + yminusx: [-31185513, -813383, 22271204, 11835308, 10201545, 15351028, 17099662, 3988035, 21721536, -3148940], + xy2d: [10202177, -6545839, -31373232, -9574638, -32150642, -8119683, -12906320, 3852694, 13216206, 14842320], + }, + Precomp { + yplusx: [-15815640, -10601066, -6538952, -7258995, -6984659, -6581778, -31500847, 13765824, -27434397, 9900184], + yminusx: [14465505, -13833331, -32133984, -14738873, -27443187, 12990492, 33046193, 15796406, -7051866, -8040114], + xy2d: [30924417, -8279620, 6359016, -12816335, 16508377, 9071735, -25488601, 15413635, 9524356, -7018878], + }, + Precomp { + yplusx: [12274201, -13175547, 32627641, -1785326, 6736625, 13267305, 5237659, -5109483, 15663516, 4035784], + yminusx: [-2951309, 8903985, 17349946, 601635, -16432815, -4612556, -13732739, -15889334, -22258478, 4659091], + xy2d: [-16916263, -4952973, -30393711, -15158821, 20774812, 15897498, 5736189, 15026997, -2178256, -13455585], + }, + ], + [ + Precomp { + yplusx: [-8858980, -2219056, 28571666, -10155518, -474467, -10105698, -3801496, 278095, 23440562, -290208], + yminusx: [10226241, -5928702, 15139956, 120818, -14867693, 5218603, 32937275, 11551483, -16571960, -7442864], + xy2d: [17932739, -12437276, -24039557, 10749060, 11316803, 7535897, 22503767, 5561594, -3646624, 3898661], + }, + Precomp { + yplusx: [7749907, -969567, -16339731, -16464, -25018111, 15122143, -1573531, 7152530, 21831162, 1245233], + yminusx: [26958459, -14658026, 4314586, 8346991, -5677764, 11960072, -32589295, -620035, -30402091, -16716212], + xy2d: [-12165896, 9166947, 33491384, 13673479, 29787085, 13096535, 6280834, 14587357, -22338025, 13987525], + }, + Precomp { + yplusx: [-24349909, 7778775, 21116000, 15572597, -4833266, -5357778, -4300898, -5124639, -7469781, -2858068], + yminusx: [9681908, -6737123, -31951644, 13591838, -6883821, 386950, 31622781, 6439245, -14581012, 4091397], + xy2d: [-8426427, 1470727, -28109679, -1596990, 3978627, -5123623, -19622683, 12092163, 29077877, -14741988], + }, + Precomp { + yplusx: [5269168, -6859726, -13230211, -8020715, 25932563, 1763552, -5606110, -5505881, -20017847, 2357889], + yminusx: [32264008, -15407652, -5387735, -1160093, -2091322, -3946900, 23104804, -12869908, 5727338, 189038], + xy2d: [14609123, -8954470, -6000566, -16622781, -14577387, -7743898, -26745169, 10942115, -25888931, -14884697], + }, + Precomp { + yplusx: [20513500, 5557931, -15604613, 7829531, 26413943, -2019404, -21378968, 7471781, 13913677, -5137875], + yminusx: [-25574376, 11967826, 29233242, 12948236, -6754465, 4713227, -8940970, 14059180, 12878652, 8511905], + xy2d: [-25656801, 3393631, -2955415, -7075526, -2250709, 9366908, -30223418, 6812974, 5568676, -3127656], + }, + Precomp { + yplusx: [11630004, 12144454, 2116339, 13606037, 27378885, 15676917, -17408753, -13504373, -14395196, 8070818], + yminusx: [27117696, -10007378, -31282771, -5570088, 1127282, 12772488, -29845906, 10483306, -11552749, -1028714], + xy2d: [10637467, -5688064, 5674781, 1072708, -26343588, -6982302, -1683975, 9177853, -27493162, 15431203], + }, + Precomp { + yplusx: [20525145, 10892566, -12742472, 12779443, -29493034, 16150075, -28240519, 14943142, -15056790, -7935931], + yminusx: [-30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767, -3239766, -3356550, 9594024], + xy2d: [-23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683, -6492290, 13352335, -10977084], + }, + Precomp { + yplusx: [-1931799, -5407458, 3304649, -12884869, 17015806, -4877091, -29783850, -7752482, -13215537, -319204], + yminusx: [20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742, 15077870, -22750759, 14523817], + xy2d: [27406042, -6041657, 27423596, -4497394, 4996214, 10002360, -28842031, -4545494, -30172742, -4805667], + }, + ], + [ + Precomp { + yplusx: [11374242, 12660715, 17861383, -12540833, 10935568, 1099227, -13886076, -9091740, -27727044, 11358504], + yminusx: [-12730809, 10311867, 1510375, 10778093, -2119455, -9145702, 32676003, 11149336, -26123651, 4985768], + xy2d: [-19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043, 13794114, -19414307, -15621255], + }, + Precomp { + yplusx: [6490081, 11940286, 25495923, -7726360, 8668373, -8751316, 3367603, 6970005, -1691065, -9004790], + yminusx: [1656497, 13457317, 15370807, 6364910, 13605745, 8362338, -19174622, -5475723, -16796596, -5031438], + xy2d: [-22273315, -13524424, -64685, -4334223, -18605636, -10921968, -20571065, -7007978, -99853, -10237333], + }, + Precomp { + yplusx: [17747465, 10039260, 19368299, -4050591, -20630635, -16041286, 31992683, -15857976, -29260363, -5511971], + yminusx: [31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999, -3744247, 4882242, -10626905], + xy2d: [29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198, 3272828, -5190932, -4162409], + }, + Precomp { + yplusx: [12501286, 4044383, -8612957, -13392385, -32430052, 5136599, -19230378, -3529697, 330070, -3659409], + yminusx: [6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522, -8573892, -271295, 12071499], + xy2d: [-8365515, -4042521, 25133448, -4517355, -6211027, 2265927, -32769618, 1936675, -5159697, 3829363], + }, + Precomp { + yplusx: [28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550, -6567787, 26333140, 14267664], + yminusx: [-11067219, 11871231, 27385719, -10559544, -4585914, -11189312, 10004786, -8709488, -21761224, 8930324], + xy2d: [-21197785, -16396035, 25654216, -1725397, 12282012, 11008919, 1541940, 4757911, -26491501, -16408940], + }, + Precomp { + yplusx: [13537262, -7759490, -20604840, 10961927, -5922820, -13218065, -13156584, 6217254, -15943699, 13814990], + yminusx: [-17422573, 15157790, 18705543, 29619, 24409717, -260476, 27361681, 9257833, -1956526, -1776914], + xy2d: [-25045300, -10191966, 15366585, 15166509, -13105086, 8423556, -29171540, 12361135, -18685978, 4578290], + }, + Precomp { + yplusx: [24579768, 3711570, 1342322, -11180126, -27005135, 14124956, -22544529, 14074919, 21964432, 8235257], + yminusx: [-6528613, -2411497, 9442966, -5925588, 12025640, -1487420, -2981514, -1669206, 13006806, 2355433], + xy2d: [-16304899, -13605259, -6632427, -5142349, 16974359, -10911083, 27202044, 1719366, 1141648, -12796236], + }, + Precomp { + yplusx: [-12863944, -13219986, -8318266, -11018091, -6810145, -4843894, 13475066, -3133972, 32674895, 13715045], + yminusx: [11423335, -5468059, 32344216, 8962751, 24989809, 9241752, -13265253, 16086212, -28740881, -15642093], + xy2d: [-1409668, 12530728, -6368726, 10847387, 19531186, -14132160, -11709148, 7791794, -27245943, 4383347], + }, + ], + [ + Precomp { + yplusx: [-28970898, 5271447, -1266009, -9736989, -12455236, 16732599, -4862407, -4906449, 27193557, 6245191], + yminusx: [-15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898, 3260492, 22510453, 8577507], + xy2d: [-12632451, 11257346, -32692994, 13548177, -721004, 10879011, 31168030, 13952092, -29571492, -3635906], + }, + Precomp { + yplusx: [3877321, -9572739, 32416692, 5405324, -11004407, -13656635, 3759769, 11935320, 5611860, 8164018], + yminusx: [-16275802, 14667797, 15906460, 12155291, -22111149, -9039718, 32003002, -8832289, 5773085, -8422109], + xy2d: [-23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725, 12376320, 31632953, 190926], + }, + Precomp { + yplusx: [-24593607, -16138885, -8423991, 13378746, 14162407, 6901328, -8288749, 4508564, -25341555, -3627528], + yminusx: [8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941, -14786005, -1672488, 827625], + xy2d: [-32720583, -16289296, -32503547, 7101210, 13354605, 2659080, -1800575, -14108036, -24878478, 1541286], + }, + Precomp { + yplusx: [2901347, -1117687, 3880376, -10059388, -17620940, -3612781, -21802117, -3567481, 20456845, -1885033], + yminusx: [27019610, 12299467, -13658288, -1603234, -12861660, -4861471, -19540150, -5016058, 29439641, 15138866], + xy2d: [21536104, -6626420, -32447818, -10690208, -22408077, 5175814, -5420040, -16361163, 7779328, 109896], + }, + Precomp { + yplusx: [30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390, 12180118, 23177719, -554075], + yminusx: [26572847, 3405927, -31701700, 12890905, -19265668, 5335866, -6493768, 2378492, 4439158, -13279347], + xy2d: [-22716706, 3489070, -9225266, -332753, 18875722, -1140095, 14819434, -12731527, -17717757, -5461437], + }, + Precomp { + yplusx: [-5056483, 16566551, 15953661, 3767752, -10436499, 15627060, -820954, 2177225, 8550082, -15114165], + yminusx: [-18473302, 16596775, -381660, 15663611, 22860960, 15585581, -27844109, -3582739, -23260460, -8428588], + xy2d: [-32480551, 15707275, -8205912, -5652081, 29464558, 2713815, -22725137, 15860482, -21902570, 1494193], + }, + Precomp { + yplusx: [-19562091, -14087393, -25583872, -9299552, 13127842, 759709, 21923482, 16529112, 8742704, 12967017], + yminusx: [-28464899, 1553205, 32536856, -10473729, -24691605, -406174, -8914625, -2933896, -29903758, 15553883], + xy2d: [21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572, 14513274, 19375923, -12647961], + }, + Precomp { + yplusx: [8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818, -6222716, 2862653, 9455043], + yminusx: [29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124, -2990080, 15511449, 4789663], + xy2d: [-20679756, 7004547, 8824831, -9434977, -4045704, -3750736, -5754762, 108893, 23513200, 16652362], + }, + ], + [ + Precomp { + yplusx: [-33256173, 4144782, -4476029, -6579123, 10770039, -7155542, -6650416, -12936300, -18319198, 10212860], + yminusx: [2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801, 2600940, -9988298, -12506466], + xy2d: [-24645692, 13317462, -30449259, -15653928, 21365574, -10869657, 11344424, 864440, -2499677, -16710063], + }, + Precomp { + yplusx: [-26432803, 6148329, -17184412, -14474154, 18782929, -275997, -22561534, 211300, 2719757, 4940997], + yminusx: [-1323882, 3911313, -6948744, 14759765, -30027150, 7851207, 21690126, 8518463, 26699843, 5276295], + xy2d: [-13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586, 149635, -15452774, 7159369], + }, + Precomp { + yplusx: [9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009, 8312176, 22477218, -8403385], + yminusx: [18155857, -16504990, 19744716, 9006923, 15154154, -10538976, 24256460, -4864995, -22548173, 9334109], + xy2d: [2986088, -4911893, 10776628, -3473844, 10620590, -7083203, -21413845, 14253545, -22587149, 536906], + }, + Precomp { + yplusx: [4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551, 10589625, 10838060, -15420424], + yminusx: [-19342404, 867880, 9277171, -3218459, -14431572, -1986443, 19295826, -15796950, 6378260, 699185], + xy2d: [7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039, 15693155, -5045064, -13373962], + }, + Precomp { + yplusx: [-7737563, -5869402, -14566319, -7406919, 11385654, 13201616, 31730678, -10962840, -3918636, -9669325], + yminusx: [10188286, -15770834, -7336361, 13427543, 22223443, 14896287, 30743455, 7116568, -21786507, 5427593], + xy2d: [696102, 13206899, 27047647, -10632082, 15285305, -9853179, 10798490, -4578720, 19236243, 12477404], + }, + Precomp { + yplusx: [-11229439, 11243796, -17054270, -8040865, -788228, -8167967, -3897669, 11180504, -23169516, 7733644], + yminusx: [17800790, -14036179, -27000429, -11766671, 23887827, 3149671, 23466177, -10538171, 10322027, 15313801], + xy2d: [26246234, 11968874, 32263343, -5468728, 6830755, -13323031, -15794704, -101982, -24449242, 10890804], + }, + Precomp { + yplusx: [-31365647, 10271363, -12660625, -6267268, 16690207, -13062544, -14982212, 16484931, 25180797, -5334884], + yminusx: [-586574, 10376444, -32586414, -11286356, 19801893, 10997610, 2276632, 9482883, 316878, 13820577], + xy2d: [-9882808, -4510367, -2115506, 16457136, -11100081, 11674996, 30756178, -7515054, 30696930, -3712849], + }, + Precomp { + yplusx: [32988917, -9603412, 12499366, 7910787, -10617257, -11931514, -7342816, -9985397, -32349517, 7392473], + yminusx: [-8855661, 15927861, 9866406, -3649411, -2396914, -16655781, -30409476, -9134995, 25112947, -2926644], + xy2d: [-2504044, -436966, 25621774, -5678772, 15085042, -5479877, -24884878, -13526194, 5537438, -13914319], + }, + ], + [ + Precomp { + yplusx: [-11225584, 2320285, -9584280, 10149187, -33444663, 5808648, -14876251, -1729667, 31234590, 6090599], + yminusx: [-9633316, 116426, 26083934, 2897444, -6364437, -2688086, 609721, 15878753, -6970405, -9034768], + xy2d: [-27757857, 247744, -15194774, -9002551, 23288161, -10011936, -23869595, 6503646, 20650474, 1804084], + }, + Precomp { + yplusx: [-27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995, -10329713, 27842616, -202328], + yminusx: [-15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656, 5031932, -11375082, 12714369], + xy2d: [20807691, -7270825, 29286141, 11421711, -27876523, -13868230, -21227475, 1035546, -19733229, 12796920], + }, + Precomp { + yplusx: [12076899, -14301286, -8785001, -11848922, -25012791, 16400684, -17591495, -12899438, 3480665, -15182815], + yminusx: [-32361549, 5457597, 28548107, 7833186, 7303070, -11953545, -24363064, -15921875, -33374054, 2771025], + xy2d: [-21389266, 421932, 26597266, 6860826, 22486084, -6737172, -17137485, -4210226, -24552282, 15673397], + }, + Precomp { + yplusx: [-20184622, 2338216, 19788685, -9620956, -4001265, -8740893, -20271184, 4733254, 3727144, -12934448], + yminusx: [6120119, 814863, -11794402, -622716, 6812205, -15747771, 2019594, 7975683, 31123697, -10958981], + xy2d: [30069250, -11435332, 30434654, 2958439, 18399564, -976289, 12296869, 9204260, -16432438, 9648165], + }, + Precomp { + yplusx: [32705432, -1550977, 30705658, 7451065, -11805606, 9631813, 3305266, 5248604, -26008332, -11377501], + yminusx: [17219865, 2375039, -31570947, -5575615, -19459679, 9219903, 294711, 15298639, 2662509, -16297073], + xy2d: [-1172927, -7558695, -4366770, -4287744, -21346413, -8434326, 32087529, -1222777, 32247248, -14389861], + }, + Precomp { + yplusx: [14312628, 1221556, 17395390, -8700143, -4945741, -8684635, -28197744, -9637817, -16027623, -13378845], + yminusx: [-1428825, -9678990, -9235681, 6549687, -7383069, -468664, 23046502, 9803137, 17597934, 2346211], + xy2d: [18510800, 15337574, 26171504, 981392, -22241552, 7827556, -23491134, -11323352, 3059833, -11782870], + }, + Precomp { + yplusx: [10141598, 6082907, 17829293, -1947643, 9830092, 13613136, -25556636, -5544586, -33502212, 3592096], + yminusx: [33114168, -15889352, -26525686, -13343397, 33076705, 8716171, 1151462, 1521897, -982665, -6837803], + xy2d: [-32939165, -4255815, 23947181, -324178, -33072974, -12305637, -16637686, 3891704, 26353178, 693168], + }, + Precomp { + yplusx: [30374239, 1595580, -16884039, 13186931, 4600344, 406904, 9585294, -400668, 31375464, 14369965], + yminusx: [-14370654, -7772529, 1510301, 6434173, -18784789, -6262728, 32732230, -13108839, 17901441, 16011505], + xy2d: [18171223, -11934626, -12500402, 15197122, -11038147, -15230035, -19172240, -16046376, 8764035, 12309598], + }, + ], + [ + Precomp { + yplusx: [5975908, -5243188, -19459362, -9681747, -11541277, 14015782, -23665757, 1228319, 17544096, -10593782], + yminusx: [5811932, -1715293, 3442887, -2269310, -18367348, -8359541, -18044043, -15410127, -5565381, 12348900], + xy2d: [-31399660, 11407555, 25755363, 6891399, -3256938, 14872274, -24849353, 8141295, -10632534, -585479], + }, + Precomp { + yplusx: [-12675304, 694026, -5076145, 13300344, 14015258, -14451394, -9698672, -11329050, 30944593, 1130208], + yminusx: [8247766, -6710942, -26562381, -7709309, -14401939, -14648910, 4652152, 2488540, 23550156, -271232], + xy2d: [17294316, -3788438, 7026748, 15626851, 22990044, 113481, 2267737, -5908146, -408818, -137719], + }, + Precomp { + yplusx: [16091085, -16253926, 18599252, 7340678, 2137637, -1221657, -3364161, 14550936, 3260525, -7166271], + yminusx: [-4910104, -13332887, 18550887, 10864893, -16459325, -7291596, -23028869, -13204905, -12748722, 2701326], + xy2d: [-8574695, 16099415, 4629974, -16340524, -20786213, -6005432, -10018363, 9276971, 11329923, 1862132], + }, + Precomp { + yplusx: [14763076, -15903608, -30918270, 3689867, 3511892, 10313526, -21951088, 12219231, -9037963, -940300], + yminusx: [8894987, -3446094, 6150753, 3013931, 301220, 15693451, -31981216, -2909717, -15438168, 11595570], + xy2d: [15214962, 3537601, -26238722, -14058872, 4418657, -15230761, 13947276, 10730794, -13489462, -4363670], + }, + Precomp { + yplusx: [-2538306, 7682793, 32759013, 263109, -29984731, -7955452, -22332124, -10188635, 977108, 699994], + yminusx: [-12466472, 4195084, -9211532, 550904, -15565337, 12917920, 19118110, -439841, -30534533, -14337913], + xy2d: [31788461, -14507657, 4799989, 7372237, 8808585, -14747943, 9408237, -10051775, 12493932, -5409317], + }, + Precomp { + yplusx: [-25680606, 5260744, -19235809, -6284470, -3695942, 16566087, 27218280, 2607121, 29375955, 6024730], + yminusx: [842132, -2794693, -4763381, -8722815, 26332018, -12405641, 11831880, 6985184, -9940361, 2854096], + xy2d: [-4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645, 960770, 12121869, 16648078], + }, + Precomp { + yplusx: [-15218652, 14667096, -13336229, 2013717, 30598287, -464137, -31504922, -7882064, 20237806, 2838411], + yminusx: [-19288047, 4453152, 15298546, -16178388, 22115043, -15972604, 12544294, -13470457, 1068881, -12499905], + xy2d: [-9558883, -16518835, 33238498, 13506958, 30505848, -1114596, -8486907, -2630053, 12521378, 4845654], + }, + Precomp { + yplusx: [-28198521, 10744108, -2958380, 10199664, 7759311, -13088600, 3409348, -873400, -6482306, -12885870], + yminusx: [-23561822, 6230156, -20382013, 10655314, -24040585, -11621172, 10477734, -1240216, -3113227, 13974498], + xy2d: [12966261, 15550616, -32038948, -1615346, 21025980, -629444, 5642325, 7188737, 18895762, 12629579], + }, + ], + [ + Precomp { + yplusx: [14741879, -14946887, 22177208, -11721237, 1279741, 8058600, 11758140, 789443, 32195181, 3895677], + yminusx: [10758205, 15755439, -4509950, 9243698, -4879422, 6879879, -2204575, -3566119, -8982069, 4429647], + xy2d: [-2453894, 15725973, -20436342, -10410672, -5803908, -11040220, -7135870, -11642895, 18047436, -15281743], + }, + Precomp { + yplusx: [-25173001, -11307165, 29759956, 11776784, -22262383, -15820455, 10993114, -12850837, -17620701, -9408468], + yminusx: [21987233, 700364, -24505048, 14972008, -7774265, -5718395, 32155026, 2581431, -29958985, 8773375], + xy2d: [-25568350, 454463, -13211935, 16126715, 25240068, 8594567, 20656846, 12017935, -7874389, -13920155], + }, + Precomp { + yplusx: [6028182, 6263078, -31011806, -11301710, -818919, 2461772, -31841174, -5468042, -1721788, -2776725], + yminusx: [-12278994, 16624277, 987579, -5922598, 32908203, 1248608, 7719845, -4166698, 28408820, 6816612], + xy2d: [-10358094, -8237829, 19549651, -12169222, 22082623, 16147817, 20613181, 13982702, -10339570, 5067943], + }, + Precomp { + yplusx: [-30505967, -3821767, 12074681, 13582412, -19877972, 2443951, -19719286, 12746132, 5331210, -10105944], + yminusx: [30528811, 3601899, -1957090, 4619785, -27361822, -15436388, 24180793, -12570394, 27679908, -1648928], + xy2d: [9402404, -13957065, 32834043, 10838634, -26580150, -13237195, 26653274, -8685565, 22611444, -12715406], + }, + Precomp { + yplusx: [22190590, 1118029, 22736441, 15130463, -30460692, -5991321, 19189625, -4648942, 4854859, 6622139], + yminusx: [-8310738, -2953450, -8262579, -3388049, -10401731, -271929, 13424426, -3567227, 26404409, 13001963], + xy2d: [-31241838, -15415700, -2994250, 8939346, 11562230, -12840670, -26064365, -11621720, -15405155, 11020693], + }, + Precomp { + yplusx: [1866042, -7949489, -7898649, -10301010, 12483315, 13477547, 3175636, -12424163, 28761762, 1406734], + yminusx: [-448555, -1777666, 13018551, 3194501, -9580420, -11161737, 24760585, -4347088, 25577411, -13378680], + xy2d: [-24290378, 4759345, -690653, -1852816, 2066747, 10693769, -29595790, 9884936, -9368926, 4745410], + }, + Precomp { + yplusx: [-9141284, 6049714, -19531061, -4341411, -31260798, 9944276, -15462008, -11311852, 10931924, -11931931], + yminusx: [-16561513, 14112680, -8012645, 4817318, -8040464, -11414606, -22853429, 10856641, -20470770, 13434654], + xy2d: [22759489, -10073434, -16766264, -1871422, 13637442, -10168091, 1765144, -12654326, 28445307, -5364710], + }, + Precomp { + yplusx: [29875063, 12493613, 2795536, -3786330, 1710620, 15181182, -10195717, -8788675, 9074234, 1167180], + yminusx: [-26205683, 11014233, -9842651, -2635485, -26908120, 7532294, -18716888, -9535498, 3843903, 9367684], + xy2d: [-10969595, -6403711, 9591134, 9582310, 11349256, 108879, 16235123, 8601684, -139197, 4242895], + }, + ], + [ + Precomp { + yplusx: [22092954, -13191123, -2042793, -11968512, 32186753, -11517388, -6574341, 2470660, -27417366, 16625501], + yminusx: [-11057722, 3042016, 13770083, -9257922, 584236, -544855, -7770857, 2602725, -27351616, 14247413], + xy2d: [6314175, -10264892, -32772502, 15957557, -10157730, 168750, -8618807, 14290061, 27108877, -1180880], + }, + Precomp { + yplusx: [-8586597, -7170966, 13241782, 10960156, -32991015, -13794596, 33547976, -11058889, -27148451, 981874], + yminusx: [22833440, 9293594, -32649448, -13618667, -9136966, 14756819, -22928859, -13970780, -10479804, -16197962], + xy2d: [-7768587, 3326786, -28111797, 10783824, 19178761, 14905060, 22680049, 13906969, -15933690, 3797899], + }, + Precomp { + yplusx: [21721356, -4212746, -12206123, 9310182, -3882239, -13653110, 23740224, -2709232, 20491983, -8042152], + yminusx: [9209270, -15135055, -13256557, -6167798, -731016, 15289673, 25947805, 15286587, 30997318, -6703063], + xy2d: [7392032, 16618386, 23946583, -8039892, -13265164, -1533858, -14197445, -2321576, 17649998, -250080], + }, + Precomp { + yplusx: [-9301088, -14193827, 30609526, -3049543, -25175069, -1283752, -15241566, -9525724, -2233253, 7662146], + yminusx: [-17558673, 1763594, -33114336, 15908610, -30040870, -12174295, 7335080, -8472199, -3174674, 3440183], + xy2d: [-19889700, -5977008, -24111293, -9688870, 10799743, -16571957, 40450, -4431835, 4862400, 1133], + }, + Precomp { + yplusx: [-32856209, -7873957, -5422389, 14860950, -16319031, 7956142, 7258061, 311861, -30594991, -7379421], + yminusx: [-3773428, -1565936, 28985340, 7499440, 24445838, 9325937, 29727763, 16527196, 18278453, 15405622], + xy2d: [-4381906, 8508652, -19898366, -3674424, -5984453, 15149970, -13313598, 843523, -21875062, 13626197], + }, + Precomp { + yplusx: [2281448, -13487055, -10915418, -2609910, 1879358, 16164207, -10783882, 3953792, 13340839, 15928663], + yminusx: [31727126, -7179855, -18437503, -8283652, 2875793, -16390330, -25269894, -7014826, -23452306, 5964753], + xy2d: [4100420, -5959452, -17179337, 6017714, -18705837, 12227141, -26684835, 11344144, 2538215, -7570755], + }, + Precomp { + yplusx: [-9433605, 6123113, 11159803, -2156608, 30016280, 14966241, -20474983, 1485421, -629256, -15958862], + yminusx: [-26804558, 4260919, 11851389, 9658551, -32017107, 16367492, -20205425, -13191288, 11659922, -11115118], + xy2d: [26180396, 10015009, -30844224, -8581293, 5418197, 9480663, 2231568, -10170080, 33100372, -1306171], + }, + Precomp { + yplusx: [15121113, -5201871, -10389905, 15427821, -27509937, -15992507, 21670947, 4486675, -5931810, -14466380], + yminusx: [16166486, -9483733, -11104130, 6023908, -31926798, -1364923, 2340060, -16254968, -10735770, -10039824], + xy2d: [28042865, -3557089, -12126526, 12259706, -3717498, -6945899, 6766453, -8689599, 18036436, 5803270], + }, + ], + [ + Precomp { + yplusx: [-817581, 6763912, 11803561, 1585585, 10958447, -2671165, 23855391, 4598332, -6159431, -14117438], + yminusx: [-31031306, -14256194, 17332029, -2383520, 31312682, -5967183, 696309, 50292, -20095739, 11763584], + xy2d: [-594563, -2514283, -32234153, 12643980, 12650761, 14811489, 665117, -12613632, -19773211, -10713562], + }, + Precomp { + yplusx: [30464590, -11262872, -4127476, -12734478, 19835327, -7105613, -24396175, 2075773, -17020157, 992471], + yminusx: [18357185, -6994433, 7766382, 16342475, -29324918, 411174, 14578841, 8080033, -11574335, -10601610], + xy2d: [19598397, 10334610, 12555054, 2555664, 18821899, -10339780, 21873263, 16014234, 26224780, 16452269], + }, + Precomp { + yplusx: [-30223925, 5145196, 5944548, 16385966, 3976735, 2009897, -11377804, -7618186, -20533829, 3698650], + yminusx: [14187449, 3448569, -10636236, -10810935, -22663880, -3433596, 7268410, -10890444, 27394301, 12015369], + xy2d: [19695761, 16087646, 28032085, 12999827, 6817792, 11427614, 20244189, -1312777, -13259127, -3402461], + }, + Precomp { + yplusx: [30860103, 12735208, -1888245, -4699734, -16974906, 2256940, -8166013, 12298312, -8550524, -10393462], + yminusx: [-5719826, -11245325, -1910649, 15569035, 26642876, -7587760, -5789354, -15118654, -4976164, 12651793], + xy2d: [-2848395, 9953421, 11531313, -5282879, 26895123, -12697089, -13118820, -16517902, 9768698, -2533218], + }, + Precomp { + yplusx: [-24719459, 1894651, -287698, -4704085, 15348719, -8156530, 32767513, 12765450, 4940095, 10678226], + yminusx: [18860224, 15980149, -18987240, -1562570, -26233012, -11071856, -7843882, 13944024, -24372348, 16582019], + xy2d: [-15504260, 4970268, -29893044, 4175593, -20993212, -2199756, -11704054, 15444560, -11003761, 7989037], + }, + Precomp { + yplusx: [31490452, 5568061, -2412803, 2182383, -32336847, 4531686, -32078269, 6200206, -19686113, -14800171], + yminusx: [-17308668, -15879940, -31522777, -2831, -32887382, 16375549, 8680158, -16371713, 28550068, -6857132], + xy2d: [-28126887, -5688091, 16837845, -1820458, -6850681, 12700016, -30039981, 4364038, 1155602, 5988841], + }, + Precomp { + yplusx: [21890435, -13272907, -12624011, 12154349, -7831873, 15300496, 23148983, -4470481, 24618407, 8283181], + yminusx: [-33136107, -10512751, 9975416, 6841041, -31559793, 16356536, 3070187, -7025928, 1466169, 10740210], + xy2d: [-1509399, -15488185, -13503385, -10655916, 32799044, 909394, -13938903, -5779719, -32164649, -15327040], + }, + Precomp { + yplusx: [3960823, -14267803, -28026090, -15918051, -19404858, 13146868, 15567327, 951507, -3260321, -573935], + yminusx: [24740841, 5052253, -30094131, 8961361, 25877428, 6165135, -24368180, 14397372, -7380369, -6144105], + xy2d: [-28888365, 3510803, -28103278, -1158478, -11238128, -10631454, -15441463, -14453128, -1625486, -6494814], + }, + ], + [ + Precomp { + yplusx: [793299, -9230478, 8836302, -6235707, -27360908, -2369593, 33152843, -4885251, -9906200, -621852], + yminusx: [5666233, 525582, 20782575, -8038419, -24538499, 14657740, 16099374, 1468826, -6171428, -15186581], + xy2d: [-4859255, -3779343, -2917758, -6748019, 7778750, 11688288, -30404353, -9871238, -1558923, -9863646], + }, + Precomp { + yplusx: [10896332, -7719704, 824275, 472601, -19460308, 3009587, 25248958, 14783338, -30581476, -15757844], + yminusx: [10566929, 12612572, -31944212, 11118703, -12633376, 12362879, 21752402, 8822496, 24003793, 14264025], + xy2d: [27713862, -7355973, -11008240, 9227530, 27050101, 2504721, 23886875, -13117525, 13958495, -5732453], + }, + Precomp { + yplusx: [-23481610, 4867226, -27247128, 3900521, 29838369, -8212291, -31889399, -10041781, 7340521, -15410068], + yminusx: [4646514, -8011124, -22766023, -11532654, 23184553, 8566613, 31366726, -1381061, -15066784, -10375192], + xy2d: [-17270517, 12723032, -16993061, 14878794, 21619651, -6197576, 27584817, 3093888, -8843694, 3849921], + }, + Precomp { + yplusx: [-9064912, 2103172, 25561640, -15125738, -5239824, 9582958, 32477045, -9017955, 5002294, -15550259], + yminusx: [-12057553, -11177906, 21115585, -13365155, 8808712, -12030708, 16489530, 13378448, -25845716, 12741426], + xy2d: [-5946367, 10645103, -30911586, 15390284, -3286982, -7118677, 24306472, 15852464, 28834118, -7646072], + }, + Precomp { + yplusx: [-17335748, -9107057, -24531279, 9434953, -8472084, -583362, -13090771, 455841, 20461858, 5491305], + yminusx: [13669248, -16095482, -12481974, -10203039, -14569770, -11893198, -24995986, 11293807, -28588204, -9421832], + xy2d: [28497928, 6272777, -33022994, 14470570, 8906179, -1225630, 18504674, -14165166, 29867745, -8795943], + }, + Precomp { + yplusx: [-16207023, 13517196, -27799630, -13697798, 24009064, -6373891, -6367600, -13175392, 22853429, -4012011], + yminusx: [24191378, 16712145, -13931797, 15217831, 14542237, 1646131, 18603514, -11037887, 12876623, -2112447], + xy2d: [17902668, 4518229, -411702, -2829247, 26878217, 5258055, -12860753, 608397, 16031844, 3723494], + }, + Precomp { + yplusx: [-28632773, 12763728, -20446446, 7577504, 33001348, -13017745, 17558842, -7872890, 23896954, -4314245], + yminusx: [-20005381, -12011952, 31520464, 605201, 2543521, 5991821, -2945064, 7229064, -9919646, -8826859], + xy2d: [28816045, 298879, -28165016, -15920938, 19000928, -1665890, -12680833, -2949325, -18051778, -2082915], + }, + Precomp { + yplusx: [16000882, -344896, 3493092, -11447198, -29504595, -13159789, 12577740, 16041268, -19715240, 7847707], + yminusx: [10151868, 10572098, 27312476, 7922682, 14825339, 4723128, -32855931, -6519018, -10020567, 3852848], + xy2d: [-11430470, 15697596, -21121557, -4420647, 5386314, 15063598, 16514493, -15932110, 29330899, -15076224], + }, + ], + [ + Precomp { + yplusx: [-25499735, -4378794, -15222908, -6901211, 16615731, 2051784, 3303702, 15490, -27548796, 12314391], + yminusx: [15683520, -6003043, 18109120, -9980648, 15337968, -5997823, -16717435, 15921866, 16103996, -3731215], + xy2d: [-23169824, -10781249, 13588192, -1628807, -3798557, -1074929, -19273607, 5402699, -29815713, -9841101], + }, + Precomp { + yplusx: [23190676, 2384583, -32714340, 3462154, -29903655, -1529132, -11266856, 8911517, -25205859, 2739713], + yminusx: [21374101, -3554250, -33524649, 9874411, 15377179, 11831242, -33529904, 6134907, 4931255, 11987849], + xy2d: [-7732, -2978858, -16223486, 7277597, 105524, -322051, -31480539, 13861388, -30076310, 10117930], + }, + Precomp { + yplusx: [-29501170, -10744872, -26163768, 13051539, -25625564, 5089643, -6325503, 6704079, 12890019, 15728940], + yminusx: [-21972360, -11771379, -951059, -4418840, 14704840, 2695116, 903376, -10428139, 12885167, 8311031], + xy2d: [-17516482, 5352194, 10384213, -13811658, 7506451, 13453191, 26423267, 4384730, 1888765, -5435404], + }, + Precomp { + yplusx: [-25817338, -3107312, -13494599, -3182506, 30896459, -13921729, -32251644, -12707869, -19464434, -3340243], + yminusx: [-23607977, -2665774, -526091, 4651136, 5765089, 4618330, 6092245, 14845197, 17151279, -9854116], + xy2d: [-24830458, -12733720, -15165978, 10367250, -29530908, -265356, 22825805, -7087279, -16866484, 16176525], + }, + Precomp { + yplusx: [-23583256, 6564961, 20063689, 3798228, -4740178, 7359225, 2006182, -10363426, -28746253, -10197509], + yminusx: [-10626600, -4486402, -13320562, -5125317, 3432136, -6393229, 23632037, -1940610, 32808310, 1099883], + xy2d: [15030977, 5768825, -27451236, -2887299, -6427378, -15361371, -15277896, -6809350, 2051441, -15225865], + }, + Precomp { + yplusx: [-3362323, -7239372, 7517890, 9824992, 23555850, 295369, 5148398, -14154188, -22686354, 16633660], + yminusx: [4577086, -16752288, 13249841, -15304328, 19958763, -14537274, 18559670, -10759549, 8402478, -9864273], + xy2d: [-28406330, -1051581, -26790155, -907698, -17212414, -11030789, 9453451, -14980072, 17983010, 9967138], + }, + Precomp { + yplusx: [-25762494, 6524722, 26585488, 9969270, 24709298, 1220360, -1677990, 7806337, 17507396, 3651560], + yminusx: [-10420457, -4118111, 14584639, 15971087, -15768321, 8861010, 26556809, -5574557, -18553322, -11357135], + xy2d: [2839101, 14284142, 4029895, 3472686, 14402957, 12689363, -26642121, 8459447, -5605463, -7621941], + }, + Precomp { + yplusx: [-4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813, -849066, 17258084, -7977739], + yminusx: [18164541, -10595176, -17154882, -1542417, 19237078, -9745295, 23357533, -15217008, 26908270, 12150756], + xy2d: [-30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168, -5537701, -32302074, 16215819], + }, + ], + [ + Precomp { + yplusx: [-6898905, 9824394, -12304779, -4401089, -31397141, -6276835, 32574489, 12532905, -7503072, -8675347], + yminusx: [-27343522, -16515468, -27151524, -10722951, 946346, 16291093, 254968, 7168080, 21676107, -1943028], + xy2d: [21260961, -8424752, -16831886, -11920822, -23677961, 3968121, -3651949, -6215466, -3556191, -7913075], + }, + Precomp { + yplusx: [16544754, 13250366, -16804428, 15546242, -4583003, 12757258, -2462308, -8680336, -18907032, -9662799], + yminusx: [-2415239, -15577728, 18312303, 4964443, -15272530, -12653564, 26820651, 16690659, 25459437, -4564609], + xy2d: [-25144690, 11425020, 28423002, -11020557, -6144921, -15826224, 9142795, -2391602, -6432418, -1644817], + }, + Precomp { + yplusx: [-23104652, 6253476, 16964147, -3768872, -25113972, -12296437, -27457225, -16344658, 6335692, 7249989], + yminusx: [-30333227, 13979675, 7503222, -12368314, -11956721, -4621693, -30272269, 2682242, 25993170, -12478523], + xy2d: [4364628, 5930691, 32304656, -10044554, -8054781, 15091131, 22857016, -10598955, 31820368, 15075278], + }, + Precomp { + yplusx: [31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788, -9650886, -17970238, 12833045], + yminusx: [19073683, 14851414, -24403169, -11860168, 7625278, 11091125, -19619190, 2074449, -9413939, 14905377], + xy2d: [24483667, -11935567, -2518866, -11547418, -1553130, 15355506, -25282080, 9253129, 27628530, -7555480], + }, + Precomp { + yplusx: [17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324, -9157582, -14110875, 15297016], + yminusx: [510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417, -11864220, 8683221, 2921426], + xy2d: [18606791, 11874196, 27155355, -5281482, -24031742, 6265446, -25178240, -1278924, 4674690, 13890525], + }, + Precomp { + yplusx: [13609624, 13069022, -27372361, -13055908, 24360586, 9592974, 14977157, 9835105, 4389687, 288396], + yminusx: [9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062, 8317628, 23388070, 16052080], + xy2d: [12720016, 11937594, -31970060, -5028689, 26900120, 8561328, -20155687, -11632979, -14754271, -10812892], + }, + Precomp { + yplusx: [15961858, 14150409, 26716931, -665832, -22794328, 13603569, 11829573, 7467844, -28822128, 929275], + yminusx: [11038231, -11582396, -27310482, -7316562, -10498527, -16307831, -23479533, -9371869, -21393143, 2465074], + xy2d: [20017163, -4323226, 27915242, 1529148, 12396362, 15675764, 13817261, -9658066, 2463391, -4622140], + }, + Precomp { + yplusx: [-16358878, -12663911, -12065183, 4996454, -1256422, 1073572, 9583558, 12851107, 4003896, 12673717], + yminusx: [-1731589, -15155870, -3262930, 16143082, 19294135, 13385325, 14741514, -9103726, 7903886, 2348101], + xy2d: [24536016, -16515207, 12715592, -3862155, 1511293, 10047386, -3842346, -7129159, -28377538, 10048127], + }, + ], + [ + Precomp { + yplusx: [-12622226, -6204820, 30718825, 2591312, -10617028, 12192840, 18873298, -7297090, -32297756, 15221632], + yminusx: [-26478122, -11103864, 11546244, -1852483, 9180880, 7656409, -21343950, 2095755, 29769758, 6593415], + xy2d: [-31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345, -6118678, 30958054, 8292160], + }, + Precomp { + yplusx: [31429822, -13959116, 29173532, 15632448, 12174511, -2760094, 32808831, 3977186, 26143136, -3148876], + yminusx: [22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633, -1674433, -3758243, -2304625], + xy2d: [-15491917, 8012313, -2514730, -12702462, -23965846, -10254029, -1612713, -1535569, -16664475, 8194478], + }, + Precomp { + yplusx: [27338066, -7507420, -7414224, 10140405, -19026427, -6589889, 27277191, 8855376, 28572286, 3005164], + yminusx: [26287124, 4821776, 25476601, -4145903, -3764513, -15788984, -18008582, 1182479, -26094821, -13079595], + xy2d: [-7171154, 3178080, 23970071, 6201893, -17195577, -4489192, -21876275, -13982627, 32208683, -1198248], + }, + Precomp { + yplusx: [-16657702, 2817643, -10286362, 14811298, 6024667, 13349505, -27315504, -10497842, -27672585, -11539858], + yminusx: [15941029, -9405932, -21367050, 8062055, 31876073, -238629, -15278393, -1444429, 15397331, -4130193], + xy2d: [8934485, -13485467, -23286397, -13423241, -32446090, 14047986, 31170398, -1441021, -27505566, 15087184], + }, + Precomp { + yplusx: [-18357243, -2156491, 24524913, -16677868, 15520427, -6360776, -15502406, 11461896, 16788528, -5868942], + yminusx: [-1947386, 16013773, 21750665, 3714552, -17401782, -16055433, -3770287, -10323320, 31322514, -11615635], + xy2d: [21426655, -5650218, -13648287, -5347537, -28812189, -4920970, -18275391, -14621414, 13040862, -12112948], + }, + Precomp { + yplusx: [11293895, 12478086, -27136401, 15083750, -29307421, 14748872, 14555558, -13417103, 1613711, 4896935], + yminusx: [-25894883, 15323294, -8489791, -8057900, 25967126, -13425460, 2825960, -4897045, -23971776, -11267415], + xy2d: [-15924766, -5229880, -17443532, 6410664, 3622847, 10243618, 20615400, 12405433, -23753030, -8436416], + }, + Precomp { + yplusx: [-7091295, 12556208, -20191352, 9025187, -17072479, 4333801, 4378436, 2432030, 23097949, -566018], + yminusx: [4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, 10103221, -18512313, 2424778], + xy2d: [366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, 1344109, -3642553, 12412659], + }, + Precomp { + yplusx: [-24001791, 7690286, 14929416, -168257, -32210835, -13412986, 24162697, -15326504, -3141501, 11179385], + yminusx: [18289522, -14724954, 8056945, 16430056, -21729724, 7842514, -6001441, -1486897, -18684645, -11443503], + xy2d: [476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, 13403813, 11052904, 5219329], + }, + ], + [ + Precomp { + yplusx: [20678546, -8375738, -32671898, 8849123, -5009758, 14574752, 31186971, -3973730, 9014762, -8579056], + yminusx: [-13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -33102500, 9160280, 8473550, -3256838], + xy2d: [24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -7689309, -16335821, -24568481, 11788948], + }, + Precomp { + yplusx: [-3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -20037437, 10410733, -24568470, -1458691], + yminusx: [-15659161, 16736706, -22467150, 10215878, -9097177, 7563911, 11871841, -12505194, -18513325, 8464118], + xy2d: [-23400612, 8348507, -14585951, -861714, -3950205, -6373419, 14325289, 8628612, 33313881, -8370517], + }, + Precomp { + yplusx: [-20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -24805667, -10236854, -8940735, -5818269], + yminusx: [-6948785, -1795212, -32625683, -16021179, 32635414, -7374245, 15989197, -12838188, 28358192, -4253904], + xy2d: [-23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -16637684, 4072016, -5351664, 5596589], + }, + Precomp { + yplusx: [-28236598, -3390048, 12312896, 6213178, 3117142, 16078565, 29266239, 2557221, 1768301, 15373193], + yminusx: [-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -4504991, -24660491, 3442910], + xy2d: [-30210571, 5124043, 14181784, 8197961, 18964734, -11939093, 22597931, 7176455, -18585478, 13365930], + }, + Precomp { + yplusx: [-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -8570186, -9689599, -3031667], + yminusx: [25008904, -10771599, -4305031, -9638010, 16265036, 15721635, 683793, -11823784, 15723479, -15163481], + xy2d: [-9660625, 12374379, -27006999, -7026148, -7724114, -12314514, 11879682, 5400171, 519526, -1235876], + }, + Precomp { + yplusx: [22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -20353881, 7315967, 16648397, 7605640], + yminusx: [-8081308, -8464597, -8223311, 9719710, 19259459, -15348212, 23994942, -5281555, -9468848, 4763278], + xy2d: [-21699244, 9220969, -15730624, 1084137, -25476107, -2852390, 31088447, -7764523, -11356529, 728112], + }, + Precomp { + yplusx: [26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -4273545, -12555558, -29365436, -5498272], + yminusx: [17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, 12327945, 10750447, 10014012], + xy2d: [-10312768, 3936952, 9156313, -8897683, 16498692, -994647, -27481051, -666732, 3424691, 7540221], + }, + Precomp { + yplusx: [30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -16317219, -9244265, 15258046], + yminusx: [13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, 2711395, 1062915, -5136345], + xy2d: [-19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310], + }, + ], + [ + Precomp { + yplusx: [19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937], + yminusx: [31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636], + xy2d: [-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008], + }, + Precomp { + yplusx: [-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429], + yminusx: [-15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576], + xy2d: [31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066], + }, + Precomp { + yplusx: [-9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490], + yminusx: [-12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104], + xy2d: [33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053], + }, + Precomp { + yplusx: [31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275], + yminusx: [-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511], + xy2d: [22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095], + }, + Precomp { + yplusx: [-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439], + yminusx: [23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939], + xy2d: [-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424], + }, + Precomp { + yplusx: [2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310], + yminusx: [3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608], + xy2d: [-32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079], + }, + Precomp { + yplusx: [-23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101], + yminusx: [21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418], + xy2d: [18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576], + }, + Precomp { + yplusx: [30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356], + yminusx: [9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996], + xy2d: [-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099], + }, + ], + [ + Precomp { + yplusx: [-26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728], + yminusx: [-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658], + xy2d: [-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242], + }, + Precomp { + yplusx: [-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001], + yminusx: [-4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766], + xy2d: [18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373], + }, + Precomp { + yplusx: [26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458], + yminusx: [-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628], + xy2d: [-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657], + }, + Precomp { + yplusx: [-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062], + yminusx: [25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616], + xy2d: [31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014], + }, + Precomp { + yplusx: [24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383], + yminusx: [-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814], + xy2d: [-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718], + }, + Precomp { + yplusx: [30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417], + yminusx: [2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222], + xy2d: [33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444], + }, + Precomp { + yplusx: [-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597], + yminusx: [23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970], + xy2d: [1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799], + }, + Precomp { + yplusx: [-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647], + yminusx: [13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511], + xy2d: [-29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032], + }, + ], + [ + Precomp { + yplusx: [9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834], + yminusx: [-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461], + xy2d: [29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062], + }, + Precomp { + yplusx: [-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516], + yminusx: [-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547], + xy2d: [-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240], + }, + Precomp { + yplusx: [-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038], + yminusx: [-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741], + xy2d: [16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103], + }, + Precomp { + yplusx: [-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747], + yminusx: [-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323], + xy2d: [31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016], + }, + Precomp { + yplusx: [-14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373], + yminusx: [15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228], + xy2d: [-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141], + }, + Precomp { + yplusx: [16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399], + yminusx: [11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831], + xy2d: [-185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376], + }, + Precomp { + yplusx: [-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313], + yminusx: [-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958], + xy2d: [-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577], + }, + Precomp { + yplusx: [-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743], + yminusx: [29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684], + xy2d: [-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476], + }, + ], +]; + +pub const BI: [Precomp; 8] = [ + Precomp { + yplusx: [25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, + -11754271, -6079156, 2047605], + yminusx: [-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, + 5043384, 19500929, -15469378], + xy2d: [-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, + 11864899, -24514362, -4438546], + }, + Precomp { + yplusx: [15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, + -14772189, 28944400, -1550024], + yminusx: [16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, + -11775962, 7689662, 11199574], + xy2d: [30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, + 10017326, -17749093, -9920357], + }, + Precomp { + yplusx: [10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, + 14515107, -15438304, 10819380], + yminusx: [4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, + 12483688, -12668491, 5581306], + xy2d: [19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, + 13850243, -23678021, -15815942], + }, + Precomp { + yplusx: [5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, + 5230134, -23952439, -15175766], + yminusx: [-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, + 16520125, 30598449, 7715701], + xy2d: [28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, + 1370708, 29794553, -1409300], + }, + Precomp { + yplusx: [-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, + -1361450, -13062696, 13821877], + yminusx: [-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, + -7212327, 18853322, -14220951], + xy2d: [4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, + -10431137, 2207753, -3209784], + }, + Precomp { + yplusx: [-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, + -663000, -31111463, -16132436], + yminusx: [25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, + 15725684, 171356, 6466918], + xy2d: [23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, + -14088058, -30714912, 16193877], + }, + Precomp { + yplusx: [-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, + 4729455, -18074513, 9256800], + yminusx: [-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, + 9761698, -19827198, 630305], + xy2d: [-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, + -15960994, -2449256, -14291300], + }, + Precomp { + yplusx: [-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, + 15033784, 25105118, -7894876], + yminusx: [-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, + 1573892, -2625887, 2198790, -15804619], + xy2d: [-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, + -16236442, -32461234, -12290683], + }, +]; diff --git a/src/ed25519/fe.rs b/src/ed25519/fe.rs new file mode 100644 index 0000000..14ec993 --- /dev/null +++ b/src/ed25519/fe.rs @@ -0,0 +1,1125 @@ +#[cfg(test)] +use byteorder::{LittleEndian,NativeEndian,ReadBytesExt}; +#[cfg(test)] +use cryptonum::unsigned::{Decoder,U192}; +#[cfg(test)] +use ed25519::point::curve25519_scalar_mask; +#[cfg(test)] +use quickcheck::{Arbitrary,Gen}; +#[cfg(test)] +use std::io::Cursor; +#[cfg(test)] +use testing::run_test; + +// This is all an extremely straightforward translation of the usual C +// implementation, as linked in ring and other libraries. + +pub const NUM_ELEMENT_LIMBS: usize = 10; +pub type Element = [i32; NUM_ELEMENT_LIMBS]; + +pub const KBOTTOM_25BITS : i64 = 0x1ffffffi64; +pub const KBOTTOM_26BITS : i64 = 0x3ffffffi64; +pub const KTOP_39BITS : i64 = 0xfffffffffe000000u64 as i64; +pub const KTOP_38BITS : i64 = 0xfffffffffc000000u64 as i64; + +pub fn load3(x: &[u8]) -> u64 +{ + (x[0] as u64) | ((x[1] as u64) << 8) | ((x[2] as u64) << 16) +} + +pub fn load4(x: &[u8]) -> u64 +{ + (x[0] as u64) | ((x[1] as u64) << 8) | + ((x[2] as u64) << 16) | ((x[3] as u64) << 24) +} + +#[cfg(test)] +#[test] +fn loads() { + let fname = "testdata/ed25519/load.test"; + run_test(fname.to_string(), 3, |case| { + let (negx, xbytes) = case.get("x").unwrap(); + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + + assert!(!negx && !nega && !negb); + let res3 = u64::from(U192::from_bytes(abytes)); + let res4 = u64::from(U192::from_bytes(bbytes)); + assert_eq!(res3, load3(&xbytes), "load3"); + assert_eq!(res4, load4(&xbytes), "load4"); + }); +} + +pub fn fe_frombytes(h: &mut Element, s: &[u8]) +{ + /* Ignores top bit of h. */ + let mut h0 = load4(s) as i64; + let mut h1 = (load3(&s[4..]) << 6) as i64; + let mut h2 = (load3(&s[7..]) << 5) as i64; + let mut h3 = (load3(&s[10..]) << 3) as i64; + let mut h4 = (load3(&s[13..]) << 2) as i64; + let mut h5 = load4(&s[16..]) as i64; + let mut h6 = (load3(&s[20..]) << 7) as i64; + let mut h7 = (load3(&s[23..]) << 5) as i64; + let mut h8 = (load3(&s[26..]) << 4) as i64; + let mut h9 = ((load3(&s[29..]) & 8388607) << 2) as i64; + + let carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & KTOP_39BITS; + let carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & KTOP_39BITS; + let carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & KTOP_39BITS; + let carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & KTOP_39BITS; + let carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & KTOP_39BITS; + + let carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & KTOP_38BITS; + let carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & KTOP_38BITS; + let carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & KTOP_38BITS; + let carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & KTOP_38BITS; + let carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & KTOP_38BITS; + + h[0] = h0 as i32; h[1] = h1 as i32; h[2] = h2 as i32; h[3] = h3 as i32; h[4] = h4 as i32; + h[5] = h5 as i32; h[6] = h6 as i32; h[7] = h7 as i32; h[8] = h8 as i32; h[9] = h9 as i32; +} + +pub fn fe_tobytes(s: &mut [u8], h: &Element) +{ + assert!(s.len() >= 32); + let mut h0 = h[0]; + let mut h1 = h[1]; + let mut h2 = h[2]; + let mut h3 = h[3]; + let mut h4 = h[4]; + let mut h5 = h[5]; + let mut h6 = h[6]; + let mut h7 = h[7]; + let mut h8 = h[8]; + let mut h9 = h[9]; + + let mut q = (19 * h9 + ((1i32) << 24)) >> 25; + q = (h0 + q) >> 26; + q = (h1 + q) >> 25; + q = (h2 + q) >> 26; + q = (h3 + q) >> 25; + q = (h4 + q) >> 26; + q = (h5 + q) >> 25; + q = (h6 + q) >> 26; + q = (h7 + q) >> 25; + q = (h8 + q) >> 26; + q = (h9 + q) >> 25; + + /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ + h0 += 19 * q; + /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ + h1 += h0 >> 26; h0 &= KBOTTOM_26BITS as i32; + h2 += h1 >> 25; h1 &= KBOTTOM_25BITS as i32; + h3 += h2 >> 26; h2 &= KBOTTOM_26BITS as i32; + h4 += h3 >> 25; h3 &= KBOTTOM_25BITS as i32; + h5 += h4 >> 26; h4 &= KBOTTOM_26BITS as i32; + h6 += h5 >> 25; h5 &= KBOTTOM_25BITS as i32; + h7 += h6 >> 26; h6 &= KBOTTOM_26BITS as i32; + h8 += h7 >> 25; h7 &= KBOTTOM_25BITS as i32; + h9 += h8 >> 26; h8 &= KBOTTOM_26BITS as i32; + h9 &= KBOTTOM_25BITS as i32; + /* h10 = carry9 */ + + /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. + * Have h0+...+2^230 h9 between 0 and 2^255-1; + * evidently 2^255 h10-2^255 q = 0. + * Goal: Output h0+...+2^230 h9. */ + s[0] = (h0 >> 0) as u8; + s[1] = (h0 >> 8) as u8; + s[2] = (h0 >> 16) as u8; + s[3] = ((h0 >> 24) | (((h1 as u32) << 2) as i32)) as u8; + s[4] = (h1 >> 6) as u8; + s[5] = (h1 >> 14) as u8; + s[6] = ((h1 >> 22) | (((h2 as u32) << 3) as i32)) as u8; + s[7] = (h2 >> 5) as u8; + s[8] = (h2 >> 13) as u8; + s[9] = ((h2 >> 21) | (((h3 as u32) << 5) as i32)) as u8; + s[10] = (h3 >> 3) as u8; + s[11] = (h3 >> 11) as u8; + s[12] = ((h3 >> 19) | (((h4 as u32) << 6) as i32)) as u8; + s[13] = (h4 >> 2) as u8; + s[14] = (h4 >> 10) as u8; + s[15] = (h4 >> 18) as u8; + s[16] = (h5 >> 0) as u8; + s[17] = (h5 >> 8) as u8; + s[18] = (h5 >> 16) as u8; + s[19] = ((h5 >> 24) | (((h6 as u32) << 1) as i32)) as u8; + s[20] = (h6 >> 7) as u8; + s[21] = (h6 >> 15) as u8; + s[22] = ((h6 >> 23) | (((h7 as u32) << 3) as i32)) as u8; + s[23] = (h7 >> 5) as u8; + s[24] = (h7 >> 13) as u8; + s[25] = ((h7 >> 21) | (((h8 as u32) << 4) as i32)) as u8; + s[26] = (h8 >> 4) as u8; + s[27] = (h8 >> 12) as u8; + s[28] = ((h8 >> 20) | (((h9 as u32) << 6) as i32)) as u8; + s[29] = (h9 >> 2) as u8; + s[30] = (h9 >> 10) as u8; + s[31] = (h9 >> 18) as u8; +} + +#[cfg(test)] +#[test] +fn from_to_bytes() { + let fname = "testdata/ed25519/bytes.test"; + run_test(fname.to_string(), 2, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + + assert!(!nega && !negb); + let mut e = [0; NUM_ELEMENT_LIMBS]; + let mut target = [0; NUM_ELEMENT_LIMBS]; + fe_frombytes(&mut e, abytes); + let mut cursor = Cursor::new(bbytes); + cursor.read_i32_into::(&mut target).unwrap(); + assert_eq!(e, target, "from bytes"); + let mut bytes = [0; 32]; + fe_tobytes(&mut bytes, &e); + assert_eq!(&bytes.to_vec(), abytes, "to bytes"); + }); +} + +#[cfg(test)] +#[derive(Clone,Debug)] +struct ValidElement { + values: Element +} + +#[cfg(test)] +impl Arbitrary for ValidElement { + fn arbitrary(g: &mut G) -> ValidElement + { + let mut bytes = [0; 32]; + g.fill_bytes(&mut bytes); + curve25519_scalar_mask(&mut bytes); + let mut res = ValidElement{ values: [0; NUM_ELEMENT_LIMBS] }; + fe_frombytes(&mut res.values, &bytes); + res + } +} + +#[cfg(test)] +pub fn test_from_bytes(x: &[u8]) -> Element +{ + let mut res = [0; NUM_ELEMENT_LIMBS]; + let mut helper = Cursor::new(x); + helper.read_i32_into::(&mut res).unwrap(); + res +} + +#[cfg(test)] +quickcheck! { + // this is somewhat self referential, given the definition of arbitrary, + // but more testing is more good + fn from_to_bytes_roundtrip(e: ValidElement) -> bool { + let mut bytes = [0; 32]; + fe_tobytes(&mut bytes, &e.values); + let mut trans = [0; NUM_ELEMENT_LIMBS]; + fe_frombytes(&mut trans, &bytes); + trans == e.values + } +} + +// pub fn fe_zero() -> Element +// { +// [0; NUM_ELEMENT_LIMBS] +// } + +pub fn fe0(x: &mut Element) +{ + x[0] = 0; + x[1] = 0; + x[2] = 0; + x[3] = 0; + x[4] = 0; + x[5] = 0; + x[6] = 0; + x[7] = 0; + x[8] = 0; + x[9] = 0; +} + +// pub fn fe_one() -> Element +// { +// [0, 0, 0, 0, 0, 0, 0, 0, 0, 1] +// } + +pub fn fe1(x: &mut Element) +{ + x[0] = 1; + x[1] = 0; + x[2] = 0; + x[3] = 0; + x[4] = 0; + x[5] = 0; + x[6] = 0; + x[7] = 0; + x[8] = 0; + x[9] = 0; +} + +pub fn fe_add(h: &mut Element, f: &Element, g: &Element) +{ + for i in 0..10 { + h[i] = f[i] + g[i] + } +} + +pub fn fe_sub(h: &mut Element, f: &Element, g: &Element) +{ + for i in 0..10 { + h[i] = f[i] - g[i] + } +} + +#[cfg(test)] +#[test] +fn addsub() { + let fname = "testdata/ed25519/addsub.test"; + run_test(fname.to_string(), 4, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + let (negd, dbytes) = case.get("d").unwrap(); + + assert!(!nega && !negb && !negc && !negd); + let a = test_from_bytes(&abytes); + let b = test_from_bytes(&bbytes); + let c = test_from_bytes(&cbytes); + let d = test_from_bytes(&dbytes); + let mut r = [0; NUM_ELEMENT_LIMBS]; + let mut s = [0; NUM_ELEMENT_LIMBS]; + fe_add(&mut r, &a, &b); + fe_sub(&mut s, &a, &b); + assert_eq!(r, c, "field addition"); + assert_eq!(s, d, "field subtraction"); + }); +} + +pub fn fe_mul(h: &mut Element, f: &Element, g: &Element) +{ + let f0 : i32 = f[0]; + let f1 : i32 = f[1]; + let f2 : i32 = f[2]; + let f3 : i32 = f[3]; + let f4 : i32 = f[4]; + let f5 : i32 = f[5]; + let f6 : i32 = f[6]; + let f7 : i32 = f[7]; + let f8 : i32 = f[8]; + let f9 : i32 = f[9]; + let g0 : i32 = g[0]; + let g1 : i32 = g[1]; + let g2 : i32 = g[2]; + let g3 : i32 = g[3]; + let g4 : i32 = g[4]; + let g5 : i32 = g[5]; + let g6 : i32 = g[6]; + let g7 : i32 = g[7]; + let g8 : i32 = g[8]; + let g9 : i32 = g[9]; + let g1_19 : i32 = 19 * g1; /* 1.959375*2^29 */ + let g2_19 : i32 = 19 * g2; /* 1.959375*2^30; still ok */ + let g3_19 : i32 = 19 * g3; + let g4_19 : i32 = 19 * g4; + let g5_19 : i32 = 19 * g5; + let g6_19 : i32 = 19 * g6; + let g7_19 : i32 = 19 * g7; + let g8_19 : i32 = 19 * g8; + let g9_19 : i32 = 19 * g9; + let f1_2 : i32 = 2 * f1; + let f3_2 : i32 = 2 * f3; + let f5_2 : i32 = 2 * f5; + let f7_2 : i32 = 2 * f7; + let f9_2 : i32 = 2 * f9; + + let f0g0 : i64 = (f0 as i64) * (g0 as i64); + let f0g1 : i64 = (f0 as i64) * (g1 as i64); + let f0g2 : i64 = (f0 as i64) * (g2 as i64); + let f0g3 : i64 = (f0 as i64) * (g3 as i64); + let f0g4 : i64 = (f0 as i64) * (g4 as i64); + let f0g5 : i64 = (f0 as i64) * (g5 as i64); + let f0g6 : i64 = (f0 as i64) * (g6 as i64); + let f0g7 : i64 = (f0 as i64) * (g7 as i64); + let f0g8 : i64 = (f0 as i64) * (g8 as i64); + let f0g9 : i64 = (f0 as i64) * (g9 as i64); + let f1g0 : i64 = (f1 as i64) * (g0 as i64); + let f1g1_2 : i64 = (f1_2 as i64) * (g1 as i64); + let f1g2 : i64 = (f1 as i64) * (g2 as i64); + let f1g3_2 : i64 = (f1_2 as i64) * (g3 as i64); + let f1g4 : i64 = (f1 as i64) * (g4 as i64); + let f1g5_2 : i64 = (f1_2 as i64) * (g5 as i64); + let f1g6 : i64 = (f1 as i64) * (g6 as i64); + let f1g7_2 : i64 = (f1_2 as i64) * (g7 as i64); + let f1g8 : i64 = (f1 as i64) * (g8 as i64); + let f1g9_38 : i64 = (f1_2 as i64) * (g9_19 as i64); + let f2g0 : i64 = (f2 as i64) * (g0 as i64); + let f2g1 : i64 = (f2 as i64) * (g1 as i64); + let f2g2 : i64 = (f2 as i64) * (g2 as i64); + let f2g3 : i64 = (f2 as i64) * (g3 as i64); + let f2g4 : i64 = (f2 as i64) * (g4 as i64); + let f2g5 : i64 = (f2 as i64) * (g5 as i64); + let f2g6 : i64 = (f2 as i64) * (g6 as i64); + let f2g7 : i64 = (f2 as i64) * (g7 as i64); + let f2g8_19 : i64 = (f2 as i64) * (g8_19 as i64); + let f2g9_19 : i64 = (f2 as i64) * (g9_19 as i64); + let f3g0 : i64 = (f3 as i64) * (g0 as i64); + let f3g1_2 : i64 = (f3_2 as i64) * (g1 as i64); + let f3g2 : i64 = (f3 as i64) * (g2 as i64); + let f3g3_2 : i64 = (f3_2 as i64) * (g3 as i64); + let f3g4 : i64 = (f3 as i64) * (g4 as i64); + let f3g5_2 : i64 = (f3_2 as i64) * (g5 as i64); + let f3g6 : i64 = (f3 as i64) * (g6 as i64); + let f3g7_38 : i64 = (f3_2 as i64) * (g7_19 as i64); + let f3g8_19 : i64 = (f3 as i64) * (g8_19 as i64); + let f3g9_38 : i64 = (f3_2 as i64) * (g9_19 as i64); + let f4g0 : i64 = (f4 as i64) * (g0 as i64); + let f4g1 : i64 = (f4 as i64) * (g1 as i64); + let f4g2 : i64 = (f4 as i64) * (g2 as i64); + let f4g3 : i64 = (f4 as i64) * (g3 as i64); + let f4g4 : i64 = (f4 as i64) * (g4 as i64); + let f4g5 : i64 = (f4 as i64) * (g5 as i64); + let f4g6_19 : i64 = (f4 as i64) * (g6_19 as i64); + let f4g7_19 : i64 = (f4 as i64) * (g7_19 as i64); + let f4g8_19 : i64 = (f4 as i64) * (g8_19 as i64); + let f4g9_19 : i64 = (f4 as i64) * (g9_19 as i64); + let f5g0 : i64 = (f5 as i64) * (g0 as i64); + let f5g1_2 : i64 = (f5_2 as i64) * (g1 as i64); + let f5g2 : i64 = (f5 as i64) * (g2 as i64); + let f5g3_2 : i64 = (f5_2 as i64) * (g3 as i64); + let f5g4 : i64 = (f5 as i64) * (g4 as i64); + let f5g5_38 : i64 = (f5_2 as i64) * (g5_19 as i64); + let f5g6_19 : i64 = (f5 as i64) * (g6_19 as i64); + let f5g7_38 : i64 = (f5_2 as i64) * (g7_19 as i64); + let f5g8_19 : i64 = (f5 as i64) * (g8_19 as i64); + let f5g9_38 : i64 = (f5_2 as i64) * (g9_19 as i64); + let f6g0 : i64 = (f6 as i64) * (g0 as i64); + let f6g1 : i64 = (f6 as i64) * (g1 as i64); + let f6g2 : i64 = (f6 as i64) * (g2 as i64); + let f6g3 : i64 = (f6 as i64) * (g3 as i64); + let f6g4_19 : i64 = (f6 as i64) * (g4_19 as i64); + let f6g5_19 : i64 = (f6 as i64) * (g5_19 as i64); + let f6g6_19 : i64 = (f6 as i64) * (g6_19 as i64); + let f6g7_19 : i64 = (f6 as i64) * (g7_19 as i64); + let f6g8_19 : i64 = (f6 as i64) * (g8_19 as i64); + let f6g9_19 : i64 = (f6 as i64) * (g9_19 as i64); + let f7g0 : i64 = (f7 as i64) * (g0 as i64); + let f7g1_2 : i64 = (f7_2 as i64) * (g1 as i64); + let f7g2 : i64 = (f7 as i64) * (g2 as i64); + let f7g3_38 : i64 = (f7_2 as i64) * (g3_19 as i64); + let f7g4_19 : i64 = (f7 as i64) * (g4_19 as i64); + let f7g5_38 : i64 = (f7_2 as i64) * (g5_19 as i64); + let f7g6_19 : i64 = (f7 as i64) * (g6_19 as i64); + let f7g7_38 : i64 = (f7_2 as i64) * (g7_19 as i64); + let f7g8_19 : i64 = (f7 as i64) * (g8_19 as i64); + let f7g9_38 : i64 = (f7_2 as i64) * (g9_19 as i64); + let f8g0 : i64 = (f8 as i64) * (g0 as i64); + let f8g1 : i64 = (f8 as i64) * (g1 as i64); + let f8g2_19 : i64 = (f8 as i64) * (g2_19 as i64); + let f8g3_19 : i64 = (f8 as i64) * (g3_19 as i64); + let f8g4_19 : i64 = (f8 as i64) * (g4_19 as i64); + let f8g5_19 : i64 = (f8 as i64) * (g5_19 as i64); + let f8g6_19 : i64 = (f8 as i64) * (g6_19 as i64); + let f8g7_19 : i64 = (f8 as i64) * (g7_19 as i64); + let f8g8_19 : i64 = (f8 as i64) * (g8_19 as i64); + let f8g9_19 : i64 = (f8 as i64) * (g9_19 as i64); + let f9g0 : i64 = (f9 as i64) * (g0 as i64); + let f9g1_38 : i64 = (f9_2 as i64) * (g1_19 as i64); + let f9g2_19 : i64 = (f9 as i64) * (g2_19 as i64); + let f9g3_38 : i64 = (f9_2 as i64) * (g3_19 as i64); + let f9g4_19 : i64 = (f9 as i64) * (g4_19 as i64); + let f9g5_38 : i64 = (f9_2 as i64) * (g5_19 as i64); + let f9g6_19 : i64 = (f9 as i64) * (g6_19 as i64); + let f9g7_38 : i64 = (f9_2 as i64) * (g7_19 as i64); + let f9g8_19 : i64 = (f9 as i64) * (g8_19 as i64); + let f9g9_38 : i64 = (f9_2 as i64) * (g9_19 as i64); + let mut h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; + let mut h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; + let mut h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; + let mut h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; + let mut h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; + let mut h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; + let mut h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; + let mut h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; + let mut h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; + let mut h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; + let mut carry0; + let carry1; + let carry2; + let carry3; + let mut carry4; + let carry5; + let carry6; + let carry7; + let carry8; + let carry9; + + /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) + * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 + * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) + * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & KTOP_38BITS; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & KTOP_38BITS; + /* |h0| <= 2^25 */ + /* |h4| <= 2^25 */ + /* |h1| <= 1.71*2^59 */ + /* |h5| <= 1.71*2^59 */ + + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & KTOP_39BITS; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & KTOP_39BITS; + /* |h1| <= 2^24; from now on fits into int32 */ + /* |h5| <= 2^24; from now on fits into int32 */ + /* |h2| <= 1.41*2^60 */ + /* |h6| <= 1.41*2^60 */ + + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & KTOP_38BITS; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & KTOP_38BITS; + /* |h2| <= 2^25; from now on fits into int32 unchanged */ + /* |h6| <= 2^25; from now on fits into int32 unchanged */ + /* |h3| <= 1.71*2^59 */ + /* |h7| <= 1.71*2^59 */ + + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & KTOP_39BITS; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & KTOP_39BITS; + /* |h3| <= 2^24; from now on fits into int32 unchanged */ + /* |h7| <= 2^24; from now on fits into int32 unchanged */ + /* |h4| <= 1.72*2^34 */ + /* |h8| <= 1.41*2^60 */ + + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & KTOP_38BITS; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & KTOP_38BITS; + /* |h4| <= 2^25; from now on fits into int32 unchanged */ + /* |h8| <= 2^25; from now on fits into int32 unchanged */ + /* |h5| <= 1.01*2^24 */ + /* |h9| <= 1.71*2^59 */ + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & KTOP_39BITS; + /* |h9| <= 2^24; from now on fits into int32 unchanged */ + /* |h0| <= 1.1*2^39 */ + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & KTOP_38BITS; + /* |h0| <= 2^25; from now on fits into int32 unchanged */ + /* |h1| <= 1.01*2^24 */ + + h[0] = h0 as i32; + h[1] = h1 as i32; + h[2] = h2 as i32; + h[3] = h3 as i32; + h[4] = h4 as i32; + h[5] = h5 as i32; + h[6] = h6 as i32; + h[7] = h7 as i32; + h[8] = h8 as i32; + h[9] = h9 as i32; +} + +#[cfg(test)] +#[test] +fn mul() { + let fname = "testdata/ed25519/mul.test"; + run_test(fname.to_string(), 3, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + + assert!(!nega && !negb && !negc); + let a = test_from_bytes(&abytes); + let b = test_from_bytes(&bbytes); + let c = test_from_bytes(&cbytes); + let mut r = [0; NUM_ELEMENT_LIMBS]; + fe_mul(&mut r, &a, &b); + assert_eq!(r, c); + }); +} + +pub fn fe_square(h: &mut Element, f: &Element) +{ + let f0 : i32 = f[0]; + let f1 : i32 = f[1]; + let f2 : i32 = f[2]; + let f3 : i32 = f[3]; + let f4 : i32 = f[4]; + let f5 : i32 = f[5]; + let f6 : i32 = f[6]; + let f7 : i32 = f[7]; + let f8 : i32 = f[8]; + let f9 : i32 = f[9]; + let f0_2 : i32 = 2 * f0; + let f1_2 : i32 = 2 * f1; + let f2_2 : i32 = 2 * f2; + let f3_2 : i32 = 2 * f3; + let f4_2 : i32 = 2 * f4; + let f5_2 : i32 = 2 * f5; + let f6_2 : i32 = 2 * f6; + let f7_2 : i32 = 2 * f7; + let f5_38 : i32 = 38 * f5; /* 1.959375*2^30 */ + let f6_19 : i32 = 19 * f6; /* 1.959375*2^30 */ + let f7_38 : i32 = 38 * f7; /* 1.959375*2^30 */ + let f8_19 : i32 = 19 * f8; /* 1.959375*2^30 */ + let f9_38 : i32 = 38 * f9; /* 1.959375*2^30 */ + let f0f0 : i64 = (f0 as i64) * (f0 as i64); + let f0f1_2 : i64 = (f0_2 as i64) * (f1 as i64); + let f0f2_2 : i64 = (f0_2 as i64) * (f2 as i64); + let f0f3_2 : i64 = (f0_2 as i64) * (f3 as i64); + let f0f4_2 : i64 = (f0_2 as i64) * (f4 as i64); + let f0f5_2 : i64 = (f0_2 as i64) * (f5 as i64); + let f0f6_2 : i64 = (f0_2 as i64) * (f6 as i64); + let f0f7_2 : i64 = (f0_2 as i64) * (f7 as i64); + let f0f8_2 : i64 = (f0_2 as i64) * (f8 as i64); + let f0f9_2 : i64 = (f0_2 as i64) * (f9 as i64); + let f1f1_2 : i64 = (f1_2 as i64) * (f1 as i64); + let f1f2_2 : i64 = (f1_2 as i64) * (f2 as i64); + let f1f3_4 : i64 = (f1_2 as i64) * (f3_2 as i64); + let f1f4_2 : i64 = (f1_2 as i64) * (f4 as i64); + let f1f5_4 : i64 = (f1_2 as i64) * (f5_2 as i64); + let f1f6_2 : i64 = (f1_2 as i64) * (f6 as i64); + let f1f7_4 : i64 = (f1_2 as i64) * (f7_2 as i64); + let f1f8_2 : i64 = (f1_2 as i64) * (f8 as i64); + let f1f9_76 : i64 = (f1_2 as i64) * (f9_38 as i64); + let f2f2 : i64 = (f2 as i64) * (f2 as i64); + let f2f3_2 : i64 = (f2_2 as i64) * (f3 as i64); + let f2f4_2 : i64 = (f2_2 as i64) * (f4 as i64); + let f2f5_2 : i64 = (f2_2 as i64) * (f5 as i64); + let f2f6_2 : i64 = (f2_2 as i64) * (f6 as i64); + let f2f7_2 : i64 = (f2_2 as i64) * (f7 as i64); + let f2f8_38 : i64 = (f2_2 as i64) * (f8_19 as i64); + let f2f9_38 : i64 = (f2 as i64) * (f9_38 as i64); + let f3f3_2 : i64 = (f3_2 as i64) * (f3 as i64); + let f3f4_2 : i64 = (f3_2 as i64) * (f4 as i64); + let f3f5_4 : i64 = (f3_2 as i64) * (f5_2 as i64); + let f3f6_2 : i64 = (f3_2 as i64) * (f6 as i64); + let f3f7_76 : i64 = (f3_2 as i64) * (f7_38 as i64); + let f3f8_38 : i64 = (f3_2 as i64) * (f8_19 as i64); + let f3f9_76 : i64 = (f3_2 as i64) * (f9_38 as i64); + let f4f4 : i64 = (f4 as i64) * (f4 as i64); + let f4f5_2 : i64 = (f4_2 as i64) * (f5 as i64); + let f4f6_38 : i64 = (f4_2 as i64) * (f6_19 as i64); + let f4f7_38 : i64 = (f4 as i64) * (f7_38 as i64); + let f4f8_38 : i64 = (f4_2 as i64) * (f8_19 as i64); + let f4f9_38 : i64 = (f4 as i64) * (f9_38 as i64); + let f5f5_38 : i64 = (f5 as i64) * (f5_38 as i64); + let f5f6_38 : i64 = (f5_2 as i64) * (f6_19 as i64); + let f5f7_76 : i64 = (f5_2 as i64) * (f7_38 as i64); + let f5f8_38 : i64 = (f5_2 as i64) * (f8_19 as i64); + let f5f9_76 : i64 = (f5_2 as i64) * (f9_38 as i64); + let f6f6_19 : i64 = (f6 as i64) * (f6_19 as i64); + let f6f7_38 : i64 = (f6 as i64) * (f7_38 as i64); + let f6f8_38 : i64 = (f6_2 as i64) * (f8_19 as i64); + let f6f9_38 : i64 = (f6 as i64) * (f9_38 as i64); + let f7f7_38 : i64 = (f7 as i64) * (f7_38 as i64); + let f7f8_38 : i64 = (f7_2 as i64) * (f8_19 as i64); + let f7f9_76 : i64 = (f7_2 as i64) * (f9_38 as i64); + let f8f8_19 : i64 = (f8 as i64) * (f8_19 as i64); + let f8f9_38 : i64 = (f8 as i64) * (f9_38 as i64); + let f9f9_38 : i64 = (f9 as i64) * (f9_38 as i64); + let mut h0 : i64 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; + let mut h1 : i64 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; + let mut h2 : i64 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; + let mut h3 : i64 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; + let mut h4 : i64 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; + let mut h5 : i64 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; + let mut h6 : i64 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; + let mut h7 : i64 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; + let mut h8 : i64 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; + let mut h9 : i64 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; + let mut carry0 : i64; + let carry1 : i64; + let carry2 : i64; + let carry3 : i64; + let mut carry4 : i64; + let carry5 : i64; + let carry6 : i64; + let carry7 : i64; + let carry8 : i64; + let carry9 : i64; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & KTOP_38BITS; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & KTOP_38BITS; + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & KTOP_39BITS; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & KTOP_39BITS; + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & KTOP_38BITS; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & KTOP_38BITS; + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & KTOP_39BITS; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & KTOP_39BITS; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & KTOP_38BITS; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & KTOP_38BITS; + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & KTOP_39BITS; + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & KTOP_38BITS; + + h[0] = h0 as i32; + h[1] = h1 as i32; + h[2] = h2 as i32; + h[3] = h3 as i32; + h[4] = h4 as i32; + h[5] = h5 as i32; + h[6] = h6 as i32; + h[7] = h7 as i32; + h[8] = h8 as i32; + h[9] = h9 as i32; +} + +#[cfg(test)] +#[test] +fn square() { + let fname = "testdata/ed25519/square.test"; + run_test(fname.to_string(), 2, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + + assert!(!nega && !negc); + let a = test_from_bytes(&abytes); + let c = test_from_bytes(&cbytes); + let mut r = [0; NUM_ELEMENT_LIMBS]; + fe_square(&mut r, &a); + assert_eq!(r, c); + }); +} + +pub fn fe_invert(z: &Element) -> Element +{ + let mut t0 = [0; NUM_ELEMENT_LIMBS]; + let mut t1 = [0; NUM_ELEMENT_LIMBS]; + let mut t2 = [0; NUM_ELEMENT_LIMBS]; + let mut t3 = [0; NUM_ELEMENT_LIMBS]; + let mut temp = [0; NUM_ELEMENT_LIMBS]; + let mut out = [0; NUM_ELEMENT_LIMBS]; + + fe_square(&mut t0, &z); + fe_square(&mut t1, &t0); + for _ in 1..2 { + temp.copy_from_slice(&t1); + fe_square(&mut t1, &temp); + } + temp.copy_from_slice(&t1); + fe_mul(&mut t1, &z, &temp); + temp.copy_from_slice(&t0); + fe_mul(&mut t0, &temp, &t1); + fe_square(&mut t2, &t0); + temp.copy_from_slice(&t1); + fe_mul(&mut t1, &temp, &t2); + fe_square(&mut t2, &t1); + for _ in 1..5 { + temp.copy_from_slice(&t2); + fe_square(&mut t2, &temp); + } + temp.copy_from_slice(&t1); + fe_mul(&mut t1, &t2, &temp); + fe_square(&mut t2, &t1); + for _ in 1..10 { + temp.copy_from_slice(&t2); + fe_square(&mut t2, &temp); + } + temp.copy_from_slice(&t2); + fe_mul(&mut t2, &temp, &t1); + fe_square(&mut t3, &t2); + for _ in 1..20 { + temp.copy_from_slice(&t3); + fe_square(&mut t3, &temp); + } + temp.copy_from_slice(&t2); + fe_mul(&mut t2, &t3, &temp); + temp.copy_from_slice(&t2); + fe_square(&mut t2, &temp); + for _ in 1..10 { + temp.copy_from_slice(&t2); + fe_square(&mut t2, &temp); + } + temp.copy_from_slice(&t1); + fe_mul(&mut t1, &t2, &temp); + fe_square(&mut t2, &t1); + for _ in 1..50 { + temp.copy_from_slice(&t2); + fe_square(&mut t2, &temp); + } + temp.copy_from_slice(&t2); + fe_mul(&mut t2, &temp, &t1); + fe_square(&mut t3, &t2); + for _ in 1..100 { + temp.copy_from_slice(&t3); + fe_square(&mut t3, &temp); + } + temp.copy_from_slice(&t2); + fe_mul(&mut t2, &t3, &temp); + temp.copy_from_slice(&t2); + fe_square(&mut t2, &temp); + for _ in 1..50 { + temp.copy_from_slice(&t2); + fe_square(&mut t2, &temp); + } + temp.copy_from_slice(&t1); + fe_mul(&mut t1, &t2, &temp); + temp.copy_from_slice(&t1); + fe_square(&mut t1, &temp); + for _ in 1..5 { + temp.copy_from_slice(&t1); + fe_square(&mut t1, &temp); + } + fe_mul(&mut out, &t1, &t0); + out +} + +#[cfg(test)] +#[test] +fn invert() { + let fname = "testdata/ed25519/invert.test"; + run_test(fname.to_string(), 2, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + + assert!(!nega && !negc); + let a = test_from_bytes(&abytes); + let c = test_from_bytes(&cbytes); + let r = fe_invert(&a); + assert_eq!(r, c); + }); +} + +pub fn fe_neg(h: &mut Element, f: &Element) +{ + for i in 0..NUM_ELEMENT_LIMBS { + h[i] = -f[i]; + } +} + +#[cfg(test)] +#[test] +fn negate() { + let fname = "testdata/ed25519/negate.test"; + run_test(fname.to_string(), 2, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + + assert!(!nega && !negc); + let a = test_from_bytes(&abytes); + let c = test_from_bytes(&cbytes); + let mut r = [0; NUM_ELEMENT_LIMBS]; + fe_neg(&mut r, &a); + assert_eq!(r, c); + }); +} + +pub fn fe_cmov(f: &mut Element, g: &Element, bl: bool) +{ + let b = if bl { -1 } else { 0 }; + for i in 0..10 { + let mut x = f[i] ^ g[i]; + x &= b; + f[i] ^= x; + } +} + +#[cfg(test)] +#[test] +fn cmov() { + let fname = "testdata/ed25519/cmov.test"; + run_test(fname.to_string(), 3, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + + assert!(!nega && !negb && !negc); + let a = test_from_bytes(&abytes); + let b = bbytes.len() > 1; + let c = test_from_bytes(&cbytes); + let mut r = [0; NUM_ELEMENT_LIMBS]; + fe_cmov(&mut r, &a, b); + assert_eq!(r, c); + }); +} + +pub fn fe_isnonzero(f: &Element) -> bool +{ + let mut s = [0; 32]; + let mut res = false; + fe_tobytes(&mut s, &f); + for i in 0..32 { + res |= s[i] != 0; + } + res +} + +pub fn fe_isnegative(f: &Element) -> bool +{ + let mut s = [0; 32]; + fe_tobytes(&mut s, &f); + s[0] & 1 == 1 +} + +#[cfg(test)] +#[test] +fn is_tests() { + let fname = "testdata/ed25519/istests.test"; + run_test(fname.to_string(), 3, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negz, zbytes) = case.get("z").unwrap(); + let (negn, nbytes) = case.get("n").unwrap(); + + assert!(!nega && !negz && !negn); + let a = test_from_bytes(&abytes); + println!("a: {:?}", a); + let z = zbytes.len() > 1; + let n = nbytes.len() > 1; + assert_eq!(z, fe_isnonzero(&a)); + assert_eq!(n, fe_isnegative(&a)); + }); +} + +pub fn fe_sq2(h: &mut Element, f: &Element) +{ + let f0 = f[0]; + let f1 = f[1]; + let f2 = f[2]; + let f3 = f[3]; + let f4 = f[4]; + let f5 = f[5]; + let f6 = f[6]; + let f7 = f[7]; + let f8 = f[8]; + let f9 = f[9]; + let f0_2 = 2 * f0; + let f1_2 = 2 * f1; + let f2_2 = 2 * f2; + let f3_2 = 2 * f3; + let f4_2 = 2 * f4; + let f5_2 = 2 * f5; + let f6_2 = 2 * f6; + let f7_2 = 2 * f7; + let f5_38 = 38 * f5; /* 1.959375*2^30 */ + let f6_19 = 19 * f6; /* 1.959375*2^30 */ + let f7_38 = 38 * f7; /* 1.959375*2^30 */ + let f8_19 = 19 * f8; /* 1.959375*2^30 */ + let f9_38 = 38 * f9; /* 1.959375*2^30 */ + let f0f0 = (f0 as i64) * (f0 as i64); + let f0f1_2 = (f0_2 as i64) * (f1 as i64); + let f0f2_2 = (f0_2 as i64) * (f2 as i64); + let f0f3_2 = (f0_2 as i64) * (f3 as i64); + let f0f4_2 = (f0_2 as i64) * (f4 as i64); + let f0f5_2 = (f0_2 as i64) * (f5 as i64); + let f0f6_2 = (f0_2 as i64) * (f6 as i64); + let f0f7_2 = (f0_2 as i64) * (f7 as i64); + let f0f8_2 = (f0_2 as i64) * (f8 as i64); + let f0f9_2 = (f0_2 as i64) * (f9 as i64); + let f1f1_2 = (f1_2 as i64) * (f1 as i64); + let f1f2_2 = (f1_2 as i64) * (f2 as i64); + let f1f3_4 = (f1_2 as i64) * (f3_2 as i64); + let f1f4_2 = (f1_2 as i64) * (f4 as i64); + let f1f5_4 = (f1_2 as i64) * (f5_2 as i64); + let f1f6_2 = (f1_2 as i64) * (f6 as i64); + let f1f7_4 = (f1_2 as i64) * (f7_2 as i64); + let f1f8_2 = (f1_2 as i64) * (f8 as i64); + let f1f9_76 = (f1_2 as i64) * (f9_38 as i64); + let f2f2 = (f2 as i64) * (f2 as i64); + let f2f3_2 = (f2_2 as i64) * (f3 as i64); + let f2f4_2 = (f2_2 as i64) * (f4 as i64); + let f2f5_2 = (f2_2 as i64) * (f5 as i64); + let f2f6_2 = (f2_2 as i64) * (f6 as i64); + let f2f7_2 = (f2_2 as i64) * (f7 as i64); + let f2f8_38 = (f2_2 as i64) * (f8_19 as i64); + let f2f9_38 = (f2 as i64) * (f9_38 as i64); + let f3f3_2 = (f3_2 as i64) * (f3 as i64); + let f3f4_2 = (f3_2 as i64) * (f4 as i64); + let f3f5_4 = (f3_2 as i64) * (f5_2 as i64); + let f3f6_2 = (f3_2 as i64) * (f6 as i64); + let f3f7_76 = (f3_2 as i64) * (f7_38 as i64); + let f3f8_38 = (f3_2 as i64) * (f8_19 as i64); + let f3f9_76 = (f3_2 as i64) * (f9_38 as i64); + let f4f4 = (f4 as i64) * (f4 as i64); + let f4f5_2 = (f4_2 as i64) * (f5 as i64); + let f4f6_38 = (f4_2 as i64) * (f6_19 as i64); + let f4f7_38 = (f4 as i64) * (f7_38 as i64); + let f4f8_38 = (f4_2 as i64) * (f8_19 as i64); + let f4f9_38 = (f4 as i64) * (f9_38 as i64); + let f5f5_38 = (f5 as i64) * (f5_38 as i64); + let f5f6_38 = (f5_2 as i64) * (f6_19 as i64); + let f5f7_76 = (f5_2 as i64) * (f7_38 as i64); + let f5f8_38 = (f5_2 as i64) * (f8_19 as i64); + let f5f9_76 = (f5_2 as i64) * (f9_38 as i64); + let f6f6_19 = (f6 as i64) * (f6_19 as i64); + let f6f7_38 = (f6 as i64) * (f7_38 as i64); + let f6f8_38 = (f6_2 as i64) * (f8_19 as i64); + let f6f9_38 = (f6 as i64) * (f9_38 as i64); + let f7f7_38 = (f7 as i64) * (f7_38 as i64); + let f7f8_38 = (f7_2 as i64) * (f8_19 as i64); + let f7f9_76 = (f7_2 as i64) * (f9_38 as i64); + let f8f8_19 = (f8 as i64) * (f8_19 as i64); + let f8f9_38 = (f8 as i64) * (f9_38 as i64); + let f9f9_38 = (f9 as i64) * (f9_38 as i64); + let mut h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; + let mut h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; + let mut h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; + let mut h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; + let mut h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; + let mut h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; + let mut h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; + let mut h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; + let mut h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; + let mut h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; + let mut carry0; + let carry1; + let carry2; + let carry3; + let mut carry4; + let carry5; + let carry6; + let carry7; + let carry8; + let carry9; + + h0 += h0; + h1 += h1; + h2 += h2; + h3 += h3; + h4 += h4; + h5 += h5; + h6 += h6; + h7 += h7; + h8 += h8; + h9 += h9; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & KTOP_38BITS; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & KTOP_38BITS; + + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & KTOP_39BITS; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & KTOP_39BITS; + + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & KTOP_38BITS; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & KTOP_38BITS; + + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & KTOP_39BITS; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & KTOP_39BITS; + + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & KTOP_38BITS; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & KTOP_38BITS; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & KTOP_39BITS; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & KTOP_38BITS; + + h[0] = h0 as i32; + h[1] = h1 as i32; + h[2] = h2 as i32; + h[3] = h3 as i32; + h[4] = h4 as i32; + h[5] = h5 as i32; + h[6] = h6 as i32; + h[7] = h7 as i32; + h[8] = h8 as i32; + h[9] = h9 as i32; +} + +#[cfg(test)] +#[test] +fn square2() { + let fname = "testdata/ed25519/square2.test"; + run_test(fname.to_string(), 2, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + + assert!(!nega && !negc); + let a = test_from_bytes(&abytes); + let c = test_from_bytes(&cbytes); + let mut r = [0; NUM_ELEMENT_LIMBS]; + fe_sq2(&mut r, &a); + assert_eq!(r, c); + }); +} + +pub fn fe_pow22523(out: &mut Element, z: &Element) { + let mut t0 = [0; NUM_ELEMENT_LIMBS]; + let mut t1 = [0; NUM_ELEMENT_LIMBS]; + let mut t2 = [0; NUM_ELEMENT_LIMBS]; + let mut temp; + + fe_square(&mut t0, &z); + fe_square(&mut t1, &t0); + for _ in 1..2 { + let temp = t1.clone(); + fe_square(&mut t1, &temp); + } + temp = t1.clone(); + fe_mul(&mut t1, &z, &temp); + temp = t0.clone(); + fe_mul(&mut t0, &temp, &t1); + temp = t0.clone(); + fe_square(&mut t0, &temp); + temp = t0.clone(); + fe_mul(&mut t0, &t1, &temp); + fe_square(&mut t1, &t0); + for _ in 1..5 { + temp = t1.clone(); + fe_square(&mut t1, &temp); + } + temp = t0.clone(); + fe_mul(&mut t0, &t1, &temp); + fe_square(&mut t1, &t0); + for _ in 1..10 { + temp = t1.clone(); + fe_square(&mut t1, &temp); + } + temp = t1.clone(); + fe_mul(&mut t1, &temp, &t0); + fe_square(&mut t2, &t1); + for _ in 1..20 { + temp = t2.clone(); + fe_square(&mut t2, &temp); + } + temp = t1.clone(); + fe_mul(&mut t1, &t2, &temp); + temp = t1.clone(); + fe_square(&mut t1, &temp); + for _ in 1..10 { + temp = t1.clone(); + fe_square(&mut t1, &temp); + } + temp = t0.clone(); + fe_mul(&mut t0, &t1, &temp); + fe_square(&mut t1, &t0); + for _ in 1..50 { + temp = t1.clone(); + fe_square(&mut t1, &temp); + } + temp = t1.clone(); + fe_mul(&mut t1, &temp, &t0); + fe_square(&mut t2, &t1); + for _ in 1..100 { + temp = t2.clone(); + fe_square(&mut t2, &temp); + } + temp = t1.clone(); + fe_mul(&mut t1, &t2, &temp); + temp = t1.clone(); + fe_square(&mut t1, &temp); + for _ in 1..50 { + temp = t1.clone(); + fe_square(&mut t1, &temp); + } + temp = t0.clone(); + fe_mul(&mut t0, &t1, &temp); + temp = t0.clone(); + fe_square(&mut t0, &temp); + for _ in 1..2 { + temp = t0.clone(); + fe_square(&mut t0, &temp); + } + fe_mul(out, &t0, &z); +} + +#[cfg(test)] +#[test] +fn pow22523() { + let fname = "testdata/ed25519/pow22523.test"; + run_test(fname.to_string(), 2, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + + assert!(!nega && !negc); + let a = test_from_bytes(&abytes); + let c = test_from_bytes(&cbytes); + let mut r = [0; NUM_ELEMENT_LIMBS]; + fe_pow22523(&mut r, &a); + assert_eq!(r, c); + }); +} + diff --git a/src/ed25519/mod.rs b/src/ed25519/mod.rs new file mode 100644 index 0000000..ed8fe06 --- /dev/null +++ b/src/ed25519/mod.rs @@ -0,0 +1,289 @@ +mod constants; +mod fe; +mod point; + +use digest::Digest; +use rand::Rng; +use sha2::Sha512; +use self::fe::*; +use self::point::*; + +pub struct ED25519KeyPair { + private: [u8; 32], + prefix: [u8; 32], + public: [u8; 32] +} + +impl ED25519KeyPair { + fn blank() -> ED25519KeyPair + { + ED25519KeyPair { + private: [0; 32], + prefix: [0; 32], + public: [0; 32] + } + } + + pub fn generate(rng: &mut G) -> ED25519KeyPair + { + let mut result = ED25519KeyPair::blank(); + + let mut seed: [u8; 32] = [0; 32]; + rng.fill(&mut seed); + let mut hashed = Sha512::digest(&seed); + let (private, prefix) = hashed.split_at_mut(32); + assert_eq!(private.len(), 32); + assert_eq!(prefix.len(), 32); + result.prefix.copy_from_slice(&prefix); + curve25519_scalar_mask(private); + result.private.copy_from_slice(&private); + x25519_public_from_private(&mut result.public, &private); + result + } + + pub fn sign(&self, msg: &[u8]) -> Vec + { + let mut signature_r = [0u8; 32]; + let mut signature_s = [0u8; 32]; + + let mut ctx = Sha512::new(); + ctx.input(&self.prefix); + ctx.input(&msg); + let nonce = digest_scalar(ctx.result().as_slice()); + let mut r = Point::new(); + x25519_ge_scalarmult_base(&mut r, &nonce); + into_encoded_point(&mut signature_r, &r.x, &r.y, &r.z); + let hram_digest = eddsa_digest(&signature_r, &self.public, &msg); + let hram = digest_scalar(&hram_digest); + x25519_sc_muladd(&mut signature_s, &hram, &self.private, &nonce); + let mut result = Vec::with_capacity(64); + result.extend_from_slice(&signature_r); + result.extend_from_slice(&signature_s); + result + } + + pub fn verify(&self, msg: &[u8], sig: &[u8]) -> bool + { + assert_eq!(sig.len(), 64); + + let signature_r = &sig[..32]; + let signature_s = &sig[32..]; + + if signature_s[31] & 0b11100000 != 0 { + return false; + } + + let mut a = from_encoded_point(&self.public); + invert_vartime(&mut a); + let h_digest = eddsa_digest(signature_r, &self.public, msg); + let h = digest_scalar(&h_digest); + let mut r = Point2::new(); + ge_double_scalarmult_vartime(&mut r, &h, &a, &signature_s); + let mut r_check = [0; 32]; + into_encoded_point(&mut r_check, &r.x, &r.y, &r.z); + signature_r == r_check + } +} + +fn eddsa_digest(signature_r: &[u8], public_key: &[u8], msg: &[u8]) -> Vec +{ + let mut ctx = Sha512::new(); + ctx.input(signature_r); + ctx.input(public_key); + ctx.input(msg); + ctx.result().as_slice().to_vec() +} + +fn digest_scalar(digest: &[u8]) -> Vec { + assert_eq!(digest.len(), 512/8); + let mut copy = [0; 512/8]; + copy.copy_from_slice(digest); + x25519_sc_reduce(&mut copy); + copy[..32].to_vec() +} + +fn into_encoded_point(bytes: &mut [u8], x: &Element, y: &Element, z: &Element) +{ + let mut x_over_z = [0; NUM_ELEMENT_LIMBS]; + let mut y_over_z = [0; NUM_ELEMENT_LIMBS]; + assert_eq!(bytes.len(), 32); + + let recip = fe_invert(z); + fe_mul(&mut x_over_z, x, &recip); + fe_mul(&mut y_over_z, y, &recip); + fe_tobytes(bytes, &y_over_z); + let sign_bit = if fe_isnegative(&x_over_z) { 1 } else { 0 }; + + // The preceding computations must execute in constant time, but this + // doesn't need to. + bytes[31] ^= sign_bit << 7; +} + +fn from_encoded_point(encoded: &[u8]) -> Point +{ + let mut point = Point::new(); + x25519_ge_frombytes_vartime(&mut point, encoded); + point +} + +fn invert_vartime(v: &mut Point) +{ + for i in 0..NUM_ELEMENT_LIMBS { + v.x[i] = -v.x[i]; + v.t[i] = -v.t[i]; + } +} + +// use cryptonum::signed::{I256}; +// use cryptonum::unsigned::{BarrettU256,CryptoNum,Decoder,ModExp,U256,U512}; +// use digest::Digest; +// use rand::Rng; +// use rand::distributions::Standard; +// use sha2::Sha512; +// use super::KeyPair; +// +// struct Field { +// x: U256, +// p: U256, +// pu: BarrettU256 +// } +// +// impl Field { +// fn unsafe_new(&self, v: U256) -> Field +// { +// Field{ x: v, p: self.p.clone(), pu: self.pu.clone() } +// } +// +// fn new(&self, v: U256) -> Field +// { +// let v2 = self.pu.reduce(&U512::from(v)); +// Field{ x: v2, p: self.p.clone(), pu: self.pu.clone() } +// } +// +// fn init(x: U256, p: U256) -> Field +// { +// let pu = BarrettU256::new(p.clone()); +// Field{ x, p, pu } +// } +// +// fn add(&self, y: &Field) -> Field +// { +// assert_eq!(self.p, y.p); +// assert_eq!(self.pu, y.pu); +// let v = U512::from(&self.x + &y.x); +// Field { x: self.pu.reduce(&v), p: self.p.clone(), pu: self.pu.clone() } +// } +// +// fn sub(&self, y: &Field) -> Field +// { +// assert_eq!(self.p, y.p); +// assert_eq!(self.pu, y.pu); +// let mut ix = I256::from(&self.x); +// let iy = I256::from(&y.x); +// ix -= iy; +// if ix.is_negative() { +// let mut rx = I256::from(&self.p); +// rx += ix; +// self.new(U256::from(rx)) +// } else { +// self.new(U256::from(ix)) +// } +// } +// +// fn neg(&self) -> Field +// { +// let mut rx = self.p.clone(); +// rx -= &self.x; +// self.new(rx) +// } +// +// fn mul(&self, y: &Field) -> Field +// { +// let v = &self.x * &y.x; +// self.unsafe_new(self.pu.reduce(&v)) +// } +// +// fn inv(&self) -> Field +// { +// let mut pm2 = self.p.clone(); +// pm2 -= U256::from(2u8); +// let res = self.x.modexp(&pm2, &self.pu); +// self.unsafe_new(res) +// } +// +// fn div(&self, y: &Field) -> Field +// { +// self.mul(&y.inv()) +// } +// +// fn sqrt(&self) -> Field +// { +// panic!("field sqrt") +// } +// +// fn is_zero(&self) -> bool +// { +// self.x.is_zero() +// } +// +// fn eq(&self, y: &Field) -> bool +// { +// self.x == y.x +// } +// +// fn neq(&self, y: &Field) -> bool +// { +// self.x != y.x +// } +// +// fn sign(&self) -> Field +// { +// let mut vx = I256::from(&self.x); +// vx %= I256::from(2u64); +// self.unsafe_new(U256::from(vx)) +// } +// } +// +// pub struct ED25519Public { +// } +// +// pub struct ED25519Private { +// key: U256 +// } +// +// pub struct ED25519Pair { +// public: ED25519Public, +// private: ED25519Private +// } +// +// impl KeyPair for ED25519Pair { +// type Public = ED25519Public; +// type Private = ED25519Private; +// +// fn new(pu: ED25519Public, pr: ED25519Private) -> ED25519Pair +// { +// ED25519Pair{ public: pu, private: pr } +// } +// } +// +// impl ED25519Pair { +// pub fn generate(g: &mut G) -> ED25519Pair +// { +// let bytes: Vec = g.sample_iter(&Standard).take(256 / 8).collect(); +// let key = U256::from_bytes(&bytes); +// let private = ED25519Private{ key }; +// let mut hash = Sha512::digest(&bytes); +// assert_eq!(hash.len(), 64); +// let (scalar, prefix) = hash.split_at_mut(32); +// assert_eq!(scalar.len(), 32); +// assert_eq!(prefix.len(), 32); +// // +// scalar[0] &= 0b11111000u8; +// scalar[31] &= 0b01111111u8; +// scalar[31] |= 0b01000000u8; +// // +// +// let public = ED25519Public{}; +// ED25519Pair{ public, private } +// } +// } \ No newline at end of file diff --git a/src/ed25519/point.rs b/src/ed25519/point.rs new file mode 100644 index 0000000..83549e3 --- /dev/null +++ b/src/ed25519/point.rs @@ -0,0 +1,1811 @@ +#[cfg(test)] +use testing::run_test; + +use ed25519::fe::*; +use ed25519::constants::*; + +// This is ge_p3 in the original source code +#[derive(Debug,PartialEq)] +pub struct Point { + pub x: Element, + pub y: Element, + pub z: Element, + pub t: Element +} + +impl Point { + pub fn new() -> Point + { + Point { + x: [0; NUM_ELEMENT_LIMBS], + y: [0; NUM_ELEMENT_LIMBS], + z: [0; NUM_ELEMENT_LIMBS], + t: [0; NUM_ELEMENT_LIMBS] + } + } + + #[cfg(test)] + fn load_test_value(xs: &[u8]) -> Point { + assert!(xs.len() == 160); + Point { + x: test_from_bytes(&xs[0..40]), + y: test_from_bytes(&xs[40..80]), + z: test_from_bytes(&xs[80..120]), + t: test_from_bytes(&xs[120..]) + } + } +} + +const D: Element = [-10913610, 13857413, -15372611, 6949391, 114729, + -8787816, -6275908, -3247719, -18696448, -12055116]; + +const SQRTM1: Element = [-32595792, -7943725, 9377950, 3500415, 12389472, + -272473, -25146209, -2005654, 326686, 11406482]; + +pub fn x25519_ge_frombytes_vartime(h: &mut Point, s: &[u8]) -> bool +{ + let mut u = [0; NUM_ELEMENT_LIMBS]; + let mut v = [0; NUM_ELEMENT_LIMBS]; + let mut v3 = [0; NUM_ELEMENT_LIMBS]; + let mut vxx = [0; NUM_ELEMENT_LIMBS]; + let mut check = [0; NUM_ELEMENT_LIMBS]; + let mut temp; + + fe_frombytes(&mut h.y, s); + fe1(&mut h.z); + fe_square(&mut u, &h.y); + fe_mul(&mut v, &u, &D); + temp = u.clone(); + fe_sub(&mut u, &temp, &h.z); /* u = y^2-1 */ + temp = v.clone(); + fe_add(&mut v, &temp, &h.z); /* v = dy^2+1 */ + + fe_square(&mut v3, &v); + temp = v3.clone(); + fe_mul(&mut v3, &temp, &v); /* v3 = v^3 */ + fe_square(&mut h.x, &v3); + temp = h.x.clone(); + fe_mul(&mut h.x, &temp, &v); + temp = h.x.clone(); + fe_mul(&mut h.x, &temp, &u); /* x = uv^7 */ + + temp = h.x.clone(); + fe_pow22523(&mut h.x, &temp); /* x = (uv^7)^((q-5)/8) */ + temp = h.x.clone(); + fe_mul(&mut h.x, &temp, &v3); + temp = h.x.clone(); + fe_mul(&mut h.x, &temp, &u); /* x = uv^3(uv^7)^((q-5)/8) */ + + fe_square(&mut vxx, &h.x); + temp = vxx.clone(); + fe_mul(&mut vxx, &temp, &v); + fe_sub(&mut check, &vxx, &u); /* vx^2-u */ + if fe_isnonzero(&check) { + fe_add(&mut check, &vxx, &u); /* vx^2+u */ + if fe_isnonzero(&check) { + return false; + } + temp = h.x.clone(); + fe_mul(&mut h.x, &temp, &SQRTM1); + } + + if fe_isnegative(&h.x) != ((s[31] >> 7) == 1) { + temp = h.x.clone(); + fe_neg(&mut h.x, &temp); + } + + fe_mul(&mut h.t, &h.x, &h.y); + return true; +} + +#[cfg(test)] +#[test] +fn from_bytes_vartime() { + let fname = "testdata/ed25519/fbv.test"; + run_test(fname.to_string(), 2, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + + assert!(!nega && !negc); + let target = Point::load_test_value(&cbytes); + let mut mine = Point::new(); + x25519_ge_frombytes_vartime(&mut mine, &abytes); + assert_eq!(target, mine); + }); +} + +fn ge_p3_0(h: &mut Point) +{ + fe0(&mut h.x); + fe1(&mut h.y); + fe1(&mut h.z); + fe0(&mut h.t); +} + +#[derive(Debug,PartialEq)] +pub struct Point2 { + pub x: Element, + pub y: Element, + pub z: Element, +} + +impl Point2 { + pub fn new() -> Point2 + { + Point2 { + x: [0; NUM_ELEMENT_LIMBS], + y: [0; NUM_ELEMENT_LIMBS], + z: [0; NUM_ELEMENT_LIMBS] + } + } + + #[cfg(test)] + fn load_test_value(xs: &[u8]) -> Point2 { + assert!(xs.len() == 120); + Point2 { + x: test_from_bytes(&xs[0..40]), + y: test_from_bytes(&xs[40..80]), + z: test_from_bytes(&xs[80..120]), + } + } +} + +fn ge_p2_0(h: &mut Point2) +{ + fe0(&mut h.x); + fe1(&mut h.y); + fe1(&mut h.z); +} + +fn ge_p3_to_p2(r: &mut Point2, p: &Point) +{ + r.x.copy_from_slice(&p.x); + r.y.copy_from_slice(&p.y); + r.z.copy_from_slice(&p.z); +} + +#[derive(Debug,PartialEq)] +struct PointP1P1 { + x: Element, + y: Element, + z: Element, + t: Element +} + +impl PointP1P1 { + fn new() -> PointP1P1 + { + PointP1P1 { + x: [0; NUM_ELEMENT_LIMBS], + y: [0; NUM_ELEMENT_LIMBS], + z: [0; NUM_ELEMENT_LIMBS], + t: [0; NUM_ELEMENT_LIMBS], + } + } + + #[cfg(test)] + fn load_test_value(xs: &[u8]) -> PointP1P1 { + assert!(xs.len() == 160); + PointP1P1 { + x: test_from_bytes(&xs[0..40]), + y: test_from_bytes(&xs[40..80]), + z: test_from_bytes(&xs[80..120]), + t: test_from_bytes(&xs[120..]) + } + } +} + +#[derive(Debug,PartialEq)] +struct Cached { + yplusx: Element, + yminusx: Element, + z: Element, + t2d: Element +} + +impl Cached +{ + fn new() -> Cached + { + Cached { + yplusx: [0; NUM_ELEMENT_LIMBS], + yminusx: [0; NUM_ELEMENT_LIMBS], + z: [0; NUM_ELEMENT_LIMBS], + t2d: [0; NUM_ELEMENT_LIMBS] + } + } + + #[cfg(test)] + fn load_test_value(xs: &[u8]) -> Cached { + assert!(xs.len() == 160); + Cached { + yplusx: test_from_bytes(&xs[0..40]), + yminusx: test_from_bytes(&xs[40..80]), + z: test_from_bytes(&xs[80..120]), + t2d: test_from_bytes(&xs[120..]) + } + } +} + +const D2: Element = [-21827239, -5839606, -30745221, 13898782, 229458, + 15978800, -12551817, -6495438, 29715968, 9444199]; + +fn x25519_ge_p3_to_cached(r: &mut Cached, p: &Point) +{ + fe_add(&mut r.yplusx, &p.y, &p.x); + fe_sub(&mut r.yminusx, &p.y, &p.x); + r.z.copy_from_slice(&p.z); + fe_mul(&mut r.t2d, &p.t, &D2); +} + +/* r = p */ +fn x25519_ge_p1p1_to_p2(r: &mut Point2, p: &PointP1P1) +{ + fe_mul(&mut r.x, &p.x, &p.t); + fe_mul(&mut r.y, &p.y, &p.z); + fe_mul(&mut r.z, &p.z, &p.t); +} + +/* r = p */ +fn x25519_ge_p1p1_to_p3(r: &mut Point, p: &PointP1P1) +{ + fe_mul(&mut r.x, &p.x, &p.t); + fe_mul(&mut r.y, &p.y, &p.z); + fe_mul(&mut r.z, &p.z, &p.t); + fe_mul(&mut r.t, &p.x, &p.y); +} + +#[cfg(test)] +#[test] +fn conversion() { + let fname = "testdata/ed25519/conversion.test"; + run_test(fname.to_string(), 6, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + let (negt, tbytes) = case.get("t").unwrap(); + let (nego, obytes) = case.get("o").unwrap(); + let (negd, dbytes) = case.get("d").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + + let a = Point::load_test_value(&abytes); + let c = Cached::load_test_value(&cbytes); + let t = Point2::load_test_value(&tbytes); + let o = PointP1P1::load_test_value(&obytes); + let d = Point2::load_test_value(&dbytes); + let b = Point::load_test_value(&bbytes); + + assert!(!nega && !negc && !negt && !nego && !negd && !negb); + + let mut myc = Cached::new(); + x25519_ge_p3_to_cached(&mut myc, &a); + assert_eq!(myc, c); + + let mut myt = Point2::new(); + ge_p3_to_p2(&mut myt, &a); + assert_eq!(myt, t); + + let mut myo = PointP1P1::new(); + ge_p3_dbl(&mut myo, &a); + assert_eq!(myo, o); + + let mut myd = Point2::new(); + x25519_ge_p1p1_to_p2(&mut myd, &o); + assert_eq!(myd, d); + + let mut myb = Point::new(); + x25519_ge_p1p1_to_p3(&mut myb, &o); + assert_eq!(myb, b); + }); +} + +/* r = 2 * p */ +fn ge_p2_dbl(r: &mut PointP1P1, p: &Point2) +{ + let mut t0 = [0; NUM_ELEMENT_LIMBS]; + + fe_square(&mut r.x, &p.x); + fe_square(&mut r.z, &p.y); + fe_sq2(&mut r.t, &p.z); + fe_add(&mut r.y, &p.x, &p.y); + fe_square(&mut t0, &r.y); + fe_add(&mut r.y, &r.z, &r.x); + let mut temp = r.z.clone(); + fe_sub(&mut r.z, &temp, &r.x); + fe_sub(&mut r.x, &t0, &r.y); + temp = r.t.clone(); + fe_sub(&mut r.t, &temp, &r.z); +} + +/* r = 2 * p */ +fn ge_p3_dbl(r: &mut PointP1P1, p: &Point) +{ + let mut q = Point2::new(); + ge_p3_to_p2(&mut q, p); + ge_p2_dbl(r, &q); +} + +#[cfg(test)] +#[test] +fn double() { + let fname = "testdata/ed25519/pt_double.test"; + run_test(fname.to_string(), 4, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + let (negd, dbytes) = case.get("d").unwrap(); + + assert!(!nega && !negb && !negc && !negd); + let a = Point::load_test_value(abytes); + let b = PointP1P1::load_test_value(bbytes); + let c = Point2::load_test_value(cbytes); + let d = PointP1P1::load_test_value(dbytes); + + let mut mine = PointP1P1::new(); + ge_p3_dbl(&mut mine, &a); + assert_eq!(mine, b); + ge_p2_dbl(&mut mine, &c); + assert_eq!(mine, d); + }); +} + +/* r = p + q */ +fn ge_madd(r: &mut PointP1P1, p: &Point, q: &Precomp) +{ + let mut t0 = [0; NUM_ELEMENT_LIMBS]; + let mut temp; + + fe_add(&mut r.x, &p.y, &p.x); + fe_sub(&mut r.y, &p.y, &p.x); + fe_mul(&mut r.z, &r.x, &q.yplusx); + temp = r.y.clone(); + fe_mul(&mut r.y, &temp, &q.yminusx); + fe_mul(&mut r.t, &q.xy2d, &p.t); + fe_add(&mut t0, &p.z, &p.z); + fe_sub(&mut r.x, &r.z, &r.y); + temp = r.y.clone(); + fe_add(&mut r.y, &r.z, &temp); + fe_add(&mut r.z, &t0, &r.t); + temp = r.t.clone(); + fe_sub(&mut r.t, &t0, &temp); +} + +/* r = p - q */ +fn ge_msub(r: &mut PointP1P1, p: &Point, q: &Precomp) +{ + let mut t0 = [0; NUM_ELEMENT_LIMBS]; + let mut temp; + + fe_add(&mut r.x, &p.y, &p.x); + fe_sub(&mut r.y, &p.y, &p.x); + fe_mul(&mut r.z, &r.x, &q.yminusx); + temp = r.y.clone(); + fe_mul(&mut r.y, &temp, &q.yplusx); + fe_mul(&mut r.t, &q.xy2d, &p.t); + fe_add(&mut t0, &p.z, &p.z); + fe_sub(&mut r.x, &r.z, &r.y); + temp = r.y.clone(); + fe_add(&mut r.y, &r.z, &temp); + fe_sub(&mut r.z, &t0, &r.t); + temp = r.t.clone(); + fe_add(&mut r.t, &t0, &temp); +} + +#[cfg(test)] +#[test] +fn maddsub() { + let fname = "testdata/ed25519/maddsub.test"; + run_test(fname.to_string(), 4, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + let (negd, dbytes) = case.get("d").unwrap(); + + assert!(!nega && !negb && !negc && !negd); + let a = Point::load_test_value(abytes); + let b = PointP1P1::load_test_value(bbytes); + let c = Precomp::load_test_value(cbytes); + let d = PointP1P1::load_test_value(dbytes); + + let mut mine = PointP1P1::new(); + ge_madd(&mut mine, &a, &c); + assert_eq!(mine, b); + ge_msub(&mut mine, &a, &c); + assert_eq!(mine, d); + }); +} + +/* r = p + q */ +fn x25519_ge_add(r: &mut PointP1P1, p: &Point, q: &Cached) +{ + let mut t0 = [0; NUM_ELEMENT_LIMBS]; + let mut temp; + + fe_add(&mut r.x, &p.y, &p.x); + fe_sub(&mut r.y, &p.y, &p.x); + fe_mul(&mut r.z, &r.x, &q.yplusx); + temp = r.y.clone(); + fe_mul(&mut r.y, &temp, &q.yminusx); + fe_mul(&mut r.t, &q.t2d, &p.t); + fe_mul(&mut r.x, &p.z, &q.z); + fe_add(&mut t0, &r.x, &r.x); + fe_sub(&mut r.x, &r.z, &r.y); + temp = r.y.clone(); + fe_add(&mut r.y, &r.z, &temp); + fe_add(&mut r.z, &t0, &r.t); + temp = r.t.clone(); + fe_sub(&mut r.t, &t0, &temp); +} + +/* r = p - q */ +fn x25519_ge_sub(r: &mut PointP1P1, p: &Point, q: &Cached) +{ + let mut t0 = [0; NUM_ELEMENT_LIMBS]; + let mut temp; + + fe_add(&mut r.x, &p.y, &p.x); + fe_sub(&mut r.y, &p.y, &p.x); + fe_mul(&mut r.z, &r.x, &q.yminusx); + temp = r.y.clone(); + fe_mul(&mut r.y, &temp, &q.yplusx); + fe_mul(&mut r.t, &q.t2d, &p.t); + fe_mul(&mut r.x, &p.z, &q.z); + fe_add(&mut t0, &r.x, &r.x); + fe_sub(&mut r.x, &r.z, &r.y); + temp = r.y.clone(); + fe_add(&mut r.y, &r.z, &temp); + fe_sub(&mut r.z, &t0, &r.t); + temp = r.t.clone(); + fe_add(&mut r.t, &t0, &temp); +} + +#[cfg(test)] +#[test] +fn addsub() { + let fname = "testdata/ed25519/ptaddsub.test"; + run_test(fname.to_string(), 4, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + let (negd, dbytes) = case.get("d").unwrap(); + + assert!(!nega && !negb && !negc && !negd); + let a = Point::load_test_value(abytes); + let b = PointP1P1::load_test_value(bbytes); + let c = Cached::load_test_value(cbytes); + let d = PointP1P1::load_test_value(dbytes); + + let mut mine = PointP1P1::new(); + x25519_ge_add(&mut mine, &a, &c); + assert_eq!(mine, b); + x25519_ge_sub(&mut mine, &a, &c); + assert_eq!(mine, d); + }); +} + +fn equal(b: i8, c: i8) -> bool +{ + let ub = b; + let uc = c; + let x = ub ^ uc; /* 0: yes; 1..255: no */ + (x == 0) +} + +fn cmov(t: &mut Precomp, u: &Precomp, b: bool) +{ + fe_cmov(&mut t.yplusx, &u.yplusx, b); + fe_cmov(&mut t.yminusx, &u.yminusx, b); + fe_cmov(&mut t.xy2d, &u.xy2d, b); +} + +fn negative(b: i8) -> u8 +{ + let mut x = b as u32; + x >>= 31; /* 1: yes; 0: no */ + x as u8 +} + +fn table_select(t: &mut Precomp, pos: i32, b: i8) +{ + let mut minust = Precomp::new(); + let bnegative = negative(b); + let babs = b - (((-(bnegative as i8)) & b) << 1); + + ge_precomp_0(t); + cmov(t, &K25519_PRECOMP[pos as usize][0], equal(babs, 1)); + cmov(t, &K25519_PRECOMP[pos as usize][1], equal(babs, 2)); + cmov(t, &K25519_PRECOMP[pos as usize][2], equal(babs, 3)); + cmov(t, &K25519_PRECOMP[pos as usize][3], equal(babs, 4)); + cmov(t, &K25519_PRECOMP[pos as usize][4], equal(babs, 5)); + cmov(t, &K25519_PRECOMP[pos as usize][5], equal(babs, 6)); + cmov(t, &K25519_PRECOMP[pos as usize][6], equal(babs, 7)); + cmov(t, &K25519_PRECOMP[pos as usize][7], equal(babs, 8)); + minust.yplusx.copy_from_slice(&t.yminusx); + minust.yminusx.copy_from_slice(&t.yplusx); + fe_neg(&mut minust.xy2d, &t.xy2d); + cmov(t, &minust, bnegative != 0); +} + +/* h = a * B + * where a = a[0]+256*a[1]+...+256^31 a[31] + * B is the Ed25519 base point (x,4/5) with x positive. + * + * Preconditions: + * a[31] <= 127 */ +pub fn x25519_ge_scalarmult_base(h: &mut Point, a: &[u8]) +{ + let mut e: [i8; 64] = [0; 64]; + for i in 0..32 { + e[2 * i + 0] = ((a[i] >> 0) & 15) as i8; + e[2 * i + 1] = ((a[i] >> 4) & 15) as i8; + } + /* each e[i] is between 0 and 15 */ + /* e[63] is between 0 and 7 */ + + let mut carry = 0; + for i in 0..63 { + e[i] += carry; + carry = e[i] + 8; + carry >>= 4; + e[i] -= carry << 4; + } + e[63] += carry; + /* each e[i] is between -8 and 8 */ + + let mut r = PointP1P1::new(); + let mut s = Point2::new(); + let mut t = Precomp::new(); + + ge_p3_0(h); + for i in &[1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63] { + table_select(&mut t, *i / 2, e[*i as usize]); + ge_madd(&mut r, &h, &t); + x25519_ge_p1p1_to_p3(h, &r); + } + + ge_p3_dbl(&mut r, &h); + x25519_ge_p1p1_to_p2(&mut s, &r); + ge_p2_dbl(&mut r, &s); + x25519_ge_p1p1_to_p2(&mut s, &r); + ge_p2_dbl(&mut r, &s); + x25519_ge_p1p1_to_p2(&mut s, &r); + ge_p2_dbl(&mut r, &s); + x25519_ge_p1p1_to_p3(h, &r); + + for i in &[0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62] { + table_select(&mut t, *i / 2, e[*i as usize]); + ge_madd(&mut r, &h, &t); + x25519_ge_p1p1_to_p3(h, &r); + } +} + +#[cfg(test)] +#[test] +fn scalarmult_base() { + let fname = "testdata/ed25519/scalar_mult.test"; + run_test(fname.to_string(), 2, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + + assert!(!nega && !negb); + let b = Point::load_test_value(bbytes); + let mut mine = Point::new(); + x25519_ge_scalarmult_base(&mut mine, abytes); + assert_eq!(mine, b); + }); +} + +fn slide(r: &mut [i8], a: &[u8]) +{ + for i in 0..256 { + r[i] = (1 & (a[i >> 3] >> (i & 7))) as i8; + } + + for i in 0..256 { + if r[i] != 0 { + let mut b = 1; + while (b <= 6) && ((i + b) < 256) { + if r[i + b] != 0 { + if r[i] + (r[i + b] << b) <= 15 { + r[i] += r[i + b] << b; + r[i + b] = 0; + } else if r[i] - (r[i + b] << b) >= -15 { + r[i] -= r[i + b] << b; + for k in (i+b)..256 { + if r[k] == 0 { + r[k] = 1; + break; + } + r[k] = 0; + } + } else { + break; + } + } + b += 1; + } + } + } +} + +#[cfg(test)] +#[test] +fn helper_slide() { + let fname = "testdata/ed25519/slide.test"; + run_test(fname.to_string(), 2, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + + assert!(!nega && !negb); + let mut mine = [0; 256]; + slide(&mut mine, &abytes); + for i in 0..256 { + assert_eq!(mine[i], bbytes[i] as i8); + } + }); +} + +/* r = a * A + b * B + * where a = a[0]+256*a[1]+...+256^31 a[31]. + * and b = b[0]+256*b[1]+...+256^31 b[31]. + * B is the Ed25519 base point (x,4/5) with x positive. */ +#[allow(non_snake_case)] +pub fn ge_double_scalarmult_vartime(r: &mut Point2, a: &[u8], A: &Point, b: &[u8]) +{ + let mut aslide: [i8; 256] = [0; 256]; + let mut bslide: [i8; 256] = [0; 256]; + #[allow(non_snake_case)] + let mut Ai: [Cached; 8] = [Cached::new(), Cached::new(), Cached::new(), Cached::new(), + Cached::new(), Cached::new(), Cached::new(), Cached::new()]; + let mut t = PointP1P1::new(); + let mut u = Point::new(); + #[allow(non_snake_case)] + let mut A2 = Point::new(); + + slide(&mut aslide, &a); + slide(&mut bslide, &b); + + x25519_ge_p3_to_cached(&mut Ai[0], &A); + ge_p3_dbl(&mut t, &A); + x25519_ge_p1p1_to_p3(&mut A2, &t); + x25519_ge_add(&mut t, &A2, &Ai[0]); + x25519_ge_p1p1_to_p3(&mut u, &t); + x25519_ge_p3_to_cached(&mut Ai[1], &u); + x25519_ge_add(&mut t, &A2, &Ai[1]); + x25519_ge_p1p1_to_p3(&mut u, &t); + x25519_ge_p3_to_cached(&mut Ai[2], &u); + x25519_ge_add(&mut t, &A2, &Ai[2]); + x25519_ge_p1p1_to_p3(&mut u, &t); + x25519_ge_p3_to_cached(&mut Ai[3], &u); + x25519_ge_add(&mut t, &A2, &Ai[3]); + x25519_ge_p1p1_to_p3(&mut u, &t); + x25519_ge_p3_to_cached(&mut Ai[4], &u); + x25519_ge_add(&mut t, &A2, &Ai[4]); + x25519_ge_p1p1_to_p3(&mut u, &t); + x25519_ge_p3_to_cached(&mut Ai[5], &u); + x25519_ge_add(&mut t, &A2, &Ai[5]); + x25519_ge_p1p1_to_p3(&mut u, &t); + x25519_ge_p3_to_cached(&mut Ai[6], &u); + x25519_ge_add(&mut t, &A2, &Ai[6]); + x25519_ge_p1p1_to_p3(&mut u, &t); + x25519_ge_p3_to_cached(&mut Ai[7], &u); + + ge_p2_0(r); + + let mut i: i32 = 255; + loop { + if (aslide[i as usize] != 0) || (bslide[i as usize] != 0) { + break; + } + i -= 1; + if i < 0 { + break; + } + } + + while i >= 0 { + ge_p2_dbl(&mut t, r); + + if aslide[i as usize] > 0 { + x25519_ge_p1p1_to_p3(&mut u, &t); + let idx = (aslide[i as usize] / 2) as usize; + x25519_ge_add(&mut t, &u, &Ai[idx]); + } else if aslide[i as usize] < 0 { + x25519_ge_p1p1_to_p3(&mut u, &t); + let idx = ((-aslide[i as usize]) / 2) as usize; + x25519_ge_sub(&mut t, &u, &Ai[idx]); + } + + if bslide[i as usize] > 0 { + x25519_ge_p1p1_to_p3(&mut u, &t); + let idx = (bslide[i as usize] / 2) as usize; + ge_madd(&mut t, &u, &BI[idx]); + } else if bslide[i as usize] < 0 { + x25519_ge_p1p1_to_p3(&mut u, &t); + let idx = ((-bslide[i as usize]) / 2) as usize; + ge_msub(&mut t, &u, &BI[idx]); + } + + x25519_ge_p1p1_to_p2(r, &t); + i -= 1; + } +} + +#[cfg(test)] +#[test] +fn double_scalarmult() { + let fname = "testdata/ed25519/scalar_mult_gen.test"; + run_test(fname.to_string(), 4, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + let (negd, dbytes) = case.get("d").unwrap(); + + assert!(!nega && !negb && !negc && !negd); + let b = Point::load_test_value(bbytes); + let d = Point2::load_test_value(dbytes); + let mut mine = Point2::new(); + ge_double_scalarmult_vartime(&mut mine, &abytes, &b, &cbytes); + assert_eq!(mine, d); + }); +} + +/* The set of scalars is \Z/l + * where l = 2^252 + 27742317777372353535851937790883648493. */ + +/* Input: + * s[0]+256*s[1]+...+256^63*s[63] = s + * + * Output: + * s[0]+256*s[1]+...+256^31*s[31] = s mod l + * where l = 2^252 + 27742317777372353535851937790883648493. + * Overwrites s in place. */ +pub fn x25519_sc_reduce(s: &mut [u8]) +{ + let mut s0 : i64 = 2097151 & load3(s) as i64; + let mut s1 : i64 = 2097151 & (load4(&s[2..]) >> 5) as i64; + let mut s2 : i64 = 2097151 & (load3(&s[5..]) >> 2) as i64; + let mut s3 : i64 = 2097151 & (load4(&s[7..]) >> 7) as i64; + let mut s4 : i64 = 2097151 & (load4(&s[10..]) >> 4) as i64; + let mut s5 : i64 = 2097151 & (load3(&s[13..]) >> 1) as i64; + let mut s6 : i64 = 2097151 & (load4(&s[15..]) >> 6) as i64; + let mut s7 : i64 = 2097151 & (load3(&s[18..]) >> 3) as i64; + let mut s8 : i64 = 2097151 & load3(&s[21..]) as i64; + let mut s9 : i64 = 2097151 & (load4(&s[23..]) >> 5) as i64; + let mut s10 : i64 = 2097151 & (load3(&s[26..]) >> 2) as i64; + let mut s11 : i64 = 2097151 & (load4(&s[28..]) >> 7) as i64; + let mut s12 : i64 = 2097151 & (load4(&s[31..]) >> 4) as i64; + let mut s13 : i64 = 2097151 & (load3(&s[34..]) >> 1) as i64; + let mut s14 : i64 = 2097151 & (load4(&s[36..]) >> 6) as i64; + let mut s15 : i64 = 2097151 & (load3(&s[39..]) >> 3) as i64; + let mut s16 : i64 = 2097151 & load3(&s[42..]) as i64; + let mut s17 : i64 = 2097151 & (load4(&s[44..]) >> 5) as i64; + let s18 : i64 = 2097151 & (load3(&s[47..]) >> 2) as i64; + let s19 : i64 = 2097151 & (load4(&s[49..]) >> 7) as i64; + let s20 : i64 = 2097151 & (load4(&s[52..]) >> 4) as i64; + let s21 : i64 = 2097151 & (load3(&s[55..]) >> 1) as i64; + let s22 : i64 = 2097151 & (load4(&s[57..]) >> 6) as i64; + let s23 : i64 = (load4(&s[60..]) >> 3) as i64 as i64; + let mut carry0 : i64; + let mut carry1 : i64; + let mut carry2 : i64; + let mut carry3 : i64; + let mut carry4 : i64; + let mut carry5 : i64; + let mut carry6 : i64; + let mut carry7 : i64; + let mut carry8 : i64; + let mut carry9 : i64; + let mut carry10 : i64; + let mut carry11 : i64; + let carry12 : i64; + let carry13 : i64; + let carry14 : i64; + let carry15 : i64; + let carry16 : i64; + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + //s23 = 0; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + //s22 = 0; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + //s21 = 0; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + //s20 = 0; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + //s19 = 0; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + //s18 = 0; + + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 << 21; + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 << 21; + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 << 21; + + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 << 21; + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 << 21; + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + //s17 = 0; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + //s16 = 0; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + //s15 = 0; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + //s14 = 0; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + //s13 = 0; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (1 << 20)) >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry11 = s11 >> 21; + s12 += carry11; + s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + //s12 = 0; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 << 21; + + s[0] = (s0 >> 0) as u8; + s[1] = (s0 >> 8) as u8; + s[2] = ((s0 >> 16) | (s1 << 5)) as u8; + s[3] = (s1 >> 3) as u8; + s[4] = (s1 >> 11) as u8; + s[5] = ((s1 >> 19) | (s2 << 2)) as u8; + s[6] = (s2 >> 6) as u8; + s[7] = ((s2 >> 14) | (s3 << 7)) as u8; + s[8] = (s3 >> 1) as u8; + s[9] = (s3 >> 9) as u8; + s[10] = ((s3 >> 17) | (s4 << 4)) as u8; + s[11] = (s4 >> 4) as u8; + s[12] = (s4 >> 12) as u8; + s[13] = ((s4 >> 20) | (s5 << 1)) as u8; + s[14] = (s5 >> 7) as u8; + s[15] = ((s5 >> 15) | (s6 << 6)) as u8; + s[16] = (s6 >> 2) as u8; + s[17] = (s6 >> 10) as u8; + s[18] = ((s6 >> 18) | (s7 << 3)) as u8; + s[19] = (s7 >> 5) as u8; + s[20] = (s7 >> 13) as u8; + s[21] = (s8 >> 0) as u8; + s[22] = (s8 >> 8) as u8; + s[23] = ((s8 >> 16) | (s9 << 5)) as u8; + s[24] = (s9 >> 3) as u8; + s[25] = (s9 >> 11) as u8; + s[26] = ((s9 >> 19) | (s10 << 2)) as u8; + s[27] = (s10 >> 6) as u8; + s[28] = ((s10 >> 14) | (s11 << 7)) as u8; + s[29] = (s11 >> 1) as u8; + s[30] = (s11 >> 9) as u8; + s[31] = (s11 >> 17) as u8; +} + +#[cfg(test)] +#[test] +fn reduce() { + let fname = "testdata/ed25519/reduce.test"; + run_test(fname.to_string(), 2, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + + assert!(!nega && !negb); + assert_eq!(abytes.len(), 64); + assert_eq!(bbytes.len(), 32); + let mut copy = abytes.clone(); + x25519_sc_reduce(&mut copy); + assert_eq!(©[0..32], &bbytes[0..]); + }); +} + +/* Input: + * a[0]+256*a[1]+...+256^31*a[31] = a + * b[0]+256*b[1]+...+256^31*b[31] = b + * c[0]+256*c[1]+...+256^31*c[31] = c + * + * Output: + * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l + * where l = 2^252 + 27742317777372353535851937790883648493. */ +pub fn x25519_sc_muladd(s: &mut [u8], a: &[u8], b: &[u8], c: &[u8]) +{ + let a0 : i64 = 2097151 & load3(a) as i64; + let a1 : i64 = 2097151 & (load4(&a[2..]) >> 5) as i64; + let a2 : i64 = 2097151 & (load3(&a[5..]) >> 2) as i64; + let a3 : i64 = 2097151 & (load4(&a[7..]) >> 7) as i64; + let a4 : i64 = 2097151 & (load4(&a[10..]) >> 4) as i64; + let a5 : i64 = 2097151 & (load3(&a[13..]) >> 1) as i64; + let a6 : i64 = 2097151 & (load4(&a[15..]) >> 6) as i64; + let a7 : i64 = 2097151 & (load3(&a[18..]) >> 3) as i64; + let a8 : i64 = 2097151 & load3(&a[21..]) as i64; + let a9 : i64 = 2097151 & (load4(&a[23..]) >> 5) as i64; + let a10 : i64 = 2097151 & (load3(&a[26..]) >> 2) as i64; + let a11 : i64 = (load4(&a[28..]) >> 7) as i64; + let b0 : i64 = 2097151 & load3(b) as i64; + let b1 : i64 = 2097151 & (load4(&b[2..]) >> 5) as i64; + let b2 : i64 = 2097151 & (load3(&b[5..]) >> 2) as i64; + let b3 : i64 = 2097151 & (load4(&b[7..]) >> 7) as i64; + let b4 : i64 = 2097151 & (load4(&b[10..]) >> 4) as i64; + let b5 : i64 = 2097151 & (load3(&b[13..]) >> 1) as i64; + let b6 : i64 = 2097151 & (load4(&b[15..]) >> 6) as i64; + let b7 : i64 = 2097151 & (load3(&b[18..]) >> 3) as i64; + let b8 : i64 = 2097151 & load3(&b[21..]) as i64; + let b9 : i64 = 2097151 & (load4(&b[23..]) >> 5) as i64; + let b10 : i64 = 2097151 & (load3(&b[26..]) >> 2) as i64; + let b11 : i64 = (load4(&b[28..]) >> 7) as i64; + let c0 : i64 = 2097151 & load3(c) as i64; + let c1 : i64 = 2097151 & (load4(&c[2..]) >> 5) as i64; + let c2 : i64 = 2097151 & (load3(&c[5..]) >> 2) as i64; + let c3 : i64 = 2097151 & (load4(&c[7..]) >> 7) as i64; + let c4 : i64 = 2097151 & (load4(&c[10..]) >> 4) as i64; + let c5 : i64 = 2097151 & (load3(&c[13..]) >> 1) as i64; + let c6 : i64 = 2097151 & (load4(&c[15..]) >> 6) as i64; + let c7 : i64 = 2097151 & (load3(&c[18..]) >> 3) as i64; + let c8 : i64 = 2097151 & load3(&c[21..]) as i64; + let c9 : i64 = 2097151 & (load4(&c[23..]) >> 5) as i64; + let c10 : i64 = 2097151 & (load3(&c[26..]) >> 2) as i64; + let c11 : i64 = (load4(&c[28..]) >> 7) as i64; + let mut s0 : i64; + let mut s1 : i64; + let mut s2 : i64; + let mut s3 : i64; + let mut s4 : i64; + let mut s5 : i64; + let mut s6 : i64; + let mut s7 : i64; + let mut s8 : i64; + let mut s9 : i64; + let mut s10 : i64; + let mut s11 : i64; + let mut s12 : i64; + let mut s13 : i64; + let mut s14 : i64; + let mut s15 : i64; + let mut s16 : i64; + let mut s17 : i64; + let mut s18 : i64; + let mut s19 : i64; + let mut s20 : i64; + let mut s21 : i64; + let mut s22 : i64; + let mut s23 : i64; + let mut carry0 : i64; + let mut carry1 : i64; + let mut carry2 : i64; + let mut carry3 : i64; + let mut carry4 : i64; + let mut carry5 : i64; + let mut carry6 : i64; + let mut carry7 : i64; + let mut carry8 : i64; + let mut carry9 : i64; + let mut carry10 : i64; + let mut carry11 : i64; + let mut carry12 : i64; + let mut carry13 : i64; + let mut carry14 : i64; + let mut carry15 : i64; + let mut carry16 : i64; + let carry17 : i64; + let carry18 : i64; + let carry19 : i64; + let carry20 : i64; + let carry21 : i64; + let carry22 : i64; + + s0 = c0 + a0 * b0; + s1 = c1 + a0 * b1 + a1 * b0; + s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; + s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; + s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; + s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; + s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; + s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + + a6 * b1 + a7 * b0; + s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + + a6 * b2 + a7 * b1 + a8 * b0; + s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; + s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; + s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; + s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; + s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + + a9 * b4 + a10 * b3 + a11 * b2; + s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + + a10 * b4 + a11 * b3; + s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + + a11 * b4; + s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; + s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; + s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; + s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; + s20 = a9 * b11 + a10 * b10 + a11 * b9; + s21 = a10 * b11 + a11 * b10; + s22 = a11 * b11; + s23 = 0; + + carry0 = (s0 + (1 << 20)) >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 << 21; + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 << 21; + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 << 21; + carry18 = (s18 + (1 << 20)) >> 21; + s19 += carry18; + s18 -= carry18 << 21; + carry20 = (s20 + (1 << 20)) >> 21; + s21 += carry20; + s20 -= carry20 << 21; + carry22 = (s22 + (1 << 20)) >> 21; + s23 += carry22; + s22 -= carry22 << 21; + + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 << 21; + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 << 21; + carry17 = (s17 + (1 << 20)) >> 21; + s18 += carry17; + s17 -= carry17 << 21; + carry19 = (s19 + (1 << 20)) >> 21; + s20 += carry19; + s19 -= carry19 << 21; + carry21 = (s21 + (1 << 20)) >> 21; + s22 += carry21; + s21 -= carry21 << 21; + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + //s23 = 0; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + //s22 = 0; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + //s21 = 0; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + //s20 = 0; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + //s19 = 0; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + //s18 = 0; + + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 << 21; + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 << 21; + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 << 21; + + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 << 21; + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 << 21; + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + //s17 = 0; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + //s16 = 0; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + //s15 = 0; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + //s14 = 0; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + //s13 = 0; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (1 << 20)) >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry11 = s11 >> 21; + s12 += carry11; + s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + //s12 = 0; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 << 21; + + s[0] = (s0 >> 0) as u8; + s[1] = (s0 >> 8) as u8; + s[2] = ((s0 >> 16) | (s1 << 5)) as u8; + s[3] = (s1 >> 3) as u8; + s[4] = (s1 >> 11) as u8; + s[5] = ((s1 >> 19) | (s2 << 2)) as u8; + s[6] = (s2 >> 6) as u8; + s[7] = ((s2 >> 14) | (s3 << 7)) as u8; + s[8] = (s3 >> 1) as u8; + s[9] = (s3 >> 9) as u8; + s[10] = ((s3 >> 17) | (s4 << 4)) as u8; + s[11] = (s4 >> 4) as u8; + s[12] = (s4 >> 12) as u8; + s[13] = ((s4 >> 20) | (s5 << 1)) as u8; + s[14] = (s5 >> 7) as u8; + s[15] = ((s5 >> 15) | (s6 << 6)) as u8; + s[16] = (s6 >> 2) as u8; + s[17] = (s6 >> 10) as u8; + s[18] = ((s6 >> 18) | (s7 << 3)) as u8; + s[19] = (s7 >> 5) as u8; + s[20] = (s7 >> 13) as u8; + s[21] = (s8 >> 0) as u8; + s[22] = (s8 >> 8) as u8; + s[23] = ((s8 >> 16) | (s9 << 5)) as u8; + s[24] = (s9 >> 3) as u8; + s[25] = (s9 >> 11) as u8; + s[26] = ((s9 >> 19) | (s10 << 2)) as u8; + s[27] = (s10 >> 6) as u8; + s[28] = ((s10 >> 14) | (s11 << 7)) as u8; + s[29] = (s11 >> 1) as u8; + s[30] = (s11 >> 9) as u8; + s[31] = (s11 >> 17) as u8; +} + +#[cfg(test)] +#[test] +fn muladd() { + let fname = "testdata/ed25519/muladd.test"; + run_test(fname.to_string(), 4, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + let (negc, cbytes) = case.get("c").unwrap(); + let (negd, dbytes) = case.get("d").unwrap(); + + assert!(!nega && !negb && !negc && !negd); + let mut mine = [0; 32]; + x25519_sc_muladd(&mut mine, abytes, bbytes, cbytes); + for i in 0..32 { + assert_eq!(&mine[i], &dbytes[i]); + } + }); +} + +pub fn curve25519_scalar_mask(a: &mut [u8]) +{ + assert_eq!(a.len(), 32); + a[0] &= 248; + a[31] &= 127; + a[31] |= 64; +} + +/* Replace (f,g) with (g,f) if b == 1; + * replace (f,g) with (f,g) if b == 0. + * + * Preconditions: b in {0,1}. */ +//fn fe_cswap(f: &mut Element, g: &mut Element, inb: bool) { +// let b = if inb { 0xFFFFFFFFu32 as i32 } else { 0x00000000 }; +// for i in 0..NUM_ELEMENT_LIMBS { +// let mut x = f[i] ^ g[i]; +// x &= b; +// f[i] ^= x; +// g[i] ^= x; +// } +//} + +/* h = f * 121666 + * Can overlap h with f. + * + * Preconditions: + * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + * + * Postconditions: + * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ +//fn fe_mul121666(h: &mut Element, f: &Element) +//{ +// let f0 = f[0]; +// let f1 = f[1]; +// let f2 = f[2]; +// let f3 = f[3]; +// let f4 = f[4]; +// let f5 = f[5]; +// let f6 = f[6]; +// let f7 = f[7]; +// let f8 = f[8]; +// let f9 = f[9]; +// let mut h0 = (f0 as i64) * 121666; +// let mut h1 = (f1 as i64) * 121666; +// let mut h2 = (f2 as i64) * 121666; +// let mut h3 = (f3 as i64) * 121666; +// let mut h4 = (f4 as i64) * 121666; +// let mut h5 = (f5 as i64) * 121666; +// let mut h6 = (f6 as i64) * 121666; +// let mut h7 = (f7 as i64) * 121666; +// let mut h8 = (f8 as i64) * 121666; +// let mut h9 = (f9 as i64) * 121666; +// +// let carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & KTOP_39BITS; +// let carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & KTOP_39BITS; +// let carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & KTOP_39BITS; +// let carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & KTOP_39BITS; +// let carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & KTOP_39BITS; +// +// let carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & KTOP_38BITS; +// let carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & KTOP_38BITS; +// let carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & KTOP_38BITS; +// let carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & KTOP_38BITS; +// let carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & KTOP_38BITS; +// +// h[0] = h0 as i32; +// h[1] = h1 as i32; +// h[2] = h2 as i32; +// h[3] = h3 as i32; +// h[4] = h4 as i32; +// h[5] = h5 as i32; +// h[6] = h6 as i32; +// h[7] = h7 as i32; +// h[8] = h8 as i32; +// h[9] = h9 as i32; +//} + +//fn x25519_scalar_mult(out: &mut [u8], scalar: &[u8], point: &[u8]) +//{ +// assert_eq!(out.len(), 32); +// assert_eq!(scalar.len(), 32); +// assert_eq!(point.len(), 32); +// +// let mut x1 = [0; NUM_ELEMENT_LIMBS]; +// let mut x2 = [0; NUM_ELEMENT_LIMBS]; +// let mut z2 = [0; NUM_ELEMENT_LIMBS]; +// let mut x3 = [0; NUM_ELEMENT_LIMBS]; +// let mut z3 = [0; NUM_ELEMENT_LIMBS]; +// let mut tmp0 = [0; NUM_ELEMENT_LIMBS]; +// let mut tmp1 = [0; NUM_ELEMENT_LIMBS]; +// let mut tmp2; +// let mut e = [0; 32]; +// +// e.copy_from_slice(scalar); +// curve25519_scalar_mask(&mut e); +// fe_frombytes(&mut x1, &point); +// fe1(&mut x2); +// fe0(&mut z2); +// x3.copy_from_slice(&x1); +// fe1(&mut z3); +// +// let mut swap = 0; +// let mut pos = 254; +// loop { +// let b = 1 & (e[pos / 8] >> (pos & 7)); +// swap ^= b; +// fe_cswap(&mut x2, &mut x3, swap != 0); +// fe_cswap(&mut z2, &mut z3, swap != 0); +// swap = b; +// fe_sub(&mut tmp0, &x3, &z3); +// fe_sub(&mut tmp1, &x2, &z2); +// tmp2 = x2.clone(); +// fe_add(&mut x2, &tmp2, &z2); +// fe_add(&mut z2, &x3, &z3); +// fe_mul(&mut z3, &tmp0, &x2); +// tmp2 = z2.clone(); +// fe_mul(&mut z2, &tmp2, &tmp1); +// fe_square(&mut tmp0, &tmp1); +// fe_square(&mut tmp1, &x2); +// fe_add(&mut x3, &z3, &z2); +// tmp2 = z2.clone(); +// fe_sub(&mut z2, &z3, &tmp2); +// fe_mul(&mut x2, &tmp1, &tmp0); +// tmp2 = tmp1.clone(); +// fe_sub(&mut tmp1, &tmp2, &tmp0); +// tmp2 = z2.clone(); +// fe_square(&mut z2, &tmp2); +// fe_mul121666(&mut z3, &tmp1); +// tmp2 = x3.clone(); +// fe_square( &mut x3, &tmp2); +// tmp2 = tmp0.clone(); +// fe_add(&mut tmp0, &tmp2, &z3); +// fe_mul(&mut z3, &x1, &z2); +// fe_mul(&mut z2, &tmp1, &tmp0); +// if pos == 0 { +// break; +// } else { +// pos -= 1; +// } +// } +// fe_cswap(&mut x2, &mut x3, swap != 0); +// fe_cswap(&mut z2, &mut z3, swap != 0); +// +// z2 = fe_invert(&z2); +// tmp2 = x2.clone(); +// fe_mul(&mut x2, &tmp2, &z2); +// fe_tobytes(out, &x2); +//} + +pub fn x25519_public_from_private(public: &mut [u8], private: &[u8]) +{ + assert_eq!(private.len(), 32); + assert_eq!(public.len(), 32); + + let mut e = [0; 32]; + e.copy_from_slice(private); + curve25519_scalar_mask(&mut e); + + #[allow(non_snake_case)] + let mut A = Point::new(); + x25519_ge_scalarmult_base(&mut A, &e); + + /* We only need the u-coordinate of the curve25519 point. The map is + * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */ + let mut zplusy = [0; NUM_ELEMENT_LIMBS]; + let mut zminusy = [0; NUM_ELEMENT_LIMBS]; + fe_add(&mut zplusy, &A.z, &A.y); + fe_sub(&mut zminusy, &A.z, &A.y); + let zminusy_inv = fe_invert(&zminusy); + let copy = zplusy.clone(); + fe_mul(&mut zplusy, ©, &zminusy_inv); + fe_tobytes(public, &zplusy); +} + +#[cfg(test)] +#[test] +fn public_from_private() { + let fname = "testdata/ed25519/pubfrompriv.test"; + run_test(fname.to_string(), 2, |case| { + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + + assert!(!nega && !negb); + let mut mine = [0; 32]; + x25519_public_from_private(&mut mine, abytes); + for i in 0..32 { + assert_eq!(mine[i], bbytes[i]); + } + }); +} + diff --git a/src/ed25519/rfc8032.txt b/src/ed25519/rfc8032.txt new file mode 100644 index 0000000..b5dfdf0 --- /dev/null +++ b/src/ed25519/rfc8032.txt @@ -0,0 +1,3363 @@ + + + + + + +Internet Research Task Force (IRTF) S. Josefsson +Request for Comments: 8032 SJD AB +Category: Informational I. Liusvaara +ISSN: 2070-1721 Independent + January 2017 + + + Edwards-Curve Digital Signature Algorithm (EdDSA) + +Abstract + + This document describes elliptic curve signature scheme Edwards-curve + Digital Signature Algorithm (EdDSA). The algorithm is instantiated + with recommended parameters for the edwards25519 and edwards448 + curves. An example implementation and test vectors are provided. + +Status of This Memo + + This document is not an Internet Standards Track specification; it is + published for informational purposes. + + This document is a product of the Internet Research Task Force + (IRTF). The IRTF publishes the results of Internet-related research + and development activities. These results might not be suitable for + deployment. This RFC represents the consensus of the Crypto Forum + Research Group of the Internet Research Task Force (IRTF). Documents + approved for publication by the IRSG are not a candidate for any + level of Internet Standard; see Section 2 of RFC 7841. + + Information about the current status of this document, any errata, + and how to provide feedback on it may be obtained at + http://www.rfc-editor.org/info/rfc8032. + +Copyright Notice + + Copyright (c) 2017 IETF Trust and the persons identified as the + document authors. All rights reserved. + + This document is subject to BCP 78 and the IETF Trust's Legal + Provisions Relating to IETF Documents + (http://trustee.ietf.org/license-info) in effect on the date of + publication of this document. Please review these documents + carefully, as they describe your rights and restrictions with respect + to this document. + + + + + + + +Josefsson & Liusvaara Informational [Page 1] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +Table of Contents + + 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3 + 2. Notation and Conventions . . . . . . . . . . . . . . . . . . 4 + 3. EdDSA Algorithm . . . . . . . . . . . . . . . . . . . . . . . 5 + 3.1. Encoding . . . . . . . . . . . . . . . . . . . . . . . . 7 + 3.2. Keys . . . . . . . . . . . . . . . . . . . . . . . . . . 7 + 3.3. Sign . . . . . . . . . . . . . . . . . . . . . . . . . . 8 + 3.4. Verify . . . . . . . . . . . . . . . . . . . . . . . . . 8 + 4. PureEdDSA, HashEdDSA, and Naming . . . . . . . . . . . . . . 8 + 5. EdDSA Instances . . . . . . . . . . . . . . . . . . . . . . . 9 + 5.1. Ed25519ph, Ed25519ctx, and Ed25519 . . . . . . . . . . . 9 + 5.1.1. Modular Arithmetic . . . . . . . . . . . . . . . . . 10 + 5.1.2. Encoding . . . . . . . . . . . . . . . . . . . . . . 10 + 5.1.3. Decoding . . . . . . . . . . . . . . . . . . . . . . 11 + 5.1.4. Point Addition . . . . . . . . . . . . . . . . . . . 11 + 5.1.5. Key Generation . . . . . . . . . . . . . . . . . . . 13 + 5.1.6. Sign . . . . . . . . . . . . . . . . . . . . . . . . 13 + 5.1.7. Verify . . . . . . . . . . . . . . . . . . . . . . . 14 + 5.2. Ed448ph and Ed448 . . . . . . . . . . . . . . . . . . . . 15 + 5.2.1. Modular Arithmetic . . . . . . . . . . . . . . . . . 16 + 5.2.2. Encoding . . . . . . . . . . . . . . . . . . . . . . 16 + 5.2.3. Decoding . . . . . . . . . . . . . . . . . . . . . . 16 + 5.2.4. Point Addition . . . . . . . . . . . . . . . . . . . 17 + 5.2.5. Key Generation . . . . . . . . . . . . . . . . . . . 18 + 5.2.6. Sign . . . . . . . . . . . . . . . . . . . . . . . . 19 + 5.2.7. Verify . . . . . . . . . . . . . . . . . . . . . . . 19 + 6. Ed25519 Python Illustration . . . . . . . . . . . . . . . . . 20 + 7. Test Vectors . . . . . . . . . . . . . . . . . . . . . . . . 23 + 7.1. Test Vectors for Ed25519 . . . . . . . . . . . . . . . . 24 + 7.2. Test Vectors for Ed25519ctx . . . . . . . . . . . . . . . 27 + 7.3. Test Vectors for Ed25519ph . . . . . . . . . . . . . . . 30 + 7.4. Test Vectors for Ed448 . . . . . . . . . . . . . . . . . 30 + 7.5. Test Vectors for Ed448ph . . . . . . . . . . . . . . . . 38 + 8. Security Considerations . . . . . . . . . . . . . . . . . . . 40 + 8.1. Side-Channel Leaks . . . . . . . . . . . . . . . . . . . 40 + 8.2. Randomness Considerations . . . . . . . . . . . . . . . . 40 + 8.3. Use of Contexts . . . . . . . . . . . . . . . . . . . . . 41 + 8.4. Signature Malleability . . . . . . . . . . . . . . . . . 41 + 8.5. Choice of Signature Primitive . . . . . . . . . . . . . . 41 + 8.6. Mixing Different Prehashes . . . . . . . . . . . . . . . 42 + 8.7. Signing Large Amounts of Data at Once . . . . . . . . . . 42 + 8.8. Multiplication by Cofactor in Verification . . . . . . . 43 + 8.9. Use of SHAKE256 as a Hash Function . . . . . . . . . . . 43 + 9. References . . . . . . . . . . . . . . . . . . . . . . . . . 43 + 9.1. Normative References . . . . . . . . . . . . . . . . . . 43 + 9.2. Informative References . . . . . . . . . . . . . . . . . 44 + + + + +Josefsson & Liusvaara Informational [Page 2] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + Appendix A. Ed25519/Ed448 Python Library . . . . . . . . . . . . 46 + Appendix B. Library Driver . . . . . . . . . . . . . . . . . . . 58 + Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 60 + Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 60 + +1. Introduction + + The Edwards-curve Digital Signature Algorithm (EdDSA) is a variant of + Schnorr's signature system with (possibly twisted) Edwards curves. + EdDSA needs to be instantiated with certain parameters, and this + document describes some recommended variants. + + To facilitate adoption of EdDSA in the Internet community, this + document describes the signature scheme in an implementation-oriented + way and provides sample code and test vectors. + + The advantages with EdDSA are as follows: + + 1. EdDSA provides high performance on a variety of platforms; + + 2. The use of a unique random number for each signature is not + required; + + 3. It is more resilient to side-channel attacks; + + 4. EdDSA uses small public keys (32 or 57 bytes) and signatures (64 + or 114 bytes) for Ed25519 and Ed448, respectively; + + 5. The formulas are "complete", i.e., they are valid for all points + on the curve, with no exceptions. This obviates the need for + EdDSA to perform expensive point validation on untrusted public + values; and + + 6. EdDSA provides collision resilience, meaning that hash-function + collisions do not break this system (only holds for PureEdDSA). + + The original EdDSA paper [EDDSA] and the generalized version + described in "EdDSA for more curves" [EDDSA2] provide further + background. RFC 7748 [RFC7748] discusses specific curves, including + Curve25519 [CURVE25519] and Ed448-Goldilocks [ED448]. + + Ed25519 is intended to operate at around the 128-bit security level + and Ed448 at around the 224-bit security level. A sufficiently large + quantum computer would be able to break both. Reasonable projections + of the abilities of classical computers conclude that Ed25519 is + perfectly safe. Ed448 is provided for those applications with + relaxed performance requirements and where there is a desire to hedge + against analytical attacks on elliptic curves. + + + +Josefsson & Liusvaara Informational [Page 3] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +2. Notation and Conventions + + The following notation is used throughout the document: + + p Denotes the prime number defining the underlying field + + GF(p) Finite field with p elements + + x^y x multiplied by itself y times + + B Generator of the group or subgroup of interest + + [n]X X added to itself n times + + h[i] The i'th octet of octet string + + h_i The i'th bit of h + + a || b (bit-)string a concatenated with (bit-)string b + + a <= b a is less than or equal to b + + a >= b a is greater than or equal to b + + i+j Sum of i and j + + i*j Multiplication of i and j + + i-j Subtraction of j from i + + i/j Division of i by j + + i x j Cartesian product of i and j + + (u,v) Elliptic curve point with x-coordinate u and + y-coordinate v + + SHAKE256(x, y) The y first octets of SHAKE256 [FIPS202] output for + input x + + OCTET(x) The octet with value x + + OLEN(x) The number of octets in string x + + + + + + + + +Josefsson & Liusvaara Informational [Page 4] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + dom2(x, y) The blank octet string when signing or verifying + Ed25519. Otherwise, the octet string: "SigEd25519 no + Ed25519 collisions" || octet(x) || octet(OLEN(y)) || + y, where x is in range 0-255 and y is an octet string + of at most 255 octets. "SigEd25519 no Ed25519 + collisions" is in ASCII (32 octets). + + dom4(x, y) The octet string "SigEd448" || octet(x) || + octet(OLEN(y)) || y, where x is in range 0-255 and y + is an octet string of at most 255 octets. "SigEd448" + is in ASCII (8 octets). + + Parentheses (i.e., '(' and ')') are used to group expressions, in + order to avoid having the description depend on a binding order + between operators. + + Bit strings are converted to octet strings by taking bits from left + to right, packing those from the least significant bit of each octet + to the most significant bit, and moving to the next octet when each + octet fills up. The conversion from octet string to bit string is + the reverse of this process; for example, the 16-bit bit string + + b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 + + is converted into two octets x0 and x1 (in this order) as + + x0 = b7*128+b6*64+b5*32+b4*16+b3*8+b2*4+b1*2+b0 + x1 = b15*128+b14*64+b13*32+b12*16+b11*8+b10*4+b9*2+b8 + + Little-endian encoding into bits places bits from left to right and + from least significant to most significant. If combined with + bit-string-to-octet-string conversion defined above, this results in + little-endian encoding into octets (if length is not a multiple of 8, + the most significant bits of the last octet remain unused). + + The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", + "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this + document are to be interpreted as described in [RFC2119]. + +3. EdDSA Algorithm + + EdDSA is a digital signature system with 11 parameters. + + The generic EdDSA digital signature system with its 11 input + parameters is not intended to be implemented directly. Choosing + parameters is critical for secure and efficient operation. Instead, + you would implement a particular parameter choice for EdDSA (such as + + + + +Josefsson & Liusvaara Informational [Page 5] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + Ed25519 or Ed448), sometimes slightly generalized to achieve code + reuse to cover Ed25519 and Ed448. + + Therefore, a precise explanation of the generic EdDSA is thus not + particularly useful for implementers. For background and + completeness, a succinct description of the generic EdDSA algorithm + is given here. + + The definition of some parameters, such as n and c, may help to + explain some steps of the algorithm that are not intuitive. + + This description closely follows [EDDSA2]. + + EdDSA has 11 parameters: + + 1. An odd prime power p. EdDSA uses an elliptic curve over the + finite field GF(p). + + 2. An integer b with 2^(b-1) > p. EdDSA public keys have exactly b + bits, and EdDSA signatures have exactly 2*b bits. b is + recommended to be a multiple of 8, so public key and signature + lengths are an integral number of octets. + + 3. A (b-1)-bit encoding of elements of the finite field GF(p). + + 4. A cryptographic hash function H producing 2*b-bit output. + Conservative hash functions (i.e., hash functions where it is + infeasible to create collisions) are recommended and do not have + much impact on the total cost of EdDSA. + + 5. An integer c that is 2 or 3. Secret EdDSA scalars are multiples + of 2^c. The integer c is the base-2 logarithm of the so-called + cofactor. + + 6. An integer n with c <= n < b. Secret EdDSA scalars have exactly + n + 1 bits, with the top bit (the 2^n position) always set and + the bottom c bits always cleared. + + 7. A non-square element d of GF(p). The usual recommendation is to + take it as the value nearest to zero that gives an acceptable + curve. + + 8. A non-zero square element a of GF(p). The usual recommendation + for best performance is a = -1 if p mod 4 = 1, and a = 1 if + p mod 4 = 3. + + 9. An element B != (0,1) of the set E = { (x,y) is a member of + GF(p) x GF(p) such that a * x^2 + y^2 = 1 + d * x^2 * y^2 }. + + + +Josefsson & Liusvaara Informational [Page 6] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + 10. An odd prime L such that [L]B = 0 and 2^c * L = #E. The number + #E (the number of points on the curve) is part of the standard + data provided for an elliptic curve E, or it can be computed as + cofactor * order. + + 11. A "prehash" function PH. PureEdDSA means EdDSA where PH is the + identity function, i.e., PH(M) = M. HashEdDSA means EdDSA where + PH generates a short output, no matter how long the message is; + for example, PH(M) = SHA-512(M). + + Points on the curve form a group under addition, (x3, y3) = (x1, y1) + + (x2, y2), with the formulas + + x1 * y2 + x2 * y1 y1 * y2 - a * x1 * x2 + x3 = --------------------------, y3 = --------------------------- + 1 + d * x1 * x2 * y1 * y2 1 - d * x1 * x2 * y1 * y2 + + The neutral element in the group is (0,1). + + Unlike many other curves used for cryptographic applications, these + formulas are "complete"; they are valid for all points on the curve, + with no exceptions. In particular, the denominators are non-zero for + all input points. + + There are more efficient formulas, which are still complete, that use + homogeneous coordinates to avoid the expensive modulo p inversions. + See [Faster-ECC] and [Edwards-revisited]. + +3.1. Encoding + + An integer 0 < S < L - 1 is encoded in little-endian form as a b-bit + string ENC(S). + + An element (x,y) of E is encoded as a b-bit string called ENC(x,y), + which is the (b-1)-bit encoding of y concatenated with one bit that + is 1 if x is negative and 0 if x is not negative. + + The encoding of GF(p) is used to define "negative" elements of GF(p): + specifically, x is negative if the (b-1)-bit encoding of x is + lexicographically larger than the (b-1)-bit encoding of -x. + +3.2. Keys + + An EdDSA private key is a b-bit string k. Let the hash H(k) = + (h_0, h_1, ..., h_(2b-1)) determine an integer s, which is 2^n plus + the sum of m = 2^i * h_i for all integer i, c <= i < n. Let s + determine the multiple A = [s]B. The EdDSA public key is ENC(A). + The bits h_b, ..., h_(2b-1) are used below during signing. + + + +Josefsson & Liusvaara Informational [Page 7] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +3.3. Sign + + The EdDSA signature of a message M under a private key k is defined + as the PureEdDSA signature of PH(M). In other words, EdDSA simply + uses PureEdDSA to sign PH(M). + + The PureEdDSA signature of a message M under a private key k is the + 2*b-bit string ENC(R) || ENC(S). R and S are derived as follows. + First define r = H(h_b || ... || h_(2b-1) || M) interpreting 2*b-bit + strings in little-endian form as integers in {0, 1, ..., 2^(2*b) - + 1}. Let R = [r]B and S = (r + H(ENC(R) || ENC(A) || PH(M)) * s) mod + L. The s used here is from the previous section. + +3.4. Verify + + To verify a PureEdDSA signature ENC(R) || ENC(S) on a message M under + a public key ENC(A), proceed as follows. Parse the inputs so that A + and R are elements of E, and S is a member of the set {0, 1, ..., + L-1}. Compute h = H(ENC(R) || ENC(A) || M), and check the group + equation [2^c * S] B = 2^c * R + [2^c * h] A in E. The signature is + rejected if parsing fails (including S being out of range) or if the + group equation does not hold. + + EdDSA verification for a message M is defined as PureEdDSA + verification for PH(M). + +4. PureEdDSA, HashEdDSA, and Naming + + One of the parameters of the EdDSA algorithm is the "prehash" + function. This may be the identity function, resulting in an + algorithm called PureEdDSA, or a collision-resistant hash function + such as SHA-512, resulting in an algorithm called HashEdDSA. + + Choosing which variant to use depends on which property is deemed to + be more important between 1) collision resilience and 2) a single- + pass interface for creating signatures. The collision resilience + property means EdDSA is secure even if it is feasible to compute + collisions for the hash function. The single-pass interface property + means that only one pass over the input message is required to create + a signature. PureEdDSA requires two passes over the input. Many + existing APIs, protocols, and environments assume digital signature + algorithms only need one pass over the input and may have API or + bandwidth concerns supporting anything else. + + Note that single-pass verification is not possible with most uses of + signatures, no matter which signature algorithm is chosen. This is + because most of the time, one can't process the message until the + signature is validated, which needs a pass on the entire message. + + + +Josefsson & Liusvaara Informational [Page 8] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + This document specifies parameters resulting in the HashEdDSA + variants Ed25519ph and Ed448ph and the PureEdDSA variants Ed25519 and + Ed448. + +5. EdDSA Instances + + This section instantiates the general EdDSA algorithm for the + edwards25519 and edwards448 curves, each for the PureEdDSA and + HashEdDSA variants (plus a contextualized extension of the Ed25519 + scheme). Thus, five different parameter sets are described. + +5.1. Ed25519ph, Ed25519ctx, and Ed25519 + + Ed25519 is EdDSA instantiated with: + + +-----------+-------------------------------------------------------+ + | Parameter | Value | + +-----------+-------------------------------------------------------+ + | p | p of edwards25519 in [RFC7748] (i.e., 2^255 - 19) | + | b | 256 | + | encoding | 255-bit little-endian encoding of {0, 1, ..., p-1} | + | of GF(p) | | + | H(x) | SHA-512(dom2(phflag,context)||x) [RFC6234] | + | c | base 2 logarithm of cofactor of edwards25519 in | + | | [RFC7748] (i.e., 3) | + | n | 254 | + | d | d of edwards25519 in [RFC7748] (i.e., -121665/121666 | + | | = 370957059346694393431380835087545651895421138798432 | + | | 19016388785533085940283555) | + | a | -1 | + | B | (X(P),Y(P)) of edwards25519 in [RFC7748] (i.e., (1511 | + | | 22213495354007725011514095885315114540126930418572060 | + | | 46113283949847762202, 4631683569492647816942839400347 | + | | 5163141307993866256225615783033603165251855960)) | + | L | order of edwards25519 in [RFC7748] (i.e., | + | | 2^252+27742317777372353535851937790883648493). | + | PH(x) | x (i.e., the identity function) | + +-----------+-------------------------------------------------------+ + + Table 1: Parameters of Ed25519 + + For Ed25519, dom2(f,c) is the empty string. The phflag value is + irrelevant. The context (if present at all) MUST be empty. This + causes the scheme to be one and the same with the Ed25519 scheme + published earlier. + + For Ed25519ctx, phflag=0. The context input SHOULD NOT be empty. + + + + +Josefsson & Liusvaara Informational [Page 9] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + For Ed25519ph, phflag=1 and PH is SHA512 instead. That is, the input + is hashed using SHA-512 before signing with Ed25519. + + Value of context is set by the signer and verifier (maximum of 255 + octets; the default is empty string, except for Ed25519, which can't + have context) and has to match octet by octet for verification to be + successful. + + The curve used is equivalent to Curve25519 [CURVE25519], under a + change of coordinates, which means that the difficulty of the + discrete logarithm problem is the same as for Curve25519. + +5.1.1. Modular Arithmetic + + For advice on how to implement arithmetic modulo p = 2^255 - 19 + efficiently and securely, see Curve25519 [CURVE25519]. For inversion + modulo p, it is recommended to use the identity x^-1 = x^(p-2) (mod + p). Inverting zero should never happen, as it would require invalid + input, which would have been detected before, or would be a + calculation error. + + For point decoding or "decompression", square roots modulo p are + needed. They can be computed using the Tonelli-Shanks algorithm or + the special case for p = 5 (mod 8). To find a square root of a, + first compute the candidate root x = a^((p+3)/8) (mod p). Then there + are three cases: + + x^2 = a (mod p). Then x is a square root. + + x^2 = -a (mod p). Then 2^((p-1)/4) * x is a square root. + + a is not a square modulo p. + +5.1.2. Encoding + + All values are coded as octet strings, and integers are coded using + little-endian convention, i.e., a 32-octet string h h[0],...h[31] + represents the integer h[0] + 2^8 * h[1] + ... + 2^248 * h[31]. + + A curve point (x,y), with coordinates in the range 0 <= x,y < p, is + coded as follows. First, encode the y-coordinate as a little-endian + string of 32 octets. The most significant bit of the final octet is + always zero. To form the encoding of the point, copy the least + significant bit of the x-coordinate to the most significant bit of + the final octet. + + + + + + +Josefsson & Liusvaara Informational [Page 10] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +5.1.3. Decoding + + Decoding a point, given as a 32-octet string, is a little more + complicated. + + 1. First, interpret the string as an integer in little-endian + representation. Bit 255 of this number is the least significant + bit of the x-coordinate and denote this value x_0. The + y-coordinate is recovered simply by clearing this bit. If the + resulting value is >= p, decoding fails. + + 2. To recover the x-coordinate, the curve equation implies + x^2 = (y^2 - 1) / (d y^2 + 1) (mod p). The denominator is always + non-zero mod p. Let u = y^2 - 1 and v = d y^2 + 1. To compute + the square root of (u/v), the first step is to compute the + candidate root x = (u/v)^((p+3)/8). This can be done with the + following trick, using a single modular powering for both the + inversion of v and the square root: + + (p+3)/8 3 (p-5)/8 + x = (u/v) = u v (u v^7) (mod p) + + 3. Again, there are three cases: + + 1. If v x^2 = u (mod p), x is a square root. + + 2. If v x^2 = -u (mod p), set x <-- x * 2^((p-1)/4), which is a + square root. + + 3. Otherwise, no square root exists for modulo p, and decoding + fails. + + 4. Finally, use the x_0 bit to select the right square root. If + x = 0, and x_0 = 1, decoding fails. Otherwise, if x_0 != x mod + 2, set x <-- p - x. Return the decoded point (x,y). + +5.1.4. Point Addition + + For point addition, the following method is recommended. A point + (x,y) is represented in extended homogeneous coordinates (X, Y, Z, + T), with x = X/Z, y = Y/Z, x * y = T/Z. + + The neutral point is (0,1), or equivalently in extended homogeneous + coordinates (0, Z, Z, 0) for any non-zero Z. + + + + + + + +Josefsson & Liusvaara Informational [Page 11] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + The following formulas for adding two points, (x3,y3) = + (x1,y1)+(x2,y2), on twisted Edwards curves with a=-1, square a, and + non-square d are described in Section 3.1 of [Edwards-revisited] and + in [EFD-TWISTED-ADD]. They are complete, i.e., they work for any + pair of valid input points. + + A = (Y1-X1)*(Y2-X2) + B = (Y1+X1)*(Y2+X2) + C = T1*2*d*T2 + D = Z1*2*Z2 + E = B-A + F = D-C + G = D+C + H = B+A + X3 = E*F + Y3 = G*H + T3 = E*H + Z3 = F*G + + For point doubling, (x3,y3) = (x1,y1)+(x1,y1), one could just + substitute equal points in the above (because of completeness, such + substitution is valid) and observe that four multiplications turn + into squares. However, using the formulas described in Section 3.2 + of [Edwards-revisited] and in [EFD-TWISTED-DBL] saves a few smaller + operations. + + A = X1^2 + B = Y1^2 + C = 2*Z1^2 + H = A+B + E = H-(X1+Y1)^2 + G = A-B + F = C+G + X3 = E*F + Y3 = G*H + T3 = E*H + Z3 = F*G + + + + + + + + + + + + + + +Josefsson & Liusvaara Informational [Page 12] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +5.1.5. Key Generation + + The private key is 32 octets (256 bits, corresponding to b) of + cryptographically secure random data. See [RFC4086] for a discussion + about randomness. + + The 32-byte public key is generated by the following steps. + + 1. Hash the 32-byte private key using SHA-512, storing the digest in + a 64-octet large buffer, denoted h. Only the lower 32 bytes are + used for generating the public key. + + 2. Prune the buffer: The lowest three bits of the first octet are + cleared, the highest bit of the last octet is cleared, and the + second highest bit of the last octet is set. + + 3. Interpret the buffer as the little-endian integer, forming a + secret scalar s. Perform a fixed-base scalar multiplication + [s]B. + + 4. The public key A is the encoding of the point [s]B. First, + encode the y-coordinate (in the range 0 <= y < p) as a little- + endian string of 32 octets. The most significant bit of the + final octet is always zero. To form the encoding of the point + [s]B, copy the least significant bit of the x coordinate to the + most significant bit of the final octet. The result is the + public key. + +5.1.6. Sign + + The inputs to the signing procedure is the private key, a 32-octet + string, and a message M of arbitrary size. For Ed25519ctx and + Ed25519ph, there is additionally a context C of at most 255 octets + and a flag F, 0 for Ed25519ctx and 1 for Ed25519ph. + + 1. Hash the private key, 32 octets, using SHA-512. Let h denote the + resulting digest. Construct the secret scalar s from the first + half of the digest, and the corresponding public key A, as + described in the previous section. Let prefix denote the second + half of the hash digest, h[32],...,h[63]. + + 2. Compute SHA-512(dom2(F, C) || prefix || PH(M)), where M is the + message to be signed. Interpret the 64-octet digest as a little- + endian integer r. + + 3. Compute the point [r]B. For efficiency, do this by first + reducing r modulo L, the group order of B. Let the string R be + the encoding of this point. + + + +Josefsson & Liusvaara Informational [Page 13] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + 4. Compute SHA512(dom2(F, C) || R || A || PH(M)), and interpret the + 64-octet digest as a little-endian integer k. + + 5. Compute S = (r + k * s) mod L. For efficiency, again reduce k + modulo L first. + + 6. Form the signature of the concatenation of R (32 octets) and the + little-endian encoding of S (32 octets; the three most + significant bits of the final octet are always zero). + +5.1.7. Verify + + 1. To verify a signature on a message M using public key A, with F + being 0 for Ed25519ctx, 1 for Ed25519ph, and if Ed25519ctx or + Ed25519ph is being used, C being the context, first split the + signature into two 32-octet halves. Decode the first half as a + point R, and the second half as an integer S, in the range + 0 <= s < L. Decode the public key A as point A'. If any of the + decodings fail (including S being out of range), the signature is + invalid. + + 2. Compute SHA512(dom2(F, C) || R || A || PH(M)), and interpret the + 64-octet digest as a little-endian integer k. + + 3. Check the group equation [8][S]B = [8]R + [8][k]A'. It's + sufficient, but not required, to instead check [S]B = R + [k]A'. + + + + + + + + + + + + + + + + + + + + + + + + + +Josefsson & Liusvaara Informational [Page 14] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +5.2. Ed448ph and Ed448 + + Ed448 is EdDSA instantiated with: + + +-----------+-------------------------------------------------------+ + | Parameter | Value | + +-----------+-------------------------------------------------------+ + | p | p of edwards448 in [RFC7748] (i.e., 2^448 - 2^224 - | + | | 1) | + | b | 456 | + | encoding | 455-bit little-endian encoding of {0, 1, ..., p-1} | + | of GF(p) | | + | H(x) | SHAKE256(dom4(phflag,context)||x, 114) | + | phflag | 0 | + | c | base 2 logarithm of cofactor of edwards448 in | + | | [RFC7748] (i.e., 2) | + | n | 447 | + | d | d of edwards448 in [RFC7748] (i.e., -39081) | + | a | 1 | + | B | (X(P),Y(P)) of edwards448 in [RFC7748] (i.e., (224580 | + | | 04029592430018760433409989603624678964163256413424612 | + | | 54616869504154674060329090291928693579532825780320751 | + | | 46446173674602635247710, 2988192100784814926760179304 | + | | 43930673437544040154080242095928241372331506189835876 | + | | 00353687865541878473398230323350346250053154506283266 | + | | 0)) | + | L | order of edwards448 in [RFC7748] (i.e., 2^446 - 13818 | + | | 06680989511535200738674851542688033669247488217860989 | + | | 4547503885). | + | PH(x) | x (i.e., the identity function) | + +-----------+-------------------------------------------------------+ + + Table 2: Parameters of Ed448 + + Ed448ph is the same but with PH being SHAKE256(x, 64) and phflag + being 1, i.e., the input is hashed before signing with Ed448 with a + hash constant modified. + + Value of context is set by signer and verifier (maximum of 255 + octets; the default is empty string) and has to match octet by octet + for verification to be successful. + + The curve is equivalent to Ed448-Goldilocks under change of the + basepoint, which preserves difficulty of the discrete logarithm. + + + + + + + +Josefsson & Liusvaara Informational [Page 15] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +5.2.1. Modular Arithmetic + + For advice on how to implement arithmetic modulo p = 2^448 - 2^224 - + 1 efficiently and securely, see [ED448]. For inversion modulo p, it + is recommended to use the identity x^-1 = x^(p-2) (mod p). Inverting + zero should never happen, as it would require invalid input, which + would have been detected before, or would be a calculation error. + + For point decoding or "decompression", square roots modulo p are + needed. They can be computed by first computing candidate root + x = a ^ (p+1)/4 (mod p) and then checking if x^2 = a. If it is, then + x is the square root of a; if it isn't, then a does not have a square + root. + +5.2.2. Encoding + + All values are coded as octet strings, and integers are coded using + little-endian convention, i.e., a 57-octet string h h[0],...h[56] + represents the integer h[0] + 2^8 * h[1] + ... + 2^448 * h[56]. + + A curve point (x,y), with coordinates in the range 0 <= x,y < p, is + coded as follows. First, encode the y-coordinate as a little-endian + string of 57 octets. The final octet is always zero. To form the + encoding of the point, copy the least significant bit of the + x-coordinate to the most significant bit of the final octet. + +5.2.3. Decoding + + Decoding a point, given as a 57-octet string, is a little more + complicated. + + 1. First, interpret the string as an integer in little-endian + representation. Bit 455 of this number is the least significant + bit of the x-coordinate, and denote this value x_0. The + y-coordinate is recovered simply by clearing this bit. If the + resulting value is >= p, decoding fails. + + 2. To recover the x-coordinate, the curve equation implies + x^2 = (y^2 - 1) / (d y^2 - 1) (mod p). The denominator is always + non-zero mod p. Let u = y^2 - 1 and v = d y^2 - 1. To compute + the square root of (u/v), the first step is to compute the + candidate root x = (u/v)^((p+1)/4). This can be done using the + following trick, to use a single modular powering for both the + inversion of v and the square root: + + (p+1)/4 3 (p-3)/4 + x = (u/v) = u v (u^5 v^3) (mod p) + + + + +Josefsson & Liusvaara Informational [Page 16] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + 3. If v * x^2 = u, the recovered x-coordinate is x. Otherwise, no + square root exists, and the decoding fails. + + 4. Finally, use the x_0 bit to select the right square root. If + x = 0, and x_0 = 1, decoding fails. Otherwise, if x_0 != x mod + 2, set x <-- p - x. Return the decoded point (x,y). + +5.2.4. Point Addition + + For point addition, the following method is recommended. A point + (x,y) is represented in projective coordinates (X, Y, Z), with + x = X/Z, y = Y/Z. + + The neutral point is (0,1), or equivalently in projective coordinates + (0, Z, Z) for any non-zero Z. + + The following formulas for adding two points, (x3,y3) = + (x1,y1)+(x2,y2) on untwisted Edwards curve (i.e., a=1) with non- + square d, are described in Section 4 of [Faster-ECC] and in + [EFD-ADD]. They are complete, i.e., they work for any pair of valid + input points. + + A = Z1*Z2 + B = A^2 + C = X1*X2 + D = Y1*Y2 + E = d*C*D + F = B-E + G = B+E + H = (X1+Y1)*(X2+Y2) + X3 = A*F*(H-C-D) + Y3 = A*G*(D-C) + Z3 = F*G + + + + + + + + + + + + + + + + + + +Josefsson & Liusvaara Informational [Page 17] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + Again, similar to the other curve, doubling formulas can be obtained + by substituting equal points, turning four multiplications into + squares. However, this is not even nearly optimal; the following + formulas described in Section 4 of [Faster-ECC] and in [EFD-DBL] save + multiple multiplications. + + B = (X1+Y1)^2 + C = X1^2 + D = Y1^2 + E = C+D + H = Z1^2 + J = E-2*H + X3 = (B-E)*J + Y3 = E*(C-D) + Z3 = E*J + +5.2.5. Key Generation + + The private key is 57 octets (456 bits, corresponding to b) of + cryptographically secure random data. See [RFC4086] for a discussion + about randomness. + + The 57-byte public key is generated by the following steps: + + 1. Hash the 57-byte private key using SHAKE256(x, 114), storing the + digest in a 114-octet large buffer, denoted h. Only the lower 57 + bytes are used for generating the public key. + + 2. Prune the buffer: The two least significant bits of the first + octet are cleared, all eight bits the last octet are cleared, and + the highest bit of the second to last octet is set. + + 3. Interpret the buffer as the little-endian integer, forming a + secret scalar s. Perform a known-base-point scalar + multiplication [s]B. + + 4. The public key A is the encoding of the point [s]B. First encode + the y-coordinate (in the range 0 <= y < p) as a little-endian + string of 57 octets. The most significant bit of the final octet + is always zero. To form the encoding of the point [s]B, copy the + least significant bit of the x coordinate to the most significant + bit of the final octet. The result is the public key. + + + + + + + + + +Josefsson & Liusvaara Informational [Page 18] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +5.2.6. Sign + + The inputs to the signing procedure is the private key, a 57-octet + string, a flag F, which is 0 for Ed448, 1 for Ed448ph, context C of + at most 255 octets, and a message M of arbitrary size. + + 1. Hash the private key, 57 octets, using SHAKE256(x, 114). Let h + denote the resulting digest. Construct the secret scalar s from + the first half of the digest, and the corresponding public key A, + as described in the previous section. Let prefix denote the + second half of the hash digest, h[57],...,h[113]. + + 2. Compute SHAKE256(dom4(F, C) || prefix || PH(M), 114), where M is + the message to be signed, F is 1 for Ed448ph, 0 for Ed448, and C + is the context to use. Interpret the 114-octet digest as a + little-endian integer r. + + 3. Compute the point [r]B. For efficiency, do this by first + reducing r modulo L, the group order of B. Let the string R be + the encoding of this point. + + 4. Compute SHAKE256(dom4(F, C) || R || A || PH(M), 114), and + interpret the 114-octet digest as a little-endian integer k. + + 5. Compute S = (r + k * s) mod L. For efficiency, again reduce k + modulo L first. + + 6. Form the signature of the concatenation of R (57 octets) and the + little-endian encoding of S (57 octets; the ten most significant + bits of the final octets are always zero). + +5.2.7. Verify + + 1. To verify a signature on a message M using context C and public + key A, with F being 0 for Ed448 and 1 for Ed448ph, first split + the signature into two 57-octet halves. Decode the first half as + a point R, and the second half as an integer S, in the range 0 <= + s < L. Decode the public key A as point A'. If any of the + decodings fail (including S being out of range), the signature is + invalid. + + 2. Compute SHAKE256(dom4(F, C) || R || A || PH(M), 114), and + interpret the 114-octet digest as a little-endian integer k. + + 3. Check the group equation [4][S]B = [4]R + [4][k]A'. It's + sufficient, but not required, to instead check [S]B = R + [k]A'. + + + + + +Josefsson & Liusvaara Informational [Page 19] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +6. Ed25519 Python Illustration + + The rest of this section describes how Ed25519 can be implemented in + Python (version 3.2 or later) for illustration. See Appendix A for + the complete implementation and Appendix B for a test-driver to run + it through some test vectors. + + Note that this code is not intended for production as it is not + proven to be correct for all inputs, nor does it protect against + side-channel attacks. The purpose is to illustrate the algorithm to + help implementers with their own implementation. + +## First, some preliminaries that will be needed. + +import hashlib + +def sha512(s): + return hashlib.sha512(s).digest() + +# Base field Z_p +p = 2**255 - 19 + +def modp_inv(x): + return pow(x, p-2, p) + +# Curve constant +d = -121665 * modp_inv(121666) % p + +# Group order +q = 2**252 + 27742317777372353535851937790883648493 + +def sha512_modq(s): + return int.from_bytes(sha512(s), "little") % q + +## Then follows functions to perform point operations. + +# Points are represented as tuples (X, Y, Z, T) of extended +# coordinates, with x = X/Z, y = Y/Z, x*y = T/Z + +def point_add(P, Q): + A, B = (P[1]-P[0]) * (Q[1]-Q[0]) % p, (P[1]+P[0]) * (Q[1]+Q[0]) % p; + C, D = 2 * P[3] * Q[3] * d % p, 2 * P[2] * Q[2] % p; + E, F, G, H = B-A, D-C, D+C, B+A; + return (E*F, G*H, F*G, E*H); + + + + + + + +Josefsson & Liusvaara Informational [Page 20] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +# Computes Q = s * Q +def point_mul(s, P): + Q = (0, 1, 1, 0) # Neutral element + while s > 0: + if s & 1: + Q = point_add(Q, P) + P = point_add(P, P) + s >>= 1 + return Q + +def point_equal(P, Q): + # x1 / z1 == x2 / z2 <==> x1 * z2 == x2 * z1 + if (P[0] * Q[2] - Q[0] * P[2]) % p != 0: + return False + if (P[1] * Q[2] - Q[1] * P[2]) % p != 0: + return False + return True + +## Now follows functions for point compression. + +# Square root of -1 +modp_sqrt_m1 = pow(2, (p-1) // 4, p) + +# Compute corresponding x-coordinate, with low bit corresponding to +# sign, or return None on failure +def recover_x(y, sign): + if y >= p: + return None + x2 = (y*y-1) * modp_inv(d*y*y+1) + if x2 == 0: + if sign: + return None + else: + return 0 + + # Compute square root of x2 + x = pow(x2, (p+3) // 8, p) + if (x*x - x2) % p != 0: + x = x * modp_sqrt_m1 % p + if (x*x - x2) % p != 0: + return None + + if (x & 1) != sign: + x = p - x + return x + + + + + + +Josefsson & Liusvaara Informational [Page 21] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +# Base point +g_y = 4 * modp_inv(5) % p +g_x = recover_x(g_y, 0) +G = (g_x, g_y, 1, g_x * g_y % p) + +def point_compress(P): + zinv = modp_inv(P[2]) + x = P[0] * zinv % p + y = P[1] * zinv % p + return int.to_bytes(y | ((x & 1) << 255), 32, "little") + +def point_decompress(s): + if len(s) != 32: + raise Exception("Invalid input length for decompression") + y = int.from_bytes(s, "little") + sign = y >> 255 + y &= (1 << 255) - 1 + + x = recover_x(y, sign) + if x is None: + return None + else: + return (x, y, 1, x*y % p) + +## These are functions for manipulating the private key. + +def secret_expand(secret): + if len(secret) != 32: + raise Exception("Bad size of private key") + h = sha512(secret) + a = int.from_bytes(h[:32], "little") + a &= (1 << 254) - 8 + a |= (1 << 254) + return (a, h[32:]) + +def secret_to_public(secret): + (a, dummy) = secret_expand(secret) + return point_compress(point_mul(a, G)) + + + + + + + + + + + + + +Josefsson & Liusvaara Informational [Page 22] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +## The signature function works as below. + +def sign(secret, msg): + a, prefix = secret_expand(secret) + A = point_compress(point_mul(a, G)) + r = sha512_modq(prefix + msg) + R = point_mul(r, G) + Rs = point_compress(R) + h = sha512_modq(Rs + A + msg) + s = (r + h * a) % q + return Rs + int.to_bytes(s, 32, "little") + +## And finally the verification function. + +def verify(public, msg, signature): + if len(public) != 32: + raise Exception("Bad public key length") + if len(signature) != 64: + Exception("Bad signature length") + A = point_decompress(public) + if not A: + return False + Rs = signature[:32] + R = point_decompress(Rs) + if not R: + return False + s = int.from_bytes(signature[32:], "little") + if s >= q: return False + h = sha512_modq(Rs + public + msg) + sB = point_mul(s, G) + hA = point_mul(h, A) + return point_equal(sB, point_add(R, hA)) + +7. Test Vectors + + This section contains test vectors for Ed25519ph, Ed25519ctx, + Ed448ph, Ed25519, and Ed448. + + Each section contains a sequence of test vectors. The octets are hex + encoded, and whitespace is inserted for readability. Ed25519, + Ed25519ctx, and Ed25519ph private and public keys are 32 octets; + signatures are 64 octets. Ed448 and Ed448ph private and public keys + are 57 octets; signatures are 114 octets. Messages are of arbitrary + length. If the context is non-empty, it is given as 1-255 octets. + + + + + + + +Josefsson & Liusvaara Informational [Page 23] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +7.1. Test Vectors for Ed25519 + + These test vectors are taken from [ED25519-TEST-VECTORS] (but we + removed the public key as a suffix of the private key and removed the + message from the signature) and [ED25519-LIBGCRYPT-TEST-VECTORS]. + + -----TEST 1 + + ALGORITHM: + Ed25519 + + SECRET KEY: + 9d61b19deffd5a60ba844af492ec2cc4 + 4449c5697b326919703bac031cae7f60 + + PUBLIC KEY: + d75a980182b10ab7d54bfed3c964073a + 0ee172f3daa62325af021a68f707511a + + MESSAGE (length 0 bytes): + + SIGNATURE: + e5564300c360ac729086e2cc806e828a + 84877f1eb8e5d974d873e06522490155 + 5fb8821590a33bacc61e39701cf9b46b + d25bf5f0595bbe24655141438e7a100b + + -----TEST 2 + + ALGORITHM: + Ed25519 + + SECRET KEY: + 4ccd089b28ff96da9db6c346ec114e0f + 5b8a319f35aba624da8cf6ed4fb8a6fb + + PUBLIC KEY: + 3d4017c3e843895a92b70aa74d1b7ebc + 9c982ccf2ec4968cc0cd55f12af4660c + + MESSAGE (length 1 byte): + 72 + + SIGNATURE: + 92a009a9f0d4cab8720e820b5f642540 + a2b27b5416503f8fb3762223ebdb69da + 085ac1e43e15996e458f3613d0f11d8c + 387b2eaeb4302aeeb00d291612bb0c00 + + + +Josefsson & Liusvaara Informational [Page 24] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + -----TEST 3 + + ALGORITHM: + Ed25519 + + SECRET KEY: + c5aa8df43f9f837bedb7442f31dcb7b1 + 66d38535076f094b85ce3a2e0b4458f7 + + PUBLIC KEY: + fc51cd8e6218a1a38da47ed00230f058 + 0816ed13ba3303ac5deb911548908025 + + MESSAGE (length 2 bytes): + af82 + + SIGNATURE: + 6291d657deec24024827e69c3abe01a3 + 0ce548a284743a445e3680d7db5ac3ac + 18ff9b538d16f290ae67f760984dc659 + 4a7c15e9716ed28dc027beceea1ec40a + + -----TEST 1024 + + ALGORITHM: + Ed25519 + + SECRET KEY: + f5e5767cf153319517630f226876b86c + 8160cc583bc013744c6bf255f5cc0ee5 + + PUBLIC KEY: + 278117fc144c72340f67d0f2316e8386 + ceffbf2b2428c9c51fef7c597f1d426e + + MESSAGE (length 1023 bytes): + 08b8b2b733424243760fe426a4b54908 + 632110a66c2f6591eabd3345e3e4eb98 + fa6e264bf09efe12ee50f8f54e9f77b1 + e355f6c50544e23fb1433ddf73be84d8 + 79de7c0046dc4996d9e773f4bc9efe57 + 38829adb26c81b37c93a1b270b20329d + 658675fc6ea534e0810a4432826bf58c + 941efb65d57a338bbd2e26640f89ffbc + 1a858efcb8550ee3a5e1998bd177e93a + 7363c344fe6b199ee5d02e82d522c4fe + ba15452f80288a821a579116ec6dad2b + 3b310da903401aa62100ab5d1a36553e + + + +Josefsson & Liusvaara Informational [Page 25] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + 06203b33890cc9b832f79ef80560ccb9 + a39ce767967ed628c6ad573cb116dbef + efd75499da96bd68a8a97b928a8bbc10 + 3b6621fcde2beca1231d206be6cd9ec7 + aff6f6c94fcd7204ed3455c68c83f4a4 + 1da4af2b74ef5c53f1d8ac70bdcb7ed1 + 85ce81bd84359d44254d95629e9855a9 + 4a7c1958d1f8ada5d0532ed8a5aa3fb2 + d17ba70eb6248e594e1a2297acbbb39d + 502f1a8c6eb6f1ce22b3de1a1f40cc24 + 554119a831a9aad6079cad88425de6bd + e1a9187ebb6092cf67bf2b13fd65f270 + 88d78b7e883c8759d2c4f5c65adb7553 + 878ad575f9fad878e80a0c9ba63bcbcc + 2732e69485bbc9c90bfbd62481d9089b + eccf80cfe2df16a2cf65bd92dd597b07 + 07e0917af48bbb75fed413d238f5555a + 7a569d80c3414a8d0859dc65a46128ba + b27af87a71314f318c782b23ebfe808b + 82b0ce26401d2e22f04d83d1255dc51a + ddd3b75a2b1ae0784504df543af8969b + e3ea7082ff7fc9888c144da2af58429e + c96031dbcad3dad9af0dcbaaaf268cb8 + fcffead94f3c7ca495e056a9b47acdb7 + 51fb73e666c6c655ade8297297d07ad1 + ba5e43f1bca32301651339e22904cc8c + 42f58c30c04aafdb038dda0847dd988d + cda6f3bfd15c4b4c4525004aa06eeff8 + ca61783aacec57fb3d1f92b0fe2fd1a8 + 5f6724517b65e614ad6808d6f6ee34df + f7310fdc82aebfd904b01e1dc54b2927 + 094b2db68d6f903b68401adebf5a7e08 + d78ff4ef5d63653a65040cf9bfd4aca7 + 984a74d37145986780fc0b16ac451649 + de6188a7dbdf191f64b5fc5e2ab47b57 + f7f7276cd419c17a3ca8e1b939ae49e4 + 88acba6b965610b5480109c8b17b80e1 + b7b750dfc7598d5d5011fd2dcc5600a3 + 2ef5b52a1ecc820e308aa342721aac09 + 43bf6686b64b2579376504ccc493d97e + 6aed3fb0f9cd71a43dd497f01f17c0e2 + cb3797aa2a2f256656168e6c496afc5f + b93246f6b1116398a346f1a641f3b041 + e989f7914f90cc2c7fff357876e506b5 + 0d334ba77c225bc307ba537152f3f161 + 0e4eafe595f6d9d90d11faa933a15ef1 + 369546868a7f3a45a96768d40fd9d034 + 12c091c6315cf4fde7cb68606937380d + + + +Josefsson & Liusvaara Informational [Page 26] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + b2eaaa707b4c4185c32eddcdd306705e + 4dc1ffc872eeee475a64dfac86aba41c + 0618983f8741c5ef68d3a101e8a3b8ca + c60c905c15fc910840b94c00a0b9d0 + + SIGNATURE: + 0aab4c900501b3e24d7cdf4663326a3a + 87df5e4843b2cbdb67cbf6e460fec350 + aa5371b1508f9f4528ecea23c436d94b + 5e8fcd4f681e30a6ac00a9704a188a03 + + -----TEST SHA(abc) + + ALGORITHM: + Ed25519 + + SECRET KEY: + 833fe62409237b9d62ec77587520911e + 9a759cec1d19755b7da901b96dca3d42 + + PUBLIC KEY: + ec172b93ad5e563bf4932c70e1245034 + c35467ef2efd4d64ebf819683467e2bf + + MESSAGE (length 64 bytes): + ddaf35a193617abacc417349ae204131 + 12e6fa4e89a97ea20a9eeee64b55d39a + 2192992a274fc1a836ba3c23a3feebbd + 454d4423643ce80e2a9ac94fa54ca49f + + SIGNATURE: + dc2a4459e7369633a52b1bf277839a00 + 201009a3efbf3ecb69bea2186c26b589 + 09351fc9ac90b3ecfdfbc7c66431e030 + 3dca179c138ac17ad9bef1177331a704 + ----- + +7.2. Test Vectors for Ed25519ctx + + -----foo + + ALGORITHM: + Ed25519ctx + + SECRET KEY: + 0305334e381af78f141cb666f6199f57 + bc3495335a256a95bd2a55bf546663f6 + + + + +Josefsson & Liusvaara Informational [Page 27] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + PUBLIC KEY: + dfc9425e4f968f7f0c29f0259cf5f9ae + d6851c2bb4ad8bfb860cfee0ab248292 + + MESSAGE (length 16 bytes): + f726936d19c800494e3fdaff20b276a8 + + CONTEXT: + 666f6f + + SIGNATURE: + 55a4cc2f70a54e04288c5f4cd1e45a7b + b520b36292911876cada7323198dd87a + 8b36950b95130022907a7fb7c4e9b2d5 + f6cca685a587b4b21f4b888e4e7edb0d + + -----bar + + ALGORITHM: + Ed25519ctx + + SECRET KEY: + 0305334e381af78f141cb666f6199f57 + bc3495335a256a95bd2a55bf546663f6 + + PUBLIC KEY: + dfc9425e4f968f7f0c29f0259cf5f9ae + d6851c2bb4ad8bfb860cfee0ab248292 + + MESSAGE (length 16 bytes): + f726936d19c800494e3fdaff20b276a8 + + CONTEXT: + 626172 + + SIGNATURE: + fc60d5872fc46b3aa69f8b5b4351d580 + 8f92bcc044606db097abab6dbcb1aee3 + 216c48e8b3b66431b5b186d1d28f8ee1 + 5a5ca2df6668346291c2043d4eb3e90d + + -----foo2 + + ALGORITHM: + Ed25519ctx + + + + + + +Josefsson & Liusvaara Informational [Page 28] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + SECRET KEY: + 0305334e381af78f141cb666f6199f57 + bc3495335a256a95bd2a55bf546663f6 + + PUBLIC KEY: + dfc9425e4f968f7f0c29f0259cf5f9ae + d6851c2bb4ad8bfb860cfee0ab248292 + + MESSAGE (length 16 bytes): + 508e9e6882b979fea900f62adceaca35 + + CONTEXT: + 666f6f + + SIGNATURE: + 8b70c1cc8310e1de20ac53ce28ae6e72 + 07f33c3295e03bb5c0732a1d20dc6490 + 8922a8b052cf99b7c4fe107a5abb5b2c + 4085ae75890d02df26269d8945f84b0b + + -----foo3 + + ALGORITHM: + Ed25519ctx + + SECRET KEY: + ab9c2853ce297ddab85c993b3ae14bca + d39b2c682beabc27d6d4eb20711d6560 + + PUBLIC KEY: + 0f1d1274943b91415889152e893d80e9 + 3275a1fc0b65fd71b4b0dda10ad7d772 + + MESSAGE (length 16 bytes): + f726936d19c800494e3fdaff20b276a8 + + CONTEXT: + 666f6f + + SIGNATURE: + 21655b5f1aa965996b3f97b3c849eafb + a922a0a62992f73b3d1b73106a84ad85 + e9b86a7b6005ea868337ff2d20a7f5fb + d4cd10b0be49a68da2b2e0dc0ad8960f + ----- + + + + + + +Josefsson & Liusvaara Informational [Page 29] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +7.3. Test Vectors for Ed25519ph + + -----TEST abc + + ALGORITHM: + Ed25519ph + + SECRET KEY: + 833fe62409237b9d62ec77587520911e + 9a759cec1d19755b7da901b96dca3d42 + + PUBLIC KEY: + ec172b93ad5e563bf4932c70e1245034 + c35467ef2efd4d64ebf819683467e2bf + + MESSAGE (length 3 bytes): + 616263 + + SIGNATURE: + 98a70222f0b8121aa9d30f813d683f80 + 9e462b469c7ff87639499bb94e6dae41 + 31f85042463c2a355a2003d062adf5aa + a10b8c61e636062aaad11c2a26083406 + ----- + +7.4. Test Vectors for Ed448 + + -----Blank + + ALGORITHM: + Ed448 + + SECRET KEY: + 6c82a562cb808d10d632be89c8513ebf + 6c929f34ddfa8c9f63c9960ef6e348a3 + 528c8a3fcc2f044e39a3fc5b94492f8f + 032e7549a20098f95b + + PUBLIC KEY: + 5fd7449b59b461fd2ce787ec616ad46a + 1da1342485a70e1f8a0ea75d80e96778 + edf124769b46c7061bd6783df1e50f6c + d1fa1abeafe8256180 + + MESSAGE (length 0 bytes): + + + + + + +Josefsson & Liusvaara Informational [Page 30] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + SIGNATURE: + 533a37f6bbe457251f023c0d88f976ae + 2dfb504a843e34d2074fd823d41a591f + 2b233f034f628281f2fd7a22ddd47d78 + 28c59bd0a21bfd3980ff0d2028d4b18a + 9df63e006c5d1c2d345b925d8dc00b41 + 04852db99ac5c7cdda8530a113a0f4db + b61149f05a7363268c71d95808ff2e65 + 2600 + + -----1 octet + + ALGORITHM: + Ed448 + + SECRET KEY: + c4eab05d357007c632f3dbb48489924d + 552b08fe0c353a0d4a1f00acda2c463a + fbea67c5e8d2877c5e3bc397a659949e + f8021e954e0a12274e + + PUBLIC KEY: + 43ba28f430cdff456ae531545f7ecd0a + c834a55d9358c0372bfa0c6c6798c086 + 6aea01eb00742802b8438ea4cb82169c + 235160627b4c3a9480 + + MESSAGE (length 1 byte): + 03 + + SIGNATURE: + 26b8f91727bd62897af15e41eb43c377 + efb9c610d48f2335cb0bd0087810f435 + 2541b143c4b981b7e18f62de8ccdf633 + fc1bf037ab7cd779805e0dbcc0aae1cb + cee1afb2e027df36bc04dcecbf154336 + c19f0af7e0a6472905e799f1953d2a0f + f3348ab21aa4adafd1d234441cf807c0 + 3a00 + + -----1 octet (with context) + + ALGORITHM: + Ed448 + + + + + + + +Josefsson & Liusvaara Informational [Page 31] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + SECRET KEY: + c4eab05d357007c632f3dbb48489924d + 552b08fe0c353a0d4a1f00acda2c463a + fbea67c5e8d2877c5e3bc397a659949e + f8021e954e0a12274e + + PUBLIC KEY: + 43ba28f430cdff456ae531545f7ecd0a + c834a55d9358c0372bfa0c6c6798c086 + 6aea01eb00742802b8438ea4cb82169c + 235160627b4c3a9480 + + MESSAGE (length 1 byte): + 03 + + CONTEXT: + 666f6f + + SIGNATURE: + d4f8f6131770dd46f40867d6fd5d5055 + de43541f8c5e35abbcd001b32a89f7d2 + 151f7647f11d8ca2ae279fb842d60721 + 7fce6e042f6815ea000c85741de5c8da + 1144a6a1aba7f96de42505d7a7298524 + fda538fccbbb754f578c1cad10d54d0d + 5428407e85dcbc98a49155c13764e66c + 3c00 + + -----11 octets + + ALGORITHM: + Ed448 + + SECRET KEY: + cd23d24f714274e744343237b93290f5 + 11f6425f98e64459ff203e8985083ffd + f60500553abc0e05cd02184bdb89c4cc + d67e187951267eb328 + + PUBLIC KEY: + dcea9e78f35a1bf3499a831b10b86c90 + aac01cd84b67a0109b55a36e9328b1e3 + 65fce161d71ce7131a543ea4cb5f7e9f + 1d8b00696447001400 + + MESSAGE (length 11 bytes): + 0c3e544074ec63b0265e0c + + + + +Josefsson & Liusvaara Informational [Page 32] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + SIGNATURE: + 1f0a8888ce25e8d458a21130879b840a + 9089d999aaba039eaf3e3afa090a09d3 + 89dba82c4ff2ae8ac5cdfb7c55e94d5d + 961a29fe0109941e00b8dbdeea6d3b05 + 1068df7254c0cdc129cbe62db2dc957d + bb47b51fd3f213fb8698f064774250a5 + 028961c9bf8ffd973fe5d5c206492b14 + 0e00 + + -----12 octets + + ALGORITHM: + Ed448 + + SECRET KEY: + 258cdd4ada32ed9c9ff54e63756ae582 + fb8fab2ac721f2c8e676a72768513d93 + 9f63dddb55609133f29adf86ec9929dc + cb52c1c5fd2ff7e21b + + PUBLIC KEY: + 3ba16da0c6f2cc1f30187740756f5e79 + 8d6bc5fc015d7c63cc9510ee3fd44adc + 24d8e968b6e46e6f94d19b945361726b + d75e149ef09817f580 + + MESSAGE (length 12 bytes): + 64a65f3cdedcdd66811e2915 + + SIGNATURE: + 7eeeab7c4e50fb799b418ee5e3197ff6 + bf15d43a14c34389b59dd1a7b1b85b4a + e90438aca634bea45e3a2695f1270f07 + fdcdf7c62b8efeaf00b45c2c96ba457e + b1a8bf075a3db28e5c24f6b923ed4ad7 + 47c3c9e03c7079efb87cb110d3a99861 + e72003cbae6d6b8b827e4e6c143064ff + 3c00 + + -----13 octets + + ALGORITHM: + Ed448 + + + + + + + +Josefsson & Liusvaara Informational [Page 33] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + SECRET KEY: + 7ef4e84544236752fbb56b8f31a23a10 + e42814f5f55ca037cdcc11c64c9a3b29 + 49c1bb60700314611732a6c2fea98eeb + c0266a11a93970100e + + PUBLIC KEY: + b3da079b0aa493a5772029f0467baebe + e5a8112d9d3a22532361da294f7bb381 + 5c5dc59e176b4d9f381ca0938e13c6c0 + 7b174be65dfa578e80 + + MESSAGE (length 13 bytes): + 64a65f3cdedcdd66811e2915e7 + + SIGNATURE: + 6a12066f55331b6c22acd5d5bfc5d712 + 28fbda80ae8dec26bdd306743c5027cb + 4890810c162c027468675ecf645a8317 + 6c0d7323a2ccde2d80efe5a1268e8aca + 1d6fbc194d3f77c44986eb4ab4177919 + ad8bec33eb47bbb5fc6e28196fd1caf5 + 6b4e7e0ba5519234d047155ac727a105 + 3100 + + -----64 octets + + ALGORITHM: + Ed448 + + SECRET KEY: + d65df341ad13e008567688baedda8e9d + cdc17dc024974ea5b4227b6530e339bf + f21f99e68ca6968f3cca6dfe0fb9f4fa + b4fa135d5542ea3f01 + + PUBLIC KEY: + df9705f58edbab802c7f8363cfe5560a + b1c6132c20a9f1dd163483a26f8ac53a + 39d6808bf4a1dfbd261b099bb03b3fb5 + 0906cb28bd8a081f00 + + MESSAGE (length 64 bytes): + bd0f6a3747cd561bdddf4640a332461a + 4a30a12a434cd0bf40d766d9c6d458e5 + 512204a30c17d1f50b5079631f64eb31 + 12182da3005835461113718d1a5ef944 + + + + +Josefsson & Liusvaara Informational [Page 34] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + SIGNATURE: + 554bc2480860b49eab8532d2a533b7d5 + 78ef473eeb58c98bb2d0e1ce488a98b1 + 8dfde9b9b90775e67f47d4a1c3482058 + efc9f40d2ca033a0801b63d45b3b722e + f552bad3b4ccb667da350192b61c508c + f7b6b5adadc2c8d9a446ef003fb05cba + 5f30e88e36ec2703b349ca229c267083 + 3900 + + -----256 octets + + ALGORITHM: + Ed448 + + SECRET KEY: + 2ec5fe3c17045abdb136a5e6a913e32a + b75ae68b53d2fc149b77e504132d3756 + 9b7e766ba74a19bd6162343a21c8590a + a9cebca9014c636df5 + + PUBLIC KEY: + 79756f014dcfe2079f5dd9e718be4171 + e2ef2486a08f25186f6bff43a9936b9b + fe12402b08ae65798a3d81e22e9ec80e + 7690862ef3d4ed3a00 + + MESSAGE (length 256 bytes): + 15777532b0bdd0d1389f636c5f6b9ba7 + 34c90af572877e2d272dd078aa1e567c + fa80e12928bb542330e8409f31745041 + 07ecd5efac61ae7504dabe2a602ede89 + e5cca6257a7c77e27a702b3ae39fc769 + fc54f2395ae6a1178cab4738e543072f + c1c177fe71e92e25bf03e4ecb72f47b6 + 4d0465aaea4c7fad372536c8ba516a60 + 39c3c2a39f0e4d832be432dfa9a706a6 + e5c7e19f397964ca4258002f7c0541b5 + 90316dbc5622b6b2a6fe7a4abffd9610 + 5eca76ea7b98816af0748c10df048ce0 + 12d901015a51f189f3888145c03650aa + 23ce894c3bd889e030d565071c59f409 + a9981b51878fd6fc110624dcbcde0bf7 + a69ccce38fabdf86f3bef6044819de11 + + + + + + + +Josefsson & Liusvaara Informational [Page 35] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + SIGNATURE: + c650ddbb0601c19ca11439e1640dd931 + f43c518ea5bea70d3dcde5f4191fe53f + 00cf966546b72bcc7d58be2b9badef28 + 743954e3a44a23f880e8d4f1cfce2d7a + 61452d26da05896f0a50da66a239a8a1 + 88b6d825b3305ad77b73fbac0836ecc6 + 0987fd08527c1a8e80d5823e65cafe2a + 3d00 + + -----1023 octets + + ALGORITHM: + Ed448 + + SECRET KEY: + 872d093780f5d3730df7c212664b37b8 + a0f24f56810daa8382cd4fa3f77634ec + 44dc54f1c2ed9bea86fafb7632d8be19 + 9ea165f5ad55dd9ce8 + + PUBLIC KEY: + a81b2e8a70a5ac94ffdbcc9badfc3feb + 0801f258578bb114ad44ece1ec0e799d + a08effb81c5d685c0c56f64eecaef8cd + f11cc38737838cf400 + + MESSAGE (length 1023 bytes): + 6ddf802e1aae4986935f7f981ba3f035 + 1d6273c0a0c22c9c0e8339168e675412 + a3debfaf435ed651558007db4384b650 + fcc07e3b586a27a4f7a00ac8a6fec2cd + 86ae4bf1570c41e6a40c931db27b2faa + 15a8cedd52cff7362c4e6e23daec0fbc + 3a79b6806e316efcc7b68119bf46bc76 + a26067a53f296dafdbdc11c77f7777e9 + 72660cf4b6a9b369a6665f02e0cc9b6e + dfad136b4fabe723d2813db3136cfde9 + b6d044322fee2947952e031b73ab5c60 + 3349b307bdc27bc6cb8b8bbd7bd32321 + 9b8033a581b59eadebb09b3c4f3d2277 + d4f0343624acc817804728b25ab79717 + 2b4c5c21a22f9c7839d64300232eb66e + 53f31c723fa37fe387c7d3e50bdf9813 + a30e5bb12cf4cd930c40cfb4e1fc6225 + 92a49588794494d56d24ea4b40c89fc0 + 596cc9ebb961c8cb10adde976a5d602b + 1c3f85b9b9a001ed3c6a4d3b1437f520 + + + +Josefsson & Liusvaara Informational [Page 36] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + 96cd1956d042a597d561a596ecd3d173 + 5a8d570ea0ec27225a2c4aaff26306d1 + 526c1af3ca6d9cf5a2c98f47e1c46db9 + a33234cfd4d81f2c98538a09ebe76998 + d0d8fd25997c7d255c6d66ece6fa56f1 + 1144950f027795e653008f4bd7ca2dee + 85d8e90f3dc315130ce2a00375a318c7 + c3d97be2c8ce5b6db41a6254ff264fa6 + 155baee3b0773c0f497c573f19bb4f42 + 40281f0b1f4f7be857a4e59d416c06b4 + c50fa09e1810ddc6b1467baeac5a3668 + d11b6ecaa901440016f389f80acc4db9 + 77025e7f5924388c7e340a732e554440 + e76570f8dd71b7d640b3450d1fd5f041 + 0a18f9a3494f707c717b79b4bf75c984 + 00b096b21653b5d217cf3565c9597456 + f70703497a078763829bc01bb1cbc8fa + 04eadc9a6e3f6699587a9e75c94e5bab + 0036e0b2e711392cff0047d0d6b05bd2 + a588bc109718954259f1d86678a579a3 + 120f19cfb2963f177aeb70f2d4844826 + 262e51b80271272068ef5b3856fa8535 + aa2a88b2d41f2a0e2fda7624c2850272 + ac4a2f561f8f2f7a318bfd5caf969614 + 9e4ac824ad3460538fdc25421beec2cc + 6818162d06bbed0c40a387192349db67 + a118bada6cd5ab0140ee273204f628aa + d1c135f770279a651e24d8c14d75a605 + 9d76b96a6fd857def5e0b354b27ab937 + a5815d16b5fae407ff18222c6d1ed263 + be68c95f32d908bd895cd76207ae7264 + 87567f9a67dad79abec316f683b17f2d + 02bf07e0ac8b5bc6162cf94697b3c27c + d1fea49b27f23ba2901871962506520c + 392da8b6ad0d99f7013fbc06c2c17a56 + 9500c8a7696481c1cd33e9b14e40b82e + 79a5f5db82571ba97bae3ad3e0479515 + bb0e2b0f3bfcd1fd33034efc6245eddd + 7ee2086ddae2600d8ca73e214e8c2b0b + db2b047c6a464a562ed77b73d2d841c4 + b34973551257713b753632efba348169 + abc90a68f42611a40126d7cb21b58695 + 568186f7e569d2ff0f9e745d0487dd2e + b997cafc5abf9dd102e62ff66cba87 + + + + + + + +Josefsson & Liusvaara Informational [Page 37] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + SIGNATURE: + e301345a41a39a4d72fff8df69c98075 + a0cc082b802fc9b2b6bc503f926b65bd + df7f4c8f1cb49f6396afc8a70abe6d8a + ef0db478d4c6b2970076c6a0484fe76d + 76b3a97625d79f1ce240e7c576750d29 + 5528286f719b413de9ada3e8eb78ed57 + 3603ce30d8bb761785dc30dbc320869e + 1a00 + ----- + +7.5. Test Vectors for Ed448ph + + -----TEST abc + + ALGORITHM: + Ed448ph + + SECRET KEY: + 833fe62409237b9d62ec77587520911e + 9a759cec1d19755b7da901b96dca3d42 + ef7822e0d5104127dc05d6dbefde69e3 + ab2cec7c867c6e2c49 + + PUBLIC KEY: + 259b71c19f83ef77a7abd26524cbdb31 + 61b590a48f7d17de3ee0ba9c52beb743 + c09428a131d6b1b57303d90d8132c276 + d5ed3d5d01c0f53880 + + MESSAGE (length 3 bytes): + 616263 + + SIGNATURE: + 822f6901f7480f3d5f562c592994d969 + 3602875614483256505600bbc281ae38 + 1f54d6bce2ea911574932f52a4e6cadd + 78769375ec3ffd1b801a0d9b3f4030cd + 433964b6457ea39476511214f97469b5 + 7dd32dbc560a9a94d00bff07620464a3 + ad203df7dc7ce360c3cd3696d9d9fab9 + 0f00 + + + + + + + + + +Josefsson & Liusvaara Informational [Page 38] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + -----TEST abc (with context) + + ALGORITHM: + Ed448ph + + SECRET KEY: + 833fe62409237b9d62ec77587520911e + 9a759cec1d19755b7da901b96dca3d42 + ef7822e0d5104127dc05d6dbefde69e3 + ab2cec7c867c6e2c49 + + PUBLIC KEY: + 259b71c19f83ef77a7abd26524cbdb31 + 61b590a48f7d17de3ee0ba9c52beb743 + c09428a131d6b1b57303d90d8132c276 + d5ed3d5d01c0f53880 + + MESSAGE (length 3 bytes): + 616263 + + CONTEXT: + 666f6f + + SIGNATURE: + c32299d46ec8ff02b54540982814dce9 + a05812f81962b649d528095916a2aa48 + 1065b1580423ef927ecf0af5888f90da + 0f6a9a85ad5dc3f280d91224ba9911a3 + 653d00e484e2ce232521481c8658df30 + 4bb7745a73514cdb9bf3e15784ab7128 + 4f8d0704a608c54a6b62d97beb511d13 + 2100 + ----- + + + + + + + + + + + + + + + + + + +Josefsson & Liusvaara Informational [Page 39] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +8. Security Considerations + +8.1. Side-Channel Leaks + + For implementations performing signatures, secrecy of the private key + is fundamental. It is possible to protect against some side-channel + attacks by ensuring that the implementation executes exactly the same + sequence of instructions and performs exactly the same memory + accesses, for any value of the private key. + + To make an implementation side-channel silent in this way, the modulo + p arithmetic must not use any data-dependent branches, e.g., related + to carry propagation. Side-channel silent point addition is + straightforward, thanks to the unified formulas. + + Scalar multiplication, multiplying a point by an integer, needs some + additional effort to implement in a side-channel silent manner. One + simple approach is to implement a side-channel silent conditional + assignment, and use it together with the binary algorithm to examine + one bit of the integer at a time. + + Compared to other signature schemes, avoiding data-dependent branches + is easier due to side-channel silent modulo p arithmetic being easier + (with recommended curves) and having complete addition formulas + instead of having a number of special cases. + + Note that the example implementations in this document do not attempt + to be side-channel silent. + +8.2. Randomness Considerations + + EdDSA signatures are deterministic. This protects against attacks + arising from signing with bad randomness; the effects of which can, + depending on the algorithm, range up to full private key compromise. + It can be surprisingly hard to ensure good-quality random numbers, + and there have been numerous security failures relating to this. + + Obviously, private key generation requires randomness, but due to the + fact that the private key is hashed before use, a few missing bits of + entropy doesn't constitute a disaster. + + The basic signature verification is also deterministic. However, + some speedups by verifying multiple signatures at once do require + random numbers. + + + + + + + +Josefsson & Liusvaara Informational [Page 40] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +8.3. Use of Contexts + + Contexts can be used to separate uses of the protocol between + different protocols (which is very hard to reliably do otherwise) and + between different uses within the same protocol. However, the + following SHOULD be kept in mind when using this facility: + + The context SHOULD be a constant string specified by the protocol + using it. It SHOULD NOT incorporate variable elements from the + message itself. + + Contexts SHOULD NOT be used opportunistically, as that kind of use + is very error prone. If contexts are used, one SHOULD require all + signature schemes available for use in that purpose support + contexts. + + Contexts are an extra input, which percolate out of APIs; as such, + even if the signature scheme supports contexts, those may not be + available for use. This problem is compounded by the fact that + many times the application is not invoking the signing and + verification functions directly but via some other protocol. + +8.4. Signature Malleability + + Some systems assume signatures are not malleable: that is, given a + valid signature for some message under some key, the attacker can't + produce another valid signature for the same message and key. + + Ed25519 and Ed448 signatures are not malleable due to the + verification check that decoded S is smaller than l. Without this + check, one can add a multiple of l into a scalar part and still pass + signature verification, resulting in malleable signatures. + +8.5. Choice of Signature Primitive + + Ed25519 and Ed25519ph have a nominal strength of 128 bits, whereas + Ed448 and Ed448ph have the strength of 224. While the lower strength + is sufficient for the foreseeable future, the higher level brings + some defense against possible future cryptographic advances. Both + are demolished by quantum computers just about the same. + + The Ed25519ph and Ed448ph variants are prehashed. This is mainly + useful for interoperation with legacy APIs, since in most of the + cases, either the amount of data signed is not large or the protocol + is in the position to do digesting in ways better than just + prehashing (e.g., tree hashing or splitting the data). The + + + + + +Josefsson & Liusvaara Informational [Page 41] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + prehashing also makes the functions greatly more vulnerable to + weaknesses in hash functions used. These variants SHOULD NOT be + used. + + Ed25519ctx and Ed448 have contexts. However, this is balanced by the + problems noted in Section 8.3 about contexts. + + On the implementation front, Ed25519 is widely implemented and has + many high-quality implementations. The others have much worse + support. + + In summary, if a high 128-bit security level is enough, use of + Ed25519 is RECOMMENDED; otherwise, Ed448 is RECOMMENDED. + +8.6. Mixing Different Prehashes + + The schemes described in this document are designed to be resistant + to mixing prehashes. That is, it is infeasible to find a message + that verifies using the same signature under another scheme, even if + the original signed message was chosen. Thus, one can use the same + key pair for Ed25519, Ed25519ctx, and Ed25519ph and correspondingly + with Ed448 and Ed448ph. + + The "SigEd25519 no Ed25519 collisions" constant is chosen to be a + textual string such that it does not decode as a point. Because the + inner hash input in the Ed25519 signature always starts with a valid + point, there is no way trivial collision can be constructed. In the + case of seed hash, trivial collisions are so unlikely, even with an + attacker choosing all inputs, that it is much more probable that + something else goes catastrophically wrong. + +8.7. Signing Large Amounts of Data at Once + + Avoid signing large amounts of data at once (where "large" depends on + the expected verifier). In particular, unless the underlying + protocol does not require it, the receiver MUST buffer the entire + message (or enough information to reconstruct it, e.g., compressed or + encrypted version) to be verified. + + This is needed because most of the time, it is unsafe to process + unverified data, and verifying the signature makes a pass through the + whole message, causing ultimately at least two passes through. + + As an API consideration, this means that any Initialize Update + Finalize (IFU) verification interface is prone to misuse. + + + + + + +Josefsson & Liusvaara Informational [Page 42] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + It is a bad idea to modify Ed25519 or Ed448 signing to be able to + create valid Ed25519/Ed448 signatures using an IUF interface with + only constant buffering. Pretty much any error in such would cause + catastrophic security failure. + +8.8. Multiplication by Cofactor in Verification + + The given verification formulas for both Ed25519 and Ed448 multiply + points by the cofactor. While this is not strictly necessary for + security (in fact, any signature that meets the non-multiplied + equation will satisfy the multiplied one), in some applications it is + undesirable for implementations to disagree about the exact set of + valid signatures. Such disagreements could open up, e.g., + fingerprinting attacks. + +8.9. Use of SHAKE256 as a Hash Function + + Ed448 uses SHAKE256 as a hash function, even if SHAKE256 is + specifically defined not to be a hash function. + + The first potentially troublesome property is that shorter outputs + are prefixes of longer ones. This is acceptable because output + lengths are fixed. + + The second potentially troublesome property is failing to meet + standard hash security notions (especially with preimages). However, + the estimated 256-bit security level against collisions and preimages + is sufficient to pair with a 224-bit level elliptic curve. + +9. References + +9.1. Normative References + + [FIPS202] National Institute of Standards and Technology, "SHA-3 + Standard: Permutation-Based Hash and Extendable-Output + Functions", FIPS PUB 202, August 2015, + . + + [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate + Requirement Levels", BCP 14, RFC 2119, DOI + 10.17487/RFC2119, March 1997, + . + + [RFC6234] Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms + (SHA and SHA-based HMAC and HKDF)", RFC 6234, + DOI 10.17487/RFC6234, May 2011, + . + + + + +Josefsson & Liusvaara Informational [Page 43] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + [RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves + for Security", RFC 7748, DOI 10.17487/RFC7748, January + 2016, . + +9.2. Informative References + + [CURVE25519] + Bernstein, D., "Curve25519: new Diffie-Hellman speed + records", DOI 10.1007/11745853_14, February 2006, + . + + [ED25519-LIBGCRYPT-TEST-VECTORS] + Koch, W., "Ed25519 Libgcrypt test vectors", July 2014, + . + + [ED25519-TEST-VECTORS] + Bernstein, D., Duif, N., Lange, T., Schwabe, P., and B. + Yang, "Ed25519 test vectors", July 2011, + . + + [ED448] Hamburg, M., "Ed448-Goldilocks, a new elliptic curve", + June 2015, . + + [EDDSA] Bernstein, D., Duif, N., Lange, T., Schwabe, P., and B. + Yang, "High-speed high-security signatures", + DOI 10.1007/978-3-642-23951-9_9, September 2011, + . + + [EDDSA2] Bernstein, D., Josefsson, S., Lange, T., Schwabe, P., and + B. Yang, "EdDSA for more curves", July 2015, + . + + [Edwards-revisited] + Hisil, H., Wong, K., Carter, G., and E. Dawson, "Twisted + Edwards Curves Revisited", + DOI 10.1007/978-3-540-89255-7_20, December 2008, + . + + [EFD-ADD] Bernstein, D. and T. Lange, "Projective coordinates for + Edwards curves", The 'add-2007-bl' addition formulas, + 2007, . + + + + + + +Josefsson & Liusvaara Informational [Page 44] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + [EFD-DBL] Bernstein, D. and T. Lange, "Projective coordinates for + Edwards curves", The 'dbl-2007-bl' doubling formulas, + 2007, . + + [EFD-TWISTED-ADD] + Hisil, H., Wong, K., Carter, G., and E. Dawson, "Extended + coordinates with a=-1 for twisted Edwards curves", The + 'add-2008-hwcd-3' addition formulas, December 2008, + . + + [EFD-TWISTED-DBL] + Hisil, H., Wong, K., Carter, G., and E. Dawson, "Extended + coordinates with a=-1 for twisted Edwards curves", The + 'dbl-2008-hwcd' doubling formulas, December 2008, + . + + [Faster-ECC] + Bernstein, D. and T. Lange, "Faster addition and doubling + on elliptic curves", DOI 10.1007/978-3-540-76900-2_3, + July 2007, . + + [RFC4086] Eastlake 3rd, D., Schiller, J., and S. Crocker, + "Randomness Requirements for Security", BCP 106, RFC 4086, + DOI 10.17487/RFC4086, June 2005, + . + + + + + + + + + + + + + + + + + + + + + + + +Josefsson & Liusvaara Informational [Page 45] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +Appendix A. Ed25519/Ed448 Python Library + + Below is an example implementation of Ed25519/Ed448 written in + Python; version 3.2 or higher is required. + + Note: This code is not intended for production. Although it should + produce correct results for every input, it is slow and makes no + attempt to avoid side-channel attacks. + +import hashlib; +import os; + +#Compute candidate square root of x modulo p, with p = 3 (mod 4). +def sqrt4k3(x,p): return pow(x,(p + 1)//4,p) + +#Compute candidate square root of x modulo p, with p = 5 (mod 8). +def sqrt8k5(x,p): + y = pow(x,(p+3)//8,p) + #If the square root exists, it is either y or y*2^(p-1)/4. + if (y * y) % p == x % p: return y + else: + z = pow(2,(p - 1)//4,p) + return (y * z) % p + +#Decode a hexadecimal string representation of the integer. +def hexi(s): return int.from_bytes(bytes.fromhex(s),byteorder="big") + +#Rotate a word x by b places to the left. +def rol(x,b): return ((x << b) | (x >> (64 - b))) & (2**64-1) + +#From little endian. +def from_le(s): return int.from_bytes(s, byteorder="little") + +#Do the SHA-3 state transform on state s. +def sha3_transform(s): + ROTATIONS = [0,1,62,28,27,36,44,6,55,20,3,10,43,25,39,41,45,15,\ + 21,8,18,2,61,56,14] + PERMUTATION = [1,6,9,22,14,20,2,12,13,19,23,15,4,24,21,8,16,5,3,\ + 18,17,11,7,10] + RC = [0x0000000000000001,0x0000000000008082,0x800000000000808a,\ + 0x8000000080008000,0x000000000000808b,0x0000000080000001,\ + 0x8000000080008081,0x8000000000008009,0x000000000000008a,\ + 0x0000000000000088,0x0000000080008009,0x000000008000000a,\ + 0x000000008000808b,0x800000000000008b,0x8000000000008089,\ + 0x8000000000008003,0x8000000000008002,0x8000000000000080,\ + 0x000000000000800a,0x800000008000000a,0x8000000080008081,\ + 0x8000000000008080,0x0000000080000001,0x8000000080008008] + + + + +Josefsson & Liusvaara Informational [Page 46] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + for rnd in range(0,24): + #AddColumnParity (Theta) + c = [0]*5; + d = [0]*5; + for i in range(0,25): c[i%5]^=s[i] + for i in range(0,5): d[i]=c[(i+4)%5]^rol(c[(i+1)%5],1) + for i in range(0,25): s[i]^=d[i%5] + #RotateWords (Rho) + for i in range(0,25): s[i]=rol(s[i],ROTATIONS[i]) + #PermuteWords (Pi) + t = s[PERMUTATION[0]] + for i in range(0,len(PERMUTATION)-1): + s[PERMUTATION[i]]=s[PERMUTATION[i+1]] + s[PERMUTATION[-1]]=t; + #NonlinearMixRows (Chi) + for i in range(0,25,5): + t=[s[i],s[i+1],s[i+2],s[i+3],s[i+4],s[i],s[i+1]] + for j in range(0,5): s[i+j]=t[j]^((~t[j+1])&(t[j+2])) + #AddRoundConstant (Iota) + s[0]^=RC[rnd] + +#Reinterpret octet array b to word array and XOR it to state s. +def reinterpret_to_words_and_xor(s,b): + for j in range(0,len(b)//8): + s[j]^=from_le(b[8*j:][:8]) + +#Reinterpret word array w to octet array and return it. +def reinterpret_to_octets(w): + mp=bytearray() + for j in range(0,len(w)): + mp+=w[j].to_bytes(8,byteorder="little") + return mp + + + + + + + + + + + + + + + + + + + +Josefsson & Liusvaara Informational [Page 47] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +#(semi-)generic SHA-3 implementation +def sha3_raw(msg,r_w,o_p,e_b): + r_b=8*r_w + s=[0]*25 + #Handle whole blocks. + idx=0 + blocks=len(msg)//r_b + for i in range(0,blocks): + reinterpret_to_words_and_xor(s,msg[idx:][:r_b]) + idx+=r_b + sha3_transform(s) + #Handle last block padding. + m=bytearray(msg[idx:]) + m.append(o_p) + while len(m) < r_b: m.append(0) + m[len(m)-1]|=128 + #Handle padded last block. + reinterpret_to_words_and_xor(s,m) + sha3_transform(s) + #Output. + out = bytearray() + while len(out)>((b-1)&7) + #Decode y. If this fails, fail. + y = self.base_field.frombytes(s,b) + if y is None: return (None,None) + #Try to recover x. If it does not exist, or if zero and xs + #are wrong, fail. + x=self.solve_x2(y).sqrt() + if x is None or (x.iszero() and xs!=x.sign()): + return (None,None) + #If sign of x isn't correct, flip it. + if x.sign()!=xs: x=-x + # Return the constructed point. + return (x,y) + def encode_base(self,b): + xp,yp=self.x/self.z,self.y/self.z + #Encode y. + s=bytearray(yp.tobytes(b)) + #Add sign bit of x to encoding. + if xp.sign()!=0: s[(b-1)//8]|=1<<(b-1)%8 + return s + + + +Josefsson & Liusvaara Informational [Page 50] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + def __mul__(self,x): + r=self.zero_elem() + s=self + while x > 0: + if (x%2)>0: + r=r+s + s=s.double() + x=x//2 + return r + #Check that two points are equal. + def __eq__(self,y): + #Need to check x1/z1 == x2/z2 and similarly for y, so cross + #multiply to eliminate divisions. + xn1=self.x*y.z + xn2=y.x*self.z + yn1=self.y*y.z + yn2=y.y*self.z + return xn1==xn2 and yn1==yn2 + #Check if two points are not equal. + def __ne__(self,y): return not (self==y) + +#A point on Edwards25519. +class Edwards25519Point(EdwardsPoint): + #Create a new point on the curve. + base_field=Field(1,2**255-19) + d=-base_field.make(121665)/base_field.make(121666) + f0=base_field.make(0) + f1=base_field.make(1) + xb=base_field.make(hexi("216936D3CD6E53FEC0A4E231FDD6DC5C692CC76"+\ + "09525A7B2C9562D608F25D51A")) + yb=base_field.make(hexi("666666666666666666666666666666666666666"+\ + "6666666666666666666666658")) + #The standard base point. + @staticmethod + def stdbase(): + return Edwards25519Point(Edwards25519Point.xb,\ + Edwards25519Point.yb) + def __init__(self,x,y): + #Check the point is actually on the curve. + if y*y-x*x!=self.f1+self.d*x*x*y*y: + raise ValueError("Invalid point") + self.initpoint(x, y) + self.t=x*y + #Decode a point representation. + def decode(self,s): + x,y=self.decode_base(s,256); + return Edwards25519Point(x, y) if x is not None else None + + + + +Josefsson & Liusvaara Informational [Page 51] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + #Encode a point representation. + def encode(self): + return self.encode_base(256) + #Construct a neutral point on this curve. + def zero_elem(self): + return Edwards25519Point(self.f0,self.f1) + #Solve for x^2. + def solve_x2(self,y): + return ((y*y-self.f1)/(self.d*y*y+self.f1)) + #Point addition. + def __add__(self,y): + #The formulas are from EFD. + tmp=self.zero_elem() + zcp=self.z*y.z + A=(self.y-self.x)*(y.y-y.x) + B=(self.y+self.x)*(y.y+y.x) + C=(self.d+self.d)*self.t*y.t + D=zcp+zcp + E,H=B-A,B+A + F,G=D-C,D+C + tmp.x,tmp.y,tmp.z,tmp.t=E*F,G*H,F*G,E*H + return tmp + #Point doubling. + def double(self): + #The formulas are from EFD (with assumption a=-1 propagated). + tmp=self.zero_elem() + A=self.x*self.x + B=self.y*self.y + Ch=self.z*self.z + C=Ch+Ch + H=A+B + xys=self.x+self.y + E=H-xys*xys + G=A-B + F=C+G + tmp.x,tmp.y,tmp.z,tmp.t=E*F,G*H,F*G,E*H + return tmp + #Order of basepoint. + def l(self): + return hexi("1000000000000000000000000000000014def9dea2f79cd"+\ + "65812631a5cf5d3ed") + #The logarithm of cofactor. + def c(self): return 3 + #The highest set bit + def n(self): return 254 + #The coding length + def b(self): return 256 + + + + +Josefsson & Liusvaara Informational [Page 52] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + #Validity check (for debugging) + def is_valid_point(self): + x,y,z,t=self.x,self.y,self.z,self.t + x2=x*x + y2=y*y + z2=z*z + lhs=(y2-x2)*z2 + rhs=z2*z2+self.d*x2*y2 + assert(lhs == rhs) + assert(t*z == x*y) + +#A point on Edwards448. +class Edwards448Point(EdwardsPoint): + #Create a new point on the curve. + base_field=Field(1,2**448-2**224-1) + d=base_field.make(-39081) + f0=base_field.make(0) + f1=base_field.make(1) + xb=base_field.make(hexi("4F1970C66BED0DED221D15A622BF36DA9E14657"+\ + "0470F1767EA6DE324A3D3A46412AE1AF72AB66511433B80E18B00938E26"+\ + "26A82BC70CC05E")) + yb=base_field.make(hexi("693F46716EB6BC248876203756C9C7624BEA737"+\ + "36CA3984087789C1E05A0C2D73AD3FF1CE67C39C4FDBD132C4ED7C8AD98"+\ + "08795BF230FA14")) + #The standard base point. + @staticmethod + def stdbase(): + return Edwards448Point(Edwards448Point.xb,Edwards448Point.yb) + def __init__(self,x,y): + #Check that the point is actually on the curve. + if y*y+x*x!=self.f1+self.d*x*x*y*y: + raise ValueError("Invalid point") + self.initpoint(x, y) + #Decode a point representation. + def decode(self,s): + x,y=self.decode_base(s,456); + return Edwards448Point(x, y) if x is not None else None + #Encode a point representation. + def encode(self): + return self.encode_base(456) + #Construct a neutral point on this curve. + def zero_elem(self): + return Edwards448Point(self.f0,self.f1) + #Solve for x^2. + def solve_x2(self,y): + return ((y*y-self.f1)/(self.d*y*y-self.f1)) + + + + + +Josefsson & Liusvaara Informational [Page 53] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + #Point addition. + def __add__(self,y): + #The formulas are from EFD. + tmp=self.zero_elem() + xcp,ycp,zcp=self.x*y.x,self.y*y.y,self.z*y.z + B=zcp*zcp + E=self.d*xcp*ycp + F,G=B-E,B+E + tmp.x=zcp*F*((self.x+self.y)*(y.x+y.y)-xcp-ycp) + tmp.y,tmp.z=zcp*G*(ycp-xcp),F*G + return tmp + #Point doubling. + def double(self): + #The formulas are from EFD. + tmp=self.zero_elem() + x1s,y1s,z1s=self.x*self.x,self.y*self.y,self.z*self.z + xys=self.x+self.y + F=x1s+y1s + J=F-(z1s+z1s) + tmp.x,tmp.y,tmp.z=(xys*xys-x1s-y1s)*J,F*(x1s-y1s),F*J + return tmp + #Order of basepoint. + def l(self): + return hexi("3ffffffffffffffffffffffffffffffffffffffffffffff"+\ + "fffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c2"+\ + "92ab5844f3") + #The logarithm of cofactor. + def c(self): return 2 + #The highest set bit. + def n(self): return 447 + #The coding length. + def b(self): return 456 + #Validity check (for debugging). + def is_valid_point(self): + x,y,z=self.x,self.y,self.z + x2=x*x + y2=y*y + z2=z*z + lhs=(x2+y2)*z2 + rhs=z2*z2+self.d*x2*y2 + assert(lhs == rhs) + + + + + + + + + + +Josefsson & Liusvaara Informational [Page 54] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +#Simple self-check. +def curve_self_check(point): + p=point + q=point.zero_elem() + z=q + l=p.l()+1 + p.is_valid_point() + q.is_valid_point() + for i in range(0,point.b()): + if (l>>i)&1 != 0: + q=q+p + q.is_valid_point() + p=p.double() + p.is_valid_point() + assert q.encode() == point.encode() + assert q.encode() != p.encode() + assert q.encode() != z.encode() + +#Simple self-check. +def self_check_curves(): + curve_self_check(Edwards25519Point.stdbase()) + curve_self_check(Edwards448Point.stdbase()) + +#PureEdDSA scheme. +#Limitation: only b mod 8 = 0 is handled. +class PureEdDSA: + #Create a new object. + def __init__(self,properties): + self.B=properties["B"] + self.H=properties["H"] + self.l=self.B.l() + self.n=self.B.n() + self.b=self.B.b() + self.c=self.B.c() + #Clamp a private scalar. + def __clamp(self,a): + _a = bytearray(a) + for i in range(0,self.c): _a[i//8]&=~(1<<(i%8)) + _a[self.n//8]|=1<<(self.n%8) + for i in range(self.n+1,self.b): _a[i//8]&=~(1<<(i%8)) + return _a + #Generate a key. If privkey is None, a random one is generated. + #In any case, the (privkey, pubkey) pair is returned. + def keygen(self,privkey): + #If no private key data is given, generate random. + if privkey is None: privkey=os.urandom(self.b//8) + + + + + +Josefsson & Liusvaara Informational [Page 55] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + #Expand key. + khash=self.H(privkey,None,None) + a=from_le(self.__clamp(khash[:self.b//8])) + #Return the key pair (public key is A=Enc(aB). + return privkey,(self.B*a).encode() + #Sign with key pair. + def sign(self,privkey,pubkey,msg,ctx,hflag): + #Expand key. + khash=self.H(privkey,None,None) + a=from_le(self.__clamp(khash[:self.b//8])) + seed=khash[self.b//8:] + #Calculate r and R (R only used in encoded form). + r=from_le(self.H(seed+msg,ctx,hflag))%self.l + R=(self.B*r).encode() + #Calculate h. + h=from_le(self.H(R+pubkey+msg,ctx,hflag))%self.l + #Calculate s. + S=((r+h*a)%self.l).to_bytes(self.b//8,byteorder="little") + #The final signature is a concatenation of R and S. + return R+S + #Verify signature with public key. + def verify(self,pubkey,msg,sig,ctx,hflag): + #Sanity-check sizes. + if len(sig)!=self.b//4: return False + if len(pubkey)!=self.b//8: return False + #Split signature into R and S, and parse. + Rraw,Sraw=sig[:self.b//8],sig[self.b//8:] + R,S=self.B.decode(Rraw),from_le(Sraw) + #Parse public key. + A=self.B.decode(pubkey) + #Check parse results. + if (R is None) or (A is None) or S>=self.l: return False + #Calculate h. + h=from_le(self.H(Rraw+pubkey+msg,ctx,hflag))%self.l + #Calculate left and right sides of check eq. + rhs=R+(A*h) + lhs=self.B*S + for i in range(0, self.c): + lhs = lhs.double() + rhs = rhs.double() + #Check eq. holds? + return lhs==rhs + +def Ed25519_inthash(data,ctx,hflag): + if (ctx is not None and len(ctx) > 0) or hflag: + raise ValueError("Contexts/hashes not supported") + return hashlib.sha512(data).digest() + + + + +Josefsson & Liusvaara Informational [Page 56] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +#The base PureEdDSA schemes. +pEd25519=PureEdDSA({\ + "B":Edwards25519Point.stdbase(),\ + "H":Ed25519_inthash\ +}) + +def Ed25519ctx_inthash(data,ctx,hflag): + dompfx = b"" + PREFIX=b"SigEd25519 no Ed25519 collisions" + if ctx is not None: + if len(ctx) > 255: raise ValueError("Context too big") + dompfx=PREFIX+bytes([1 if hflag else 0,len(ctx)])+ctx + return hashlib.sha512(dompfx+data).digest() + +pEd25519ctx=PureEdDSA({\ + "B":Edwards25519Point.stdbase(),\ + "H":Ed25519ctx_inthash\ +}) + +def Ed448_inthash(data,ctx,hflag): + dompfx = b"" + if ctx is not None: + if len(ctx) > 255: raise ValueError("Context too big") + dompfx=b"SigEd448"+bytes([1 if hflag else 0,len(ctx)])+ctx + return shake256(dompfx+data,114) + +pEd448 = PureEdDSA({\ + "B":Edwards448Point.stdbase(),\ + "H":Ed448_inthash\ +}) + +#EdDSA scheme. +class EdDSA: + #Create a new scheme object, with the specified PureEdDSA base + #scheme and specified prehash. + def __init__(self,pure_scheme,prehash): + self.__pflag = True + self.__pure=pure_scheme + self.__prehash=prehash + if self.__prehash is None: + self.__prehash = lambda x,y:x + self.__pflag = False + # Generate a key. If privkey is none, it generates a random + # privkey key, otherwise it uses a specified private key. + # Returns pair (privkey, pubkey). + def keygen(self,privkey): return self.__pure.keygen(privkey) + + + + + +Josefsson & Liusvaara Informational [Page 57] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + + # Sign message msg using specified key pair. + def sign(self,privkey,pubkey,msg,ctx=None): + if ctx is None: ctx=b""; + return self.__pure.sign(privkey,pubkey,self.__prehash(msg,ctx),\ + ctx,self.__pflag) + # Verify signature sig on message msg using public key pubkey. + def verify(self,pubkey,msg,sig,ctx=None): + if ctx is None: ctx=b""; + return self.__pure.verify(pubkey,self.__prehash(msg,ctx),sig,\ + ctx,self.__pflag) + +def Ed448ph_prehash(data,ctx): + return shake256(data,64) + +#Our signature schemes. +Ed25519 = EdDSA(pEd25519,None) +Ed25519ctx = EdDSA(pEd25519ctx,None) +Ed25519ph = EdDSA(pEd25519ctx,lambda x,y:hashlib.sha512(x).digest()) +Ed448 = EdDSA(pEd448,None) +Ed448ph = EdDSA(pEd448,Ed448ph_prehash) + +def eddsa_obj(name): + if name == "Ed25519": return Ed25519 + if name == "Ed25519ctx": return Ed25519ctx + if name == "Ed25519ph": return Ed25519ph + if name == "Ed448": return Ed448 + if name == "Ed448ph": return Ed448ph + raise NotImplementedError("Algorithm not implemented") + +Appendix B. Library Driver + + Below is a command-line tool that uses the library above to perform + computations for interactive use or for self-checking. + +import sys +import binascii + +from eddsa2 import Ed25519 + + +def munge_string(s, pos, change): + return (s[:pos] + + int.to_bytes(s[pos] ^ change, 1, "little") + + s[pos+1:]) + + + + + + + +Josefsson & Liusvaara Informational [Page 58] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +# Read a file in the format of +# http://ed25519.cr.yp.to/python/sign.input +lineno = 0 +while True: + line = sys.stdin.readline() + if not line: + break + lineno = lineno + 1 + print(lineno) + fields = line.split(":") + secret = (binascii.unhexlify(fields[0]))[:32] + public = binascii.unhexlify(fields[1]) + msg = binascii.unhexlify(fields[2]) + signature = binascii.unhexlify(fields[3])[:64] + + privkey,pubkey = Ed25519.keygen(secret) + assert public == pubkey + assert signature == Ed25519.sign(privkey, pubkey, msg) + assert Ed25519.verify(public, msg, signature) + if len(msg) == 0: + bad_msg = b"x" + else: + bad_msg = munge_string(msg, len(msg) // 3, 4) + assert not Ed25519.verify(public,bad_msg,signature) + assert not Ed25519.verify(public, msg, munge_string(signature,20,8)) + assert not Ed25519.verify(public,msg,munge_string(signature,40,16)) + + + + + + + + + + + + + + + + + + + + + + + + + +Josefsson & Liusvaara Informational [Page 59] + +RFC 8032 EdDSA: Ed25519 and Ed448 January 2017 + + +Acknowledgements + + EdDSA and Ed25519 were initially described in a paper due to Daniel + J. Bernstein, Niels Duif, Tanja Lange, Peter Schwabe, and Bo-Yin + Yang. The Ed448 curve is due to Mike Hamburg. + + An earlier draft version of this document was coauthored by Niels + Moeller. + + Feedback on this document was received from Werner Koch, Damien + Miller, Bob Bradley, Franck Rondepierre, Alexey Melnikov, Kenny + Paterson, and Robert Edmonds. + + The Ed25519 test vectors were double checked by Bob Bradley using + three separate implementations (one based on TweetNaCl and two + different implementations based on code from SUPERCOP). + +Authors' Addresses + + Simon Josefsson + SJD AB + + Email: simon@josefsson.org + URI: http://josefsson.org/ + + + Ilari Liusvaara + Independent + + Email: ilariliusvaara@welho.com + + + + + + + + + + + + + + + + + + + + + +Josefsson & Liusvaara Informational [Page 60] + diff --git a/src/lib.rs b/src/lib.rs index 378f34e..c132603 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -36,6 +36,8 @@ pub mod dsa; /// The `ecdsa` module provides bare-bones support for ECDSA signing, /// verification, and key generation. pub mod ecdsa; +/// The `ed25519` provides signing and verification using ED25519. +pub mod ed25519; /// The `ssh` module provides support for parsing OpenSSH-formatted SSH keys, /// both public and private. pub mod ssh; diff --git a/test-generator/ED25519.hs b/test-generator/ED25519.hs new file mode 100644 index 0000000..0abf825 --- /dev/null +++ b/test-generator/ED25519.hs @@ -0,0 +1,701 @@ +{-# LANGUAGE PackageImports #-} +module ED25519(ed25519Tasks) + where + +import Control.Monad(unless) +import "crypto-api" Crypto.Random(SystemRandom) +import "cryptonite" Crypto.Random(getRandomBytes,withDRG) +import Data.ByteString(ByteString,pack,useAsCString) +import qualified Data.ByteString as BS +import Data.Int(Int32) +import qualified Data.Map.Strict as Map +import Data.Word(Word8,Word32,Word64) +import ED25519.PrecompPoints +import Foreign.C.Types(CChar) +import Foreign.Marshal.Alloc(alloca) +import Foreign.Marshal.Array(allocaArray,peekArray,pokeArray) +import Foreign.Ptr(Ptr,castPtr) +import Foreign.Storable(Storable(..)) +import Math(showX,showBin) +import Task(Task(..)) + +cTEST_COUNT :: Int +cTEST_COUNT = 1000 + +ed25519Tasks :: [Task] +ed25519Tasks = [ loadTests, byteTests, addsubTests, mulTests, + squaringTests, inversionTests, negateTests, + cmovTests, isTests, square2Tests, + pow22523Tests, fbvTests, conversionTests, + ptDoubleTests, maddsubTests, ptAddSubTests, + scalarMultBaseTests, slideTests, scalarMultTests, + reduceTests, muladdTests, pubPrivTests ] + +loadTests :: Task +loadTests = Task { + taskName = "ed25519 byte loading", + taskFile = "../testdata/ed25519/load.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + do let (bytes, drg1) = withDRG drg0 (getRandomBytes 4) + res3 <- useAsCString bytes (\ptr -> load_3 ptr) + res4 <- useAsCString bytes (\ptr -> load_4 ptr) + let res = Map.fromList [("x", showBin bytes), ("a", showX res3), ("b", showX res4)] + return (res, fromIntegral res4, (memory0, drg1)) + +byteTests :: Task +byteTests = Task { + taskName = "ed25519 byte / element conversion", + taskFile = "../testdata/ed25519/bytes.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomPackedBytes drg0 $ \ ptra drg1 -> + alloca $ \ ptrc -> + allocaArray 32 $ \ rptr -> + do clearSpace ptrc + pokeArray (rptr :: Ptr Word8) (replicate 32 0) + fe_frombytes ptrc ptra + b <- convertFE ptrc + fe_tobytes (castPtr rptr) ptrc + start <- peek ptra + end <- peek (castPtr rptr) + unless (start == end) $ + fail "field element tobytes/frombytes doesn't round trip" + bytes' <- pack `fmap` peekArray 32 (castPtr ptra :: Ptr Word8) + let res = Map.fromList [("a", showBin bytes'), + ("b", showBin b)] + return (res, toNumber b, (memory0, drg1)) + +addsubTests :: Task +addsubTests = Task { + taskName = "ed25519 addition/subtraction tests", + taskFile = "../testdata/ed25519/addsub.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomElement drg0 $ \ ptrel1 drg1 -> + randomElement drg1 $ \ ptrel2 drg2 -> + alloca $ \ ptrc -> + alloca $ \ ptrd -> + do fe_add ptrc ptrel1 ptrel2 + fe_sub ptrd ptrel1 ptrel2 + [a, b, c, d] <- mapM convertFE [ptrel1, ptrel2, ptrc, ptrd] + let res = Map.fromList [("a", showBin a), + ("b", showBin b), + ("c", showBin c), + ("d", showBin d)] + return (res, toNumber c, (memory0, drg2)) + +mulTests :: Task +mulTests = Task { + taskName = "ed25519 multiplication tests", + taskFile = "../testdata/ed25519/mul.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomElement drg0 $ \ ptrel1 drg1 -> + randomElement drg1 $ \ ptrel2 drg2 -> + alloca $ \ ptrc -> + do fe_mul ptrc ptrel1 ptrel2 + [a, b, c] <- mapM convertFE [ptrel1, ptrel2, ptrc] + let res = Map.fromList [("a", showBin a), + ("b", showBin b), + ("c", showBin c)] + return (res, toNumber c, (memory0, drg2)) + +squaringTests :: Task +squaringTests = Task { + taskName = "ed25519 squaring tests", + taskFile = "../testdata/ed25519/square.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomElement drg0 $ \ ptrel drg1 -> + alloca $ \ ptrc -> + do fe_square ptrc ptrel + [a, c] <- mapM convertFE [ptrel, ptrc] + let res = Map.fromList [("a", showBin a), + ("c", showBin c)] + return (res, toNumber c, (memory0, drg1)) + +inversionTests :: Task +inversionTests = Task { + taskName = "ed25519 inversion tests", + taskFile = "../testdata/ed25519/invert.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomElement drg0 $ \ ptrel drg1 -> + alloca $ \ ptrc -> + do fe_invert ptrc ptrel + a <- convertFE ptrel + c <- convertFE ptrc + let res = Map.fromList [("a", showBin a), + ("c", showBin c)] + return (res, toNumber a, (memory0, drg1)) + +negateTests :: Task +negateTests = Task { + taskName = "ed25519 negation tests", + taskFile = "../testdata/ed25519/negate.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomElement drg0 $ \ ptrel drg1 -> + alloca $ \ ptrc -> + do fe_negate ptrc ptrel + a <- convertFE ptrel + c <- convertFE ptrc + let res = Map.fromList [("a", showBin a), + ("c", showBin c)] + return (res, toNumber a, (memory0, drg1)) + +cmovTests :: Task +cmovTests = Task { + taskName = "ed25519 conditional mov tests", + taskFile = "../testdata/ed25519/cmov.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomElement drg0 $ \ aelptr drg1 -> + do let (bbytes, drg2) = withDRG drg1 (getRandomBytes 1) + b = even (BS.head bbytes) + bvalLib = if b then 0 else 1 + bvalOut = if b then 0 else 0xFFFFFF :: Word32 + alloca $ \ celptr -> + do clearSpace celptr + fe_cmov celptr aelptr bvalLib + a <- convertFE aelptr + c <- convertFE celptr + let res = Map.fromList [("a", showBin a), + ("b", showX bvalOut), + ("c", showBin c)] + return (res, toNumber a, (memory0, drg2)) + +isTests :: Task +isTests = Task { + taskName = "ed25519 predicate tests", + taskFile = "../testdata/ed25519/istests.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomElement drg0 $ \ aptr drg1 -> + do a <- convertFE aptr + z <- fe_isnonzero aptr + n <- fe_isnegative aptr + let res = Map.fromList [("a", showBin a), + ("z", showX (if z == 0 then 0 :: Word32 else 0xFFFFFF)), + ("n", showX (if n == 0 then 0 :: Word32 else 0xFFFFFF))] + return (res, toNumber a, (memory0, drg1)) + +square2Tests :: Task +square2Tests = Task { + taskName = "ed25519 square2 tests", + taskFile = "../testdata/ed25519/square2.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomElement drg0 $ \ aptr drg1 -> + alloca $ \ cptr -> + do clearSpace cptr + fe_square2 cptr aptr + a <- convertFE aptr + c <- convertFE cptr + let res = Map.fromList [("a", showBin a), ("c", showBin c)] + return (res, toNumber a, (memory0, drg1)) + +pow22523Tests :: Task +pow22523Tests = Task { + taskName = "ed25519 pow22523 tests", + taskFile = "../testdata/ed25519/pow22523.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomElement drg0 $ \ aptr drg1 -> + alloca $ \ cptr -> + do clearSpace cptr + fe_pow22523 cptr aptr + a <- convertFE aptr + c <- convertFE cptr + let res = Map.fromList [("a", showBin a), ("c", showBin c)] + return (res, toNumber a, (memory0, drg1)) + +fbvTests :: Task +fbvTests = Task { + taskName = "ed25519 from bytes (vartime) tests", + taskFile = "../testdata/ed25519/fbv.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + do let (abytes, drg1) = withDRG drg0 (getRandomBytes 32) + useAsCString abytes $ \ aptr -> + do let aptr' = castPtr aptr :: Ptr PackedBytes + curve25519_scalar_mask aptr' + alloca $ \ dest -> + do clearSpace dest + point_frombytes dest aptr' + a <- pack `fmap` peekArray 32 (castPtr aptr) + c <- pack `fmap` peekArray (4 * 10 * 4) (castPtr dest) + let res = Map.fromList [("a", showBin a), ("c", showBin c)] + return (res, toNumber abytes, (memory0, drg1)) + +conversionTests :: Task +conversionTests = Task { + taskName = "ed25519 point form conversion tests", + taskFile = "../testdata/ed25519/conversion.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomPoint3 drg0 $ \ ptr3 drg' -> + alloca $ \ ptrCached -> + alloca $ \ ptr2 -> + alloca $ \ ptrP1P1 -> + alloca $ \ ptr2' -> + alloca $ \ ptr3' -> + do clearSpace ptrCached + clearSpace ptr2 + clearSpace ptrP1P1 + clearSpace ptr2' + clearSpace ptr3' + p3_to_cached ptrCached ptr3 + ge_p3_to_p2 ptr2 ptr3 + ge_p3_dbl ptrP1P1 ptr3 + p1p1_to_p2 ptr2' ptrP1P1 + p1p1_to_p3 ptr3' ptrP1P1 + a <- convertPoint ptr3 + c <- convertPoint ptrCached + t <- convertPoint ptr2 + o <- convertPoint ptrP1P1 + d <- convertPoint ptr2' + b <- convertPoint ptr3' + let res = Map.fromList [("a", showBin a), ("c", showBin c), + ("t", showBin t), ("o", showBin o), + ("d", showBin d), ("b", showBin b)] + return (res, toNumber a, (memory0, drg')) + +ptDoubleTests :: Task +ptDoubleTests = Task { + taskName = "ed25519 point doubling tests", + taskFile = "../testdata/ed25519/pt_double.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomPoint3 drg0 $ \ ptra drg1 -> + randomPoint2 drg1 $ \ ptrc drg2 -> + alloca $ \ ptrb -> + alloca $ \ ptrd -> + do clearSpace ptrb + clearSpace ptrd + ge_p3_dbl ptrb ptra + ge_p2_dbl ptrd ptrc + a <- convertPoint ptra + b <- convertPoint ptrb + c <- convertPoint ptrc + d <- convertPoint ptrd + let res = Map.fromList [("a", showBin a), ("b", showBin b), + ("c", showBin c), ("d", showBin d)] + return (res, toNumber a, (memory0, drg2)) + +maddsubTests :: Task +maddsubTests = Task { + taskName = "ed25519 point madd/msub tests", + taskFile = "../testdata/ed25519/maddsub.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomPoint3 drg0 $ \ ptra drg1 -> + randomPointPrecomp drg1 $ \ ptrc drg2 -> + alloca $ \ ptrb -> + alloca $ \ ptrd -> + do clearSpace ptrb + clearSpace ptrd + ge_madd ptrb ptra ptrc + ge_msub ptrd ptra ptrc + a <- convertPoint ptra + b <- convertPoint ptrb + c <- convertPoint ptrc + d <- convertPoint ptrd + let res = Map.fromList [("a", showBin a), ("b", showBin b), + ("c", showBin c), ("d", showBin d)] + return (res, toNumber a, (memory0, drg2)) + +ptAddSubTests :: Task +ptAddSubTests = Task { + taskName = "ed25519 point add/sub tests", + taskFile = "../testdata/ed25519/ptaddsub.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomPoint3 drg0 $ \ ptra drg1 -> + randomPointCached drg1 $ \ ptrc drg2 -> + alloca $ \ ptrb -> + alloca $ \ ptrd -> + do clearSpace ptrb + clearSpace ptrd + ge_add ptrb ptra ptrc + ge_sub ptrd ptra ptrc + a <- convertPoint ptra + b <- convertPoint ptrb + c <- convertPoint ptrc + d <- convertPoint ptrd + let res = Map.fromList [("a", showBin a), ("b", showBin b), + ("c", showBin c), ("d", showBin d)] + return (res, toNumber a, (memory0, drg2)) + +scalarMultBaseTests :: Task +scalarMultBaseTests = Task { + taskName = "ed25519 point add/sub tests", + taskFile = "../testdata/ed25519/scalar_mult.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomPackedBytes drg0 $ \ ptra drg1 -> + alloca $ \ ptrb -> + do clearSpace ptrb + x25519_ge_scalarmult_base ptrb ptra + PB abytes <- peek ptra + let a = pack abytes + b <- convertPoint ptrb + let res = Map.fromList [("a", showBin a), ("b", showBin b)] + return (res, toNumber a, (memory0, drg1)) + +slideTests :: Task +slideTests = Task { + taskName = "ed25519 slide helper function tests", + taskFile = "../testdata/ed25519/slide.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomPackedBytes drg0 $ \ ptra drg1 -> + allocaArray 256 $ \ ptrb -> + do pokeArray ptrb (replicate 256 0) + slide ptrb ptra + a <- pack `fmap` peekArray 32 (castPtr ptra) + b <- pack `fmap` peekArray 356 ptrb + let res = Map.fromList [("a", showBin a), ("b", showBin b)] + return (res, toNumber a, (memory0, drg1)) + +scalarMultTests :: Task +scalarMultTests = Task { + taskName = "ed25519 point general scalar multiplication tests", + taskFile = "../testdata/ed25519/scalar_mult_gen.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomPackedBytes drg0 $ \ ptra drg1 -> + randomPoint3 drg1 $ \ ptrb drg2 -> + randomPackedBytes drg2 $ \ ptrc drg3 -> + alloca $ \ ptrd -> + do clearSpace ptrd + ge_double_scalarmult_vartime ptrd ptra ptrb ptrc + PB abytes <- peek ptra + let a = pack abytes + b <- convertPoint ptrb + PB cbytes <- peek ptrc + let c = pack cbytes + d <- convertPoint ptrd + let res = Map.fromList [("a", showBin a), ("b", showBin b), + ("c", showBin c), ("d", showBin d)] + return (res, toNumber a, (memory0, drg3)) + +reduceTests :: Task +reduceTests = Task { + taskName = "ed25519 reduce tests", + taskFile = "../testdata/ed25519/reduce.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + do let (a, drg1) = withDRG drg0 (getRandomBytes 64) + allocaArray 64 $ \ target -> + do pokeArray target (BS.unpack a) + sc_reduce target + b <- pack `fmap` peekArray 32 target + let res = Map.fromList [("a", showBin a), ("b", showBin b)] + return (res, toNumber a, (memory0, drg1)) + +muladdTests :: Task +muladdTests = Task { + taskName = "ed25519 multiplication+addition tests", + taskFile = "../testdata/ed25519/muladd.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomPackedBytes drg0 $ \ ptra drg1 -> + randomPackedBytes drg1 $ \ ptrb drg2 -> + randomPackedBytes drg2 $ \ ptrc drg3 -> + alloca $ \ ptrd -> + do clearSpace ptrd + sc_muladd ptrd ptra ptrb ptrc + a <- repackBytes ptra + b <- repackBytes ptrb + c <- repackBytes ptrc + d <- repackBytes ptrd + let res = Map.fromList [("a", showBin a), ("b", showBin b), + ("c", showBin c), ("d", showBin d)] + return (res, toNumber a, (memory0, drg3)) + +pubPrivTests :: Task +pubPrivTests = Task { + taskName = "ed25519 private -> public conversion tests", + taskFile = "../testdata/ed25519/pubfrompriv.test", + taskTest = go, + taskCount = cTEST_COUNT + } + where + go (memory0, drg0) = + randomPackedBytes drg0 $ \ ptra drg1 -> + alloca $ \ ptrb -> + do clearSpace ptrb + public_from_private ptrb ptra + a <- repackBytes ptra + b <- repackBytes ptrb + let res = Map.fromList [("a", showBin a), ("b", showBin b)] + return (res, toNumber a, (memory0, drg1)) + +data PackedBytes = PB [Word8] + deriving (Eq) + +instance Storable PackedBytes where + sizeOf _ = 32 + alignment _ = 8 + peek p = PB `fmap` peekArray 32 (castPtr p) + poke p (PB v) = pokeArray (castPtr p) v + +randomPackedBytes :: SystemRandom -> (Ptr PackedBytes -> SystemRandom -> IO a) -> IO a +randomPackedBytes drg action = + do let (bytes, drg') = withDRG drg (getRandomBytes 32) + useAsCString bytes $ \ ptr -> + do let ptr' = castPtr ptr :: Ptr PackedBytes + curve25519_scalar_mask ptr' + action ptr' drg' + +repackBytes :: Ptr PackedBytes -> IO ByteString +repackBytes ptr = + do PB xs <- peek ptr + return (pack xs) + +data Element = FE [Int32] + +instance Storable Element where + sizeOf _ = 10 * sizeOf (undefined :: Int32) + alignment _ = 8 + peek p = FE `fmap` peekArray 10 (castPtr p) + poke p (FE v) = pokeArray (castPtr p) v + +randomElement :: SystemRandom -> (Ptr Element -> SystemRandom -> IO a) -> IO a +randomElement drg action = + randomPackedBytes drg $ \ ptrpb drg' -> alloca $ \ ptrel -> + do clearSpace ptrel + fe_frombytes ptrel ptrpb + action ptrel drg' + +data Point3 = P3 [Element] + +instance Storable Point3 where + sizeOf _ = 4 * sizeOf (undefined :: Element) + alignment _ = 8 + peek p = P3 `fmap` peekArray 4 (castPtr p) + poke p (P3 v) = pokeArray (castPtr p) v + +randomPoint3 :: SystemRandom -> (Ptr Point3 -> SystemRandom -> IO a) -> IO a +randomPoint3 drg action = + randomPackedBytes drg $ \ aptr drg' -> + allocaArray (4 * 10) $ \ dest -> + do clearSpace dest + point_frombytes dest aptr + action (castPtr dest) drg' + +data PointCached = PC [Element] + +instance Storable PointCached where + sizeOf _ = 4 * sizeOf (undefined :: Element) + alignment _ = 8 + peek p = PC `fmap` peekArray 4 (castPtr p) + poke p (PC v) = pokeArray (castPtr p) v + +randomPointCached :: SystemRandom -> (Ptr PointCached -> SystemRandom -> IO a) -> IO a +randomPointCached drg action = + randomPoint3 drg $ \ ptr drg' -> + allocaArray (4 * 10) $ \ dest -> + do pokeArray (castPtr dest :: Ptr Int32) (replicate (4 * 10) 0) + p3_to_cached dest ptr + action (castPtr dest) drg' + +data Point2 = P2 [Element] + +instance Storable Point2 where + sizeOf _ = 3 * sizeOf (undefined :: Element) + alignment _ = 8 + peek p = P2 `fmap` peekArray 3 (castPtr p) + poke p (P2 v) = pokeArray (castPtr p) v + +randomPoint2 :: SystemRandom -> (Ptr Point2 -> SystemRandom -> IO a) -> IO a +randomPoint2 drg action = + randomPoint3 drg $ \ ptr3 drg' -> + allocaArray (3 * 10) $ \ dest -> + do pokeArray (castPtr dest :: Ptr Int32) (replicate (3 * 10) 0) + ge_p3_to_p2 dest ptr3 + action (castPtr dest) drg' + +data PointP1P1 = P1P1 [Element] + +instance Storable PointP1P1 where + sizeOf _ = 4 * sizeOf (undefined :: Element) + alignment _ = 8 + peek p = P1P1 `fmap` peekArray 4 (castPtr p) + poke p (P1P1 v) = pokeArray (castPtr p) v + +_randomPointP1P1 :: SystemRandom -> (Ptr PointP1P1 -> SystemRandom -> IO a) -> IO a +_randomPointP1P1 drg action = + randomPoint3 drg $ \ ptr3 drg' -> + allocaArray (4 * 10) $ \ dest -> + do pokeArray (castPtr dest :: Ptr Int32) (replicate (4 * 10) 0) + ge_p3_dbl dest ptr3 + action (castPtr dest) drg' + +data PointPrecomp = PP [Element] + +instance Storable PointPrecomp where + sizeOf _ = 4 * sizeOf (undefined :: Element) + alignment _ = 8 + peek p = PP `fmap` peekArray 4 (castPtr p) + poke p (PP v) = pokeArray (castPtr p) v + +randomPointPrecomp :: SystemRandom -> (Ptr PointPrecomp -> SystemRandom -> IO a) -> IO a +randomPointPrecomp drg action = + do let ([a,b,c,d], drg') = withDRG drg (BS.unpack `fmap` getRandomBytes 4) + mix = fromIntegral a + fromIntegral b + fromIntegral c + fromIntegral d + idx = mix `mod` (length precompPoints) + val = PP (map FE (precompPoints !! idx)) + alloca $ \ ptr -> + do poke ptr val + action ptr drg' + +clearSpace :: Storable a => Ptr a -> IO () +clearSpace x = meh x undefined + where + meh :: Storable a => Ptr a -> a -> IO () + meh p v = pokeArray (castPtr p) (replicate (sizeOf v) (0 :: Word8)) + +convertFE :: Ptr Element -> IO ByteString +convertFE feptr = pack `fmap` peekArray 40 (castPtr feptr :: Ptr Word8) + +convertPoint :: Storable a => Ptr a -> IO ByteString +convertPoint x = meh x undefined + where + meh :: Storable a => Ptr a -> a -> IO ByteString + meh p v = pack `fmap` peekArray (sizeOf v) (castPtr p) + +toNumber :: ByteString -> Integer +toNumber = BS.foldr (\ x a -> fromIntegral x + a) 0 + +foreign import ccall unsafe "load_3" + load_3 :: Ptr CChar -> IO Word64 +foreign import ccall unsafe "load_4" + load_4 :: Ptr CChar -> IO Word64 +foreign import ccall unsafe "GFp_curve25519_scalar_mask" + curve25519_scalar_mask :: Ptr PackedBytes -> IO () +foreign import ccall unsafe "fe_frombytes" + fe_frombytes :: Ptr Element -> Ptr PackedBytes -> IO () +foreign import ccall unsafe "GFp_fe_tobytes" + fe_tobytes :: Ptr PackedBytes -> Ptr Element -> IO () +foreign import ccall unsafe "fe_add" + fe_add :: Ptr Element -> Ptr Element -> Ptr Element -> IO () +foreign import ccall unsafe "fe_sub" + fe_sub :: Ptr Element -> Ptr Element -> Ptr Element -> IO () +foreign import ccall unsafe "GFp_fe_mul" + fe_mul :: Ptr Element -> Ptr Element -> Ptr Element -> IO () +foreign import ccall unsafe "fe_sq" + fe_square :: Ptr Element -> Ptr Element -> IO () +foreign import ccall unsafe "GFp_fe_invert" + fe_invert :: Ptr Element -> Ptr Element -> IO () +foreign import ccall unsafe "fe_neg" + fe_negate :: Ptr Element -> Ptr Element -> IO () +foreign import ccall unsafe "fe_cmov" + fe_cmov :: Ptr Element -> Ptr Element -> Word32 -> IO () +foreign import ccall unsafe "fe_isnonzero" + fe_isnonzero :: Ptr Element -> IO Int32 +foreign import ccall unsafe "GFp_fe_isnegative" + fe_isnegative :: Ptr Element -> IO Word8 +foreign import ccall unsafe "fe_sq2" + fe_square2 :: Ptr Element -> Ptr Element -> IO () +foreign import ccall unsafe "fe_pow22523" + fe_pow22523 :: Ptr Element -> Ptr Element -> IO () +foreign import ccall unsafe "GFp_x25519_ge_frombytes_vartime" + point_frombytes :: Ptr Point3 -> Ptr PackedBytes -> IO () +foreign import ccall unsafe "x25519_ge_p3_to_cached" + p3_to_cached :: Ptr PointCached -> Ptr Point3 -> IO () +foreign import ccall unsafe "x25519_ge_p1p1_to_p2" + p1p1_to_p2 :: Ptr Point2 -> Ptr PointP1P1 -> IO () +foreign import ccall unsafe "x25519_ge_p1p1_to_p3" + p1p1_to_p3 :: Ptr Point3 -> Ptr PointP1P1 -> IO () +foreign import ccall unsafe "ge_p2_dbl" + ge_p2_dbl :: Ptr PointP1P1 -> Ptr Point2 -> IO () +foreign import ccall unsafe "ge_p3_dbl" + ge_p3_dbl :: Ptr PointP1P1 -> Ptr Point3 -> IO () +foreign import ccall unsafe "ge_p3_to_p2" + ge_p3_to_p2 :: Ptr Point2 -> Ptr Point3 -> IO () +foreign import ccall unsafe "ge_madd" + ge_madd :: Ptr PointP1P1 -> Ptr Point3 -> Ptr PointPrecomp -> IO () +foreign import ccall unsafe "ge_msub" + ge_msub :: Ptr PointP1P1 -> Ptr Point3 -> Ptr PointPrecomp -> IO () +foreign import ccall unsafe "x25519_ge_add" + ge_add :: Ptr PointP1P1 -> Ptr Point3 -> Ptr PointCached -> IO () +foreign import ccall unsafe "x25519_ge_sub" + ge_sub :: Ptr PointP1P1 -> Ptr Point3 -> Ptr PointCached -> IO () +foreign import ccall unsafe "GFp_x25519_ge_scalarmult_base" + x25519_ge_scalarmult_base :: Ptr Point3 -> Ptr PackedBytes -> IO () +foreign import ccall unsafe "slide" + slide :: Ptr Word8 -> Ptr PackedBytes -> IO () +foreign import ccall unsafe "GFp_ge_double_scalarmult_vartime" + ge_double_scalarmult_vartime :: Ptr Point2 -> Ptr PackedBytes -> Ptr Point3 -> Ptr PackedBytes -> IO () +foreign import ccall unsafe "GFp_x25519_sc_reduce" + sc_reduce :: Ptr Word8 -> IO () +foreign import ccall unsafe "GFp_x25519_sc_muladd" + sc_muladd :: Ptr PackedBytes -> Ptr PackedBytes -> Ptr PackedBytes -> Ptr PackedBytes -> IO () +foreign import ccall unsafe "GFp_x25519_public_from_private" + public_from_private :: Ptr PackedBytes -> Ptr PackedBytes -> IO () \ No newline at end of file diff --git a/test-generator/ED25519/PrecompPoints.hs b/test-generator/ED25519/PrecompPoints.hs new file mode 100644 index 0000000..8dbe5a4 --- /dev/null +++ b/test-generator/ED25519/PrecompPoints.hs @@ -0,0 +1,2120 @@ +module ED25519.PrecompPoints where + +import Data.Int(Int32) + +precompPoints :: [[[Int32]]] +precompPoints = [ + [ + [25967493, -14356035, 29566456, 3660896, -12694345, 4014787, + 27544626, -11754271, -6079156, 2047605], + [-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, + 5043384, 19500929, -15469378], + [-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, + 29287919, 11864899, -24514362, -4438546] + ], + [ + [-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, + -11717903, -3814571, -358445, -10211303], + [-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, + -15616551, 11189268, -26829678, -5319081], + [26966642, 11152617, 32442495, 15396054, 14353839, -12752335, + -3128826, -9541118, -15472047, -4166697] + ], + [ + [15636291, -9688557, 24204773, -7912398, 616977, -16685262, + 27787600, -14772189, 28944400, -1550024], + [16568933, 4717097, -11556148, -1102322, 15682896, -11807043, + 16354577, -11775962, 7689662, 11199574], + [30464156, -5976125, -11779434, -15670865, 23220365, 15915852, + 7512774, 10017326, -17749093, -9920357] + ], + [ + [-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, + -28926210, 15006023, 3284568, -6276540], + [23599295, -8306047, -11193664, -7687416, 13236774, 10506355, + 7464579, 9656445, 13059162, 10374397], + [7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, + -3839045, -641708, -101325] + ], + [ + [10861363, 11473154, 27284546, 1981175, -30064349, 12577861, + 32867885, 14515107, -15438304, 10819380], + [4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, + 12483688, -12668491, 5581306], + [19563160, 16186464, -29386857, 4097519, 10237984, -4348115, + 28542350, 13850243, -23678021, -15815942] + ], + [ + [-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, + -19188627, -15224819, -9818940, -12085777], + [-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, + -15689887, 1762328, 14866737], + [-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, + -28236412, 3959421, 27914454, 4383652] + ], + [ + [5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, + 5230134, -23952439, -15175766], + [-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, + 20654025, 16520125, 30598449, 7715701], + [28881845, 14381568, 9657904, 3680757, -20181635, 7843316, + 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-15804619], + [-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, + -16236442, -32461234, -12290683] + ] + ] \ No newline at end of file diff --git a/test-generator/Main.hs b/test-generator/Main.hs index 29a5c56..6f7e23f 100644 --- a/test-generator/Main.hs +++ b/test-generator/Main.hs @@ -8,6 +8,7 @@ import Control.Monad(replicateM_,void) import "crypto-api" Crypto.Random(CryptoRandomGen(..),SystemRandom) import DSA(dsaTasks) import ECDSATesting(ecdsaTasks) +import ED25519(ed25519Tasks) import GHC.Conc(getNumCapabilities) import RFC6979(rfcTasks) import RSA(rsaTasks) @@ -38,6 +39,6 @@ main = displayConsoleRegions $ do executors <- getNumCapabilities done <- newChan - tasks <- newMVar (dsaTasks ++ ecdsaTasks ++ rfcTasks ++ rsaTasks) + tasks <- newMVar (dsaTasks ++ ecdsaTasks ++ rfcTasks ++ rsaTasks ++ ed25519Tasks) replicateM_ executors (spawnExecutor tasks done) replicateM_ executors (void $ readChan done) \ No newline at end of file diff --git a/test-generator/cbits/GFp/aes.h b/test-generator/cbits/GFp/aes.h new file mode 100644 index 0000000..822142a --- /dev/null +++ b/test-generator/cbits/GFp/aes.h @@ -0,0 +1,96 @@ +/* ==================================================================== + * Copyright (c) 2002-2006 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * openssl-core@openssl.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.openssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== */ + +#ifndef OPENSSL_HEADER_AES_H +#define OPENSSL_HEADER_AES_H + +#include + +#if defined(__cplusplus) +extern "C" { +#endif + + +/* Raw AES functions. */ + + +#define AES_ENCRYPT 1 +#define AES_DECRYPT 0 + +/* AES_MAXNR is the maximum number of AES rounds. */ +#define AES_MAXNR 14 + +#define AES_BLOCK_SIZE 16 + +/* aes_key_st should be an opaque type, but EVP requires that the size be + * known. */ +struct aes_key_st { + uint32_t rd_key[4 * (AES_MAXNR + 1)]; + unsigned rounds; +}; +typedef struct aes_key_st AES_KEY; + +/* GFp_AES_set_encrypt_key configures |aeskey| to encrypt with the |bits|-bit + * key, |key|. + * + * WARNING: unlike other OpenSSL functions, this returns zero on success and a + * negative number on error. */ +OPENSSL_EXPORT int GFp_AES_set_encrypt_key(const uint8_t *key, unsigned bits, + AES_KEY *aeskey); + +/* AES_encrypt encrypts a single block from |in| to |out| with |key|. The |in| + * and |out| pointers may overlap. */ +OPENSSL_EXPORT void GFp_AES_encrypt(const uint8_t *in, uint8_t *out, + const AES_KEY *key); + + +#if defined(__cplusplus) +} /* extern C */ +#endif + +#endif /* OPENSSL_HEADER_AES_H */ diff --git a/test-generator/cbits/GFp/arm_arch.h b/test-generator/cbits/GFp/arm_arch.h new file mode 100644 index 0000000..ea08ccc --- /dev/null +++ b/test-generator/cbits/GFp/arm_arch.h @@ -0,0 +1,123 @@ +/* ==================================================================== + * Copyright (c) 1998-2011 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * openssl-core@openssl.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.openssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). */ + +#ifndef OPENSSL_HEADER_ARM_ARCH_H +#define OPENSSL_HEADER_ARM_ARCH_H + +#if !defined(__ARM_ARCH__) +# if defined(__CC_ARM) +# define __ARM_ARCH__ __TARGET_ARCH_ARM +# if defined(__BIG_ENDIAN) +# define __ARMEB__ +# else +# define __ARMEL__ +# endif +# elif defined(__GNUC__) +# if defined(__aarch64__) +# define __ARM_ARCH__ 8 +# if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ +# define __ARMEB__ +# else +# define __ARMEL__ +# endif + /* Why doesn't gcc define __ARM_ARCH__? Instead it defines + * bunch of below macros. See all_architectires[] table in + * gcc/config/arm/arm.c. On a side note it defines + * __ARMEL__/__ARMEB__ for little-/big-endian. */ +# elif defined(__ARM_ARCH) +# define __ARM_ARCH__ __ARM_ARCH +# elif defined(__ARM_ARCH_8A__) +# define __ARM_ARCH__ 8 +# elif defined(__ARM_ARCH_7__) || defined(__ARM_ARCH_7A__) || \ + defined(__ARM_ARCH_7R__)|| defined(__ARM_ARCH_7M__) || \ + defined(__ARM_ARCH_7EM__) +# define __ARM_ARCH__ 7 +# elif defined(__ARM_ARCH_6__) || defined(__ARM_ARCH_6J__) || \ + defined(__ARM_ARCH_6K__)|| defined(__ARM_ARCH_6M__) || \ + defined(__ARM_ARCH_6Z__)|| defined(__ARM_ARCH_6ZK__) || \ + defined(__ARM_ARCH_6T2__) +# define __ARM_ARCH__ 6 +# elif defined(__ARM_ARCH_5__) || defined(__ARM_ARCH_5T__) || \ + defined(__ARM_ARCH_5E__)|| defined(__ARM_ARCH_5TE__) || \ + defined(__ARM_ARCH_5TEJ__) +# define __ARM_ARCH__ 5 +# elif defined(__ARM_ARCH_4__) || defined(__ARM_ARCH_4T__) +# define __ARM_ARCH__ 4 +# else +# error "unsupported ARM architecture" +# endif +# endif +#endif + +/* Even when building for 32-bit ARM, support for aarch64 crypto instructions + * will be included. */ +#if !defined(__ARM_MAX_ARCH__) +#define __ARM_MAX_ARCH__ 8 +#endif + +/* ARMV7_NEON is true when a NEON unit is present in the current CPU. */ +#define ARMV7_NEON (1 << 0) + +/* ARMV8_AES indicates support for hardware AES instructions. */ +#define ARMV8_AES (1 << 2) + +/* ARMV8_SHA1 indicates support for hardware SHA-1 instructions. */ +#define ARMV8_SHA1 (1 << 3) + +/* ARMV8_SHA256 indicates support for hardware SHA-256 instructions. */ +#define ARMV8_SHA256 (1 << 4) + +/* ARMV8_PMULL indicates support for carryless multiplication. */ +#define ARMV8_PMULL (1 << 5) + + +#endif /* OPENSSL_HEADER_ARM_ARCH_H */ diff --git a/test-generator/cbits/GFp/base.h b/test-generator/cbits/GFp/base.h new file mode 100644 index 0000000..5886c7c --- /dev/null +++ b/test-generator/cbits/GFp/base.h @@ -0,0 +1,122 @@ +/* ==================================================================== + * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * openssl-core@openssl.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.openssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). */ + +#ifndef OPENSSL_HEADER_BASE_H +#define OPENSSL_HEADER_BASE_H + + +/* This file should be the first included by all BoringSSL headers. */ + +#include +#include +#include + +#if defined(__cplusplus) +extern "C" { +#endif + + +#if defined(__x86_64) || defined(_M_AMD64) || defined(_M_X64) +#define OPENSSL_64_BIT +#define OPENSSL_X86_64 +#elif defined(__x86) || defined(__i386) || defined(__i386__) || defined(_M_IX86) +#define OPENSSL_32_BIT +#define OPENSSL_X86 +#elif defined(__aarch64__) +#define OPENSSL_64_BIT +#define OPENSSL_AARCH64 +#elif defined(__arm) || defined(__arm__) || defined(_M_ARM) +#define OPENSSL_32_BIT +#define OPENSSL_ARM +#elif (defined(__PPC64__) || defined(__powerpc64__)) && defined(_LITTLE_ENDIAN) +#define OPENSSL_64_BIT +#define OPENSSL_PPC64LE +#elif defined(__mips__) && !defined(__LP64__) +#define OPENSSL_32_BIT +#define OPENSSL_MIPS +#elif defined(__mips__) && defined(__LP64__) +#define OPENSSL_64_BIT +#define OPENSSL_MIPS64 +#elif defined(__pnacl__) +#define OPENSSL_32_BIT +#define OPENSSL_PNACL +#elif defined(__myriad2__) +#define OPENSSL_32_BIT +#else +#error "Unknown target CPU" +#endif + +#if defined(__APPLE__) +#define OPENSSL_APPLE +#endif + +#if defined(_WIN32) +#define OPENSSL_WINDOWS +#endif + +#define OPENSSL_IS_BORINGSSL +#define OPENSSL_IS_RING +#define OPENSSL_VERSION_NUMBER 0x10002000 + +/* *ring* doesn't support the `BORINGSSL_SHARED_LIBRARY` configuration, so + * the default (usually "hidden") visibility is always used, even for exported + * items. */ +#define OPENSSL_EXPORT + +typedef struct bignum_st BIGNUM; + + +#if defined(__cplusplus) +} /* extern C */ +#endif + +#endif /* OPENSSL_HEADER_BASE_H */ diff --git a/test-generator/cbits/GFp/bn.h b/test-generator/cbits/GFp/bn.h new file mode 100644 index 0000000..e928315 --- /dev/null +++ b/test-generator/cbits/GFp/bn.h @@ -0,0 +1,256 @@ +/* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com) + * All rights reserved. + * + * This package is an SSL implementation written + * by Eric Young (eay@cryptsoft.com). + * The implementation was written so as to conform with Netscapes SSL. + * + * This library is free for commercial and non-commercial use as long as + * the following conditions are aheared to. The following conditions + * apply to all code found in this distribution, be it the RC4, RSA, + * lhash, DES, etc., code; not just the SSL code. The SSL documentation + * included with this distribution is covered by the same copyright terms + * except that the holder is Tim Hudson (tjh@cryptsoft.com). + * + * Copyright remains Eric Young's, and as such any Copyright notices in + * the code are not to be removed. + * If this package is used in a product, Eric Young should be given attribution + * as the author of the parts of the library used. + * This can be in the form of a textual message at program startup or + * in documentation (online or textual) provided with the package. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * "This product includes cryptographic software written by + * Eric Young (eay@cryptsoft.com)" + * The word 'cryptographic' can be left out if the rouines from the library + * being used are not cryptographic related :-). + * 4. If you include any Windows specific code (or a derivative thereof) from + * the apps directory (application code) you must include an acknowledgement: + * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" + * + * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * The licence and distribution terms for any publically available version or + * derivative of this code cannot be changed. i.e. this code cannot simply be + * copied and put under another distribution licence + * [including the GNU Public Licence.] + */ +/* ==================================================================== + * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * openssl-core@openssl.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.openssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). + * + */ +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * + * Portions of the attached software ("Contribution") are developed by + * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. + * + * The Contribution is licensed pursuant to the Eric Young open source + * license provided above. + * + * The binary polynomial arithmetic software is originally written by + * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems + * Laboratories. */ + +#ifndef OPENSSL_HEADER_BN_H +#define OPENSSL_HEADER_BN_H + +#include + +#if defined(__cplusplus) +extern "C" { +#endif + + +/* BN provides support for working with arbitrary sized integers. For example, + * although the largest integer supported by the compiler might be 64 bits, BN + * will allow you to work with numbers until you run out of memory. */ + + +/* BN_ULONG is the native word size when working with big integers. + * + * Note: on some platforms, inttypes.h does not define print format macros in + * C++ unless |__STDC_FORMAT_MACROS| defined. As this is a public header, bn.h + * does not define |__STDC_FORMAT_MACROS| itself. C++ source files which use the + * FMT macros must define it externally. */ +#if defined(OPENSSL_64_BIT) +#define BN_ULONG uint64_t +#define BN_BITS2 64 +#elif defined(OPENSSL_32_BIT) +#define BN_ULONG uint32_t +#define BN_BITS2 32 +#else +#error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT" +#endif + + +/* Allocation and freeing. */ + +/* GFp_BN_init initialises a stack allocated |BIGNUM|. */ +OPENSSL_EXPORT void GFp_BN_init(BIGNUM *bn); + +/* GFp_BN_free frees the data referenced by |bn| and, if |bn| was originally + * allocated on the heap, frees |bn| also. */ +OPENSSL_EXPORT void GFp_BN_free(BIGNUM *bn); + +/* GFp_BN_copy sets |dest| equal to |src| and returns one on success or zero on + * failure. */ +OPENSSL_EXPORT int GFp_BN_copy(BIGNUM *dest, const BIGNUM *src); + + +/* Basic functions. */ + +/* GFp_BN_zero sets |bn| to zero. */ +OPENSSL_EXPORT void GFp_BN_zero(BIGNUM *bn); + + +/* Internal functions. + * + * These functions are useful for code that is doing low-level manipulations of + * BIGNUM values. However, be sure that no other function in this file does + * what you want before turning to these. */ + +/* bn_correct_top decrements |bn->top| until |bn->d[top-1]| is non-zero or + * until |top| is zero. */ +OPENSSL_EXPORT void GFp_bn_correct_top(BIGNUM *bn); + +/* bn_wexpand ensures that |bn| has at least |words| works of space without + * altering its value. It returns one on success and zero on allocation + * failure. */ +OPENSSL_EXPORT int GFp_bn_wexpand(BIGNUM *bn, size_t words); + + +/* Simple arithmetic */ + +/* GFp_BN_mul_no_alias sets |r| = |a| * |b|, where |r| must not be the same pointer + * as |a| or |b|. Returns one on success and zero otherwise. */ +OPENSSL_EXPORT int GFp_BN_mul_no_alias(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); + + +/* Comparison functions */ + +/* GFp_BN_is_odd returns one if |bn| is odd and zero otherwise. */ +OPENSSL_EXPORT int GFp_BN_is_odd(const BIGNUM *bn); + + +/* Bitwise operations. */ + +/* GFp_BN_is_bit_set returns the value of the |n|th, least-significant bit in + * |a|, or zero if the bit doesn't exist. */ +OPENSSL_EXPORT int GFp_BN_is_bit_set(const BIGNUM *a, int n); + + +/* Modulo arithmetic. */ + +/* GFp_BN_mod_mul_mont set |r| equal to |a| * |b|, in the Montgomery domain. + * Both |a| and |b| must already be in the Montgomery domain (by + * |GFp_BN_to_mont|). In particular, |a| and |b| are assumed to be in the range + * [0, n), where |n| is the Montgomery modulus. It returns one on success or + * zero on error. */ +OPENSSL_EXPORT int GFp_BN_mod_mul_mont( + BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *n, + const BN_ULONG n0[/*BN_MONT_CTX_N0_LIMBS*/]); + +/* GFp_BN_reduce_montgomery returns |a % n| in constant-ish time using + * Montgomery reduction. |a| is assumed to be in the range [0, n**2), where |n| + * is the Montgomery modulus. It returns one on success or zero on error. */ +int GFp_BN_reduce_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *n, + const BN_ULONG n0[/*BN_MONT_CTX_N0_LIMBS*/]); + + +/* Exponentiation. */ + +OPENSSL_EXPORT int GFp_BN_mod_exp_mont_consttime( + BIGNUM *rr, const BIGNUM *a_mont, const BIGNUM *p, size_t p_bits, + const BIGNUM *one_mont, const BIGNUM *n, + const BN_ULONG n0[/*BN_MONT_CTX_N0_LIMBS*/]); + + +/* Private functions */ + +/* Keep in sync with `BIGNUM` in `ring::rsa::bigint`. */ +struct bignum_st { + BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks in little-endian + order. */ + int top; /* Index of last used element in |d|, plus one. */ + int dmax; /* Size of |d|, in words. */ + int flags; /* bitmask of BN_FLG_* values */ +}; + +#define BN_FLG_MALLOCED 0x01 +#define BN_FLG_STATIC_DATA 0x02 + + +#if defined(__cplusplus) +} /* extern C */ +#endif + +#endif /* OPENSSL_HEADER_BN_H */ diff --git a/test-generator/cbits/GFp/cpu.h b/test-generator/cbits/GFp/cpu.h new file mode 100644 index 0000000..44fb79d --- /dev/null +++ b/test-generator/cbits/GFp/cpu.h @@ -0,0 +1,189 @@ +/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) + * All rights reserved. + * + * This package is an SSL implementation written + * by Eric Young (eay@cryptsoft.com). + * The implementation was written so as to conform with Netscapes SSL. + * + * This library is free for commercial and non-commercial use as long as + * the following conditions are aheared to. The following conditions + * apply to all code found in this distribution, be it the RC4, RSA, + * lhash, DES, etc., code; not just the SSL code. The SSL documentation + * included with this distribution is covered by the same copyright terms + * except that the holder is Tim Hudson (tjh@cryptsoft.com). + * + * Copyright remains Eric Young's, and as such any Copyright notices in + * the code are not to be removed. + * If this package is used in a product, Eric Young should be given attribution + * as the author of the parts of the library used. + * This can be in the form of a textual message at program startup or + * in documentation (online or textual) provided with the package. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * "This product includes cryptographic software written by + * Eric Young (eay@cryptsoft.com)" + * The word 'cryptographic' can be left out if the rouines from the library + * being used are not cryptographic related :-). + * 4. If you include any Windows specific code (or a derivative thereof) from + * the apps directory (application code) you must include an acknowledgement: + * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" + * + * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * The licence and distribution terms for any publically available version or + * derivative of this code cannot be changed. i.e. this code cannot simply be + * copied and put under another distribution licence + * [including the GNU Public Licence.] + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). */ + +#ifndef OPENSSL_HEADER_CPU_H +#define OPENSSL_HEADER_CPU_H + +#include + +#if defined(__cplusplus) +extern "C" { +#endif + + +/* Runtime CPU feature support */ + + +#if defined(OPENSSL_X86) || defined(OPENSSL_X86_64) +/* GFp_ia32cap_P contains the Intel CPUID bits when running on an x86 or + * x86-64 system. + * + * Index 0: + * EDX for CPUID where EAX = 1 + * Bit 20 is always zero + * Bit 28 is adjusted to reflect whether the data cache is shared between + * multiple logical cores + * Bit 30 is used to indicate an Intel CPU + * Index 1: + * ECX for CPUID where EAX = 1 + * Bit 11 is used to indicate AMD XOP support, not SDBG + * Index 2: + * EBX for CPUID where EAX = 7 + * Index 3 is set to zero. + * + * Note: the CPUID bits are pre-adjusted for the OSXSAVE bit and the YMM and XMM + * bits in XCR0, so it is not necessary to check those. */ +extern uint32_t GFp_ia32cap_P[4]; +#endif + +#if defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64) + +#if defined(OPENSSL_APPLE) +/* iOS builds use the static ARM configuration. */ +#define OPENSSL_STATIC_ARMCAP + +#if defined(OPENSSL_AARCH64) +#define OPENSSL_STATIC_ARMCAP_AES +#define OPENSSL_STATIC_ARMCAP_SHA1 +#define OPENSSL_STATIC_ARMCAP_SHA256 +#define OPENSSL_STATIC_ARMCAP_PMULL +#endif + +#endif + +#if !defined(OPENSSL_STATIC_ARMCAP) + +/* GFp_is_NEON_capable_at_runtime returns true if the current CPU has a NEON + * unit. Note that |OPENSSL_armcap_P| also exists and contains the same + * information in a form that's easier for assembly to use. */ +OPENSSL_EXPORT uint8_t GFp_is_NEON_capable_at_runtime(void); + +/* GFp_is_NEON_capable returns true if the current CPU has a NEON unit. If + * this is known statically then it returns one immediately. */ +static inline int GFp_is_NEON_capable(void) { + /* On 32-bit ARM, one CPU is known to have a broken NEON unit which is known + * to fail with on some hand-written NEON assembly. Assume that non-Android + * applications will not use that buggy CPU but still support Android users + * that do, even when the compiler is instructed to freely emit NEON code. + * See https://crbug.com/341598 and https://crbug.com/606629. */ +#if defined(__ARM_NEON__) && (!defined(OPENSSL_ARM) || !defined(__ANDROID__)) + return 1; +#else + return GFp_is_NEON_capable_at_runtime(); +#endif +} + +#if defined(OPENSSL_ARM) +/* GFp_has_broken_NEON returns one if the current CPU is known to have a + * broken NEON unit. See https://crbug.com/341598. */ +OPENSSL_EXPORT int GFp_has_broken_NEON(void); +#endif + +/* GFp_is_ARMv8_AES_capable returns true if the current CPU supports the + * ARMv8 AES instruction. */ +int GFp_is_ARMv8_AES_capable(void); + +/* GFp_is_ARMv8_PMULL_capable returns true if the current CPU supports the + * ARMv8 PMULL instruction. */ +int GFp_is_ARMv8_PMULL_capable(void); + +#else + +static inline int GFp_is_NEON_capable(void) { +#if defined(OPENSSL_STATIC_ARMCAP_NEON) || defined(__ARM_NEON__) + return 1; +#else + return 0; +#endif +} + +static inline int GFp_is_ARMv8_AES_capable(void) { +#if defined(OPENSSL_STATIC_ARMCAP_AES) + return 1; +#else + return 0; +#endif +} + +static inline int GFp_is_ARMv8_PMULL_capable(void) { +#if defined(OPENSSL_STATIC_ARMCAP_PMULL) + return 1; +#else + return 0; +#endif +} + +#endif /* OPENSSL_STATIC_ARMCAP */ +#endif /* OPENSSL_ARM || OPENSSL_AARCH64 */ + +#if defined(OPENSSL_PPC64LE) + +/* CRYPTO_is_PPC64LE_vcrypto_capable returns true iff the current CPU supports + * the Vector.AES category of instructions. */ +int CRYPTO_is_PPC64LE_vcrypto_capable(void); + +#endif /* OPENSSL_PPC64LE */ + + +#if defined(__cplusplus) +} /* extern C */ +#endif + +#endif /* OPENSSL_HEADER_CPU_H */ diff --git a/test-generator/cbits/GFp/mem.h b/test-generator/cbits/GFp/mem.h new file mode 100644 index 0000000..e175d1e --- /dev/null +++ b/test-generator/cbits/GFp/mem.h @@ -0,0 +1,93 @@ +/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) + * All rights reserved. + * + * This package is an SSL implementation written + * by Eric Young (eay@cryptsoft.com). + * The implementation was written so as to conform with Netscapes SSL. + * + * This library is free for commercial and non-commercial use as long as + * the following conditions are aheared to. The following conditions + * apply to all code found in this distribution, be it the RC4, RSA, + * lhash, DES, etc., code; not just the SSL code. The SSL documentation + * included with this distribution is covered by the same copyright terms + * except that the holder is Tim Hudson (tjh@cryptsoft.com). + * + * Copyright remains Eric Young's, and as such any Copyright notices in + * the code are not to be removed. + * If this package is used in a product, Eric Young should be given attribution + * as the author of the parts of the library used. + * This can be in the form of a textual message at program startup or + * in documentation (online or textual) provided with the package. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * "This product includes cryptographic software written by + * Eric Young (eay@cryptsoft.com)" + * The word 'cryptographic' can be left out if the rouines from the library + * being used are not cryptographic related :-). + * 4. If you include any Windows specific code (or a derivative thereof) from + * the apps directory (application code) you must include an acknowledgement: + * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" + * + * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * The licence and distribution terms for any publically available version or + * derivative of this code cannot be changed. i.e. this code cannot simply be + * copied and put under another distribution licence + * [including the GNU Public Licence.] */ + +#ifndef OPENSSL_HEADER_MEM_H +#define OPENSSL_HEADER_MEM_H + +#include + +#include + +#if defined(__cplusplus) +extern "C" { +#endif + + +/* Memory and string functions, see also buf.h. + * + * OpenSSL has, historically, had a complex set of malloc debugging options. + * However, that was written in a time before Valgrind and ASAN. Since we now + * have those tools, the OpenSSL allocation functions are simply macros around + * the standard memory functions. */ + + +#define OPENSSL_malloc malloc +#define OPENSSL_realloc realloc +#define OPENSSL_free free + +/* GFp_memcmp returns zero iff the |len| bytes at |a| and |b| are equal. It + * takes an amount of time dependent on |len|, but independent of the contents + * of |a| and |b|. Unlike memcmp, it cannot be used to put elements into a + * defined order as the return value when a != b is undefined, other than to be + * non-zero. */ +OPENSSL_EXPORT int GFp_memcmp(const void *a, const void *b, size_t len); + + +#if defined(__cplusplus) +} /* extern C */ +#endif + +#endif /* OPENSSL_HEADER_MEM_H */ diff --git a/test-generator/cbits/GFp/type_check.h b/test-generator/cbits/GFp/type_check.h new file mode 100644 index 0000000..f7ec69a --- /dev/null +++ b/test-generator/cbits/GFp/type_check.h @@ -0,0 +1,75 @@ +/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) + * All rights reserved. + * + * This package is an SSL implementation written + * by Eric Young (eay@cryptsoft.com). + * The implementation was written so as to conform with Netscapes SSL. + * + * This library is free for commercial and non-commercial use as long as + * the following conditions are aheared to. The following conditions + * apply to all code found in this distribution, be it the RC4, RSA, + * lhash, DES, etc., code; not just the SSL code. The SSL documentation + * included with this distribution is covered by the same copyright terms + * except that the holder is Tim Hudson (tjh@cryptsoft.com). + * + * Copyright remains Eric Young's, and as such any Copyright notices in + * the code are not to be removed. + * If this package is used in a product, Eric Young should be given attribution + * as the author of the parts of the library used. + * This can be in the form of a textual message at program startup or + * in documentation (online or textual) provided with the package. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * "This product includes cryptographic software written by + * Eric Young (eay@cryptsoft.com)" + * The word 'cryptographic' can be left out if the rouines from the library + * being used are not cryptographic related :-). + * 4. If you include any Windows specific code (or a derivative thereof) from + * the apps directory (application code) you must include an acknowledgement: + * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" + * + * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * The licence and distribution terms for any publically available version or + * derivative of this code cannot be changed. i.e. this code cannot simply be + * copied and put under another distribution licence + * [including the GNU Public Licence.] */ + +#ifndef OPENSSL_HEADER_TYPE_CHECK_H +#define OPENSSL_HEADER_TYPE_CHECK_H + +#include + + +#if defined(__STDC_VERSION__) && __STDC_VERSION__ >= 201112L +#define OPENSSL_COMPILE_ASSERT(cond, msg) _Static_assert(cond, #msg) +#elif defined(__GNUC__) +#define OPENSSL_COMPILE_ASSERT(cond, msg) \ + typedef char OPENSSL_COMPILE_ASSERT_##msg[((cond) ? 1 : -1)] \ + __attribute__((unused)) +#else +#define OPENSSL_COMPILE_ASSERT(cond, msg) \ + typedef char OPENSSL_COMPILE_ASSERT_##msg[((cond) ? 1 : -1)] +#endif + + +#endif /* OPENSSL_HEADER_TYPE_CHECK_H */ diff --git a/test-generator/cbits/asm/x25519-asm-arm.S b/test-generator/cbits/asm/x25519-asm-arm.S new file mode 100644 index 0000000..220fdac --- /dev/null +++ b/test-generator/cbits/asm/x25519-asm-arm.S @@ -0,0 +1,2133 @@ +/* Copyright (c) 2015, Google Inc. + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY + * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION + * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN + * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ + +/* This file is taken from crypto_scalarmult/curve25519/neon2/scalarmult.s in + * SUPERCOP 20141124 (http://bench.cr.yp.to/supercop.html). That code is public + * domain licensed but the standard ISC license is included above to keep + * licensing simple. */ + +#if !defined(OPENSSL_NO_ASM) +#if defined(__arm__) + +#if !defined(__APPLE__) +.fpu neon +#endif +.text +.align 4 + +.global GFp_x25519_NEON + +#if defined(__APPLE__) +.private_extern _GFp_x25519_NEON +_GFp_x25519_NEON: +#else +.hidden GFp_x25519_NEON +.type GFp_x25519_NEON, %function +GFp_x25519_NEON: +#endif + +vpush {q4,q5,q6,q7} +mov r12,sp +sub sp,sp,#736 +and sp,sp,#0xffffffe0 +strd r4,[sp,#0] +strd r6,[sp,#8] +strd r8,[sp,#16] +strd r10,[sp,#24] +str r12,[sp,#480] +str r14,[sp,#484] +mov r0,r0 +mov r1,r1 +mov r2,r2 +add r3,sp,#32 +mov r4, #0 +mov r5, #254 +vmov.i32 q0,#1 +vshr.u64 q1,q0,#7 +vshr.u64 q0,q0,#8 +vmov.i32 d4,#19 +vmov.i32 d5,#38 +add r6,sp,#512 +vst1.8 {d2-d3},[r6,: 128] +add r6,sp,#528 +vst1.8 {d0-d1},[r6,: 128] +add r6,sp,#544 +vst1.8 {d4-d5},[r6,: 128] +add r6,r3,#0 +vmov.i32 q2,#0 +vst1.8 {d4-d5},[r6,: 128]! +vst1.8 {d4-d5},[r6,: 128]! +vst1.8 d4,[r6,: 64] +add r6,r3,#0 +mov r7, #960 +sub r7,r7,#2 +neg r7,r7 +sub r7,r7,r7,LSL #7 +str r7,[r6] +add r6,sp,#704 +vld1.8 {d4-d5},[r1]! +vld1.8 {d6-d7},[r1] +vst1.8 {d4-d5},[r6,: 128]! +vst1.8 {d6-d7},[r6,: 128] +sub r1,r6,#16 +ldrb r6,[r1] +and r6,r6,#248 +strb r6,[r1] +ldrb r6,[r1,#31] +and r6,r6,#127 +orr r6,r6,#64 +strb r6,[r1,#31] +vmov.i64 q2,#0xffffffff +vshr.u64 q3,q2,#7 +vshr.u64 q2,q2,#6 +vld1.8 {d8},[r2] +vld1.8 {d10},[r2] +add r2,r2,#6 +vld1.8 {d12},[r2] +vld1.8 {d14},[r2] +add r2,r2,#6 +vld1.8 {d16},[r2] +add r2,r2,#4 +vld1.8 {d18},[r2] +vld1.8 {d20},[r2] +add r2,r2,#6 +vld1.8 {d22},[r2] +add r2,r2,#2 +vld1.8 {d24},[r2] +vld1.8 {d26},[r2] +vshr.u64 q5,q5,#26 +vshr.u64 q6,q6,#3 +vshr.u64 q7,q7,#29 +vshr.u64 q8,q8,#6 +vshr.u64 q10,q10,#25 +vshr.u64 q11,q11,#3 +vshr.u64 q12,q12,#12 +vshr.u64 q13,q13,#38 +vand q4,q4,q2 +vand q6,q6,q2 +vand q8,q8,q2 +vand q10,q10,q2 +vand q2,q12,q2 +vand q5,q5,q3 +vand q7,q7,q3 +vand q9,q9,q3 +vand q11,q11,q3 +vand q3,q13,q3 +add r2,r3,#48 +vadd.i64 q12,q4,q1 +vadd.i64 q13,q10,q1 +vshr.s64 q12,q12,#26 +vshr.s64 q13,q13,#26 +vadd.i64 q5,q5,q12 +vshl.i64 q12,q12,#26 +vadd.i64 q14,q5,q0 +vadd.i64 q11,q11,q13 +vshl.i64 q13,q13,#26 +vadd.i64 q15,q11,q0 +vsub.i64 q4,q4,q12 +vshr.s64 q12,q14,#25 +vsub.i64 q10,q10,q13 +vshr.s64 q13,q15,#25 +vadd.i64 q6,q6,q12 +vshl.i64 q12,q12,#25 +vadd.i64 q14,q6,q1 +vadd.i64 q2,q2,q13 +vsub.i64 q5,q5,q12 +vshr.s64 q12,q14,#26 +vshl.i64 q13,q13,#25 +vadd.i64 q14,q2,q1 +vadd.i64 q7,q7,q12 +vshl.i64 q12,q12,#26 +vadd.i64 q15,q7,q0 +vsub.i64 q11,q11,q13 +vshr.s64 q13,q14,#26 +vsub.i64 q6,q6,q12 +vshr.s64 q12,q15,#25 +vadd.i64 q3,q3,q13 +vshl.i64 q13,q13,#26 +vadd.i64 q14,q3,q0 +vadd.i64 q8,q8,q12 +vshl.i64 q12,q12,#25 +vadd.i64 q15,q8,q1 +add r2,r2,#8 +vsub.i64 q2,q2,q13 +vshr.s64 q13,q14,#25 +vsub.i64 q7,q7,q12 +vshr.s64 q12,q15,#26 +vadd.i64 q14,q13,q13 +vadd.i64 q9,q9,q12 +vtrn.32 d12,d14 +vshl.i64 q12,q12,#26 +vtrn.32 d13,d15 +vadd.i64 q0,q9,q0 +vadd.i64 q4,q4,q14 +vst1.8 d12,[r2,: 64]! +vshl.i64 q6,q13,#4 +vsub.i64 q7,q8,q12 +vshr.s64 q0,q0,#25 +vadd.i64 q4,q4,q6 +vadd.i64 q6,q10,q0 +vshl.i64 q0,q0,#25 +vadd.i64 q8,q6,q1 +vadd.i64 q4,q4,q13 +vshl.i64 q10,q13,#25 +vadd.i64 q1,q4,q1 +vsub.i64 q0,q9,q0 +vshr.s64 q8,q8,#26 +vsub.i64 q3,q3,q10 +vtrn.32 d14,d0 +vshr.s64 q1,q1,#26 +vtrn.32 d15,d1 +vadd.i64 q0,q11,q8 +vst1.8 d14,[r2,: 64] +vshl.i64 q7,q8,#26 +vadd.i64 q5,q5,q1 +vtrn.32 d4,d6 +vshl.i64 q1,q1,#26 +vtrn.32 d5,d7 +vsub.i64 q3,q6,q7 +add r2,r2,#16 +vsub.i64 q1,q4,q1 +vst1.8 d4,[r2,: 64] +vtrn.32 d6,d0 +vtrn.32 d7,d1 +sub r2,r2,#8 +vtrn.32 d2,d10 +vtrn.32 d3,d11 +vst1.8 d6,[r2,: 64] +sub r2,r2,#24 +vst1.8 d2,[r2,: 64] +add r2,r3,#96 +vmov.i32 q0,#0 +vmov.i64 d2,#0xff +vmov.i64 d3,#0 +vshr.u32 q1,q1,#7 +vst1.8 {d2-d3},[r2,: 128]! +vst1.8 {d0-d1},[r2,: 128]! +vst1.8 d0,[r2,: 64] +add r2,r3,#144 +vmov.i32 q0,#0 +vst1.8 {d0-d1},[r2,: 128]! +vst1.8 {d0-d1},[r2,: 128]! +vst1.8 d0,[r2,: 64] +add r2,r3,#240 +vmov.i32 q0,#0 +vmov.i64 d2,#0xff +vmov.i64 d3,#0 +vshr.u32 q1,q1,#7 +vst1.8 {d2-d3},[r2,: 128]! +vst1.8 {d0-d1},[r2,: 128]! +vst1.8 d0,[r2,: 64] +add r2,r3,#48 +add r6,r3,#192 +vld1.8 {d0-d1},[r2,: 128]! +vld1.8 {d2-d3},[r2,: 128]! +vld1.8 {d4},[r2,: 64] +vst1.8 {d0-d1},[r6,: 128]! +vst1.8 {d2-d3},[r6,: 128]! +vst1.8 d4,[r6,: 64] +._mainloop: +mov r2,r5,LSR #3 +and r6,r5,#7 +ldrb r2,[r1,r2] +mov r2,r2,LSR r6 +and r2,r2,#1 +str r5,[sp,#488] +eor r4,r4,r2 +str r2,[sp,#492] +neg r2,r4 +add r4,r3,#96 +add r5,r3,#192 +add r6,r3,#144 +vld1.8 {d8-d9},[r4,: 128]! +add r7,r3,#240 +vld1.8 {d10-d11},[r5,: 128]! +veor q6,q4,q5 +vld1.8 {d14-d15},[r6,: 128]! +vdup.i32 q8,r2 +vld1.8 {d18-d19},[r7,: 128]! +veor q10,q7,q9 +vld1.8 {d22-d23},[r4,: 128]! +vand q6,q6,q8 +vld1.8 {d24-d25},[r5,: 128]! +vand q10,q10,q8 +vld1.8 {d26-d27},[r6,: 128]! +veor q4,q4,q6 +vld1.8 {d28-d29},[r7,: 128]! +veor q5,q5,q6 +vld1.8 {d0},[r4,: 64] +veor q6,q7,q10 +vld1.8 {d2},[r5,: 64] +veor q7,q9,q10 +vld1.8 {d4},[r6,: 64] +veor q9,q11,q12 +vld1.8 {d6},[r7,: 64] +veor q10,q0,q1 +sub r2,r4,#32 +vand q9,q9,q8 +sub r4,r5,#32 +vand q10,q10,q8 +sub r5,r6,#32 +veor q11,q11,q9 +sub r6,r7,#32 +veor q0,q0,q10 +veor q9,q12,q9 +veor q1,q1,q10 +veor q10,q13,q14 +veor q12,q2,q3 +vand q10,q10,q8 +vand q8,q12,q8 +veor q12,q13,q10 +veor q2,q2,q8 +veor q10,q14,q10 +veor q3,q3,q8 +vadd.i32 q8,q4,q6 +vsub.i32 q4,q4,q6 +vst1.8 {d16-d17},[r2,: 128]! +vadd.i32 q6,q11,q12 +vst1.8 {d8-d9},[r5,: 128]! +vsub.i32 q4,q11,q12 +vst1.8 {d12-d13},[r2,: 128]! +vadd.i32 q6,q0,q2 +vst1.8 {d8-d9},[r5,: 128]! +vsub.i32 q0,q0,q2 +vst1.8 d12,[r2,: 64] +vadd.i32 q2,q5,q7 +vst1.8 d0,[r5,: 64] +vsub.i32 q0,q5,q7 +vst1.8 {d4-d5},[r4,: 128]! +vadd.i32 q2,q9,q10 +vst1.8 {d0-d1},[r6,: 128]! +vsub.i32 q0,q9,q10 +vst1.8 {d4-d5},[r4,: 128]! +vadd.i32 q2,q1,q3 +vst1.8 {d0-d1},[r6,: 128]! +vsub.i32 q0,q1,q3 +vst1.8 d4,[r4,: 64] +vst1.8 d0,[r6,: 64] +add r2,sp,#544 +add r4,r3,#96 +add r5,r3,#144 +vld1.8 {d0-d1},[r2,: 128] +vld1.8 {d2-d3},[r4,: 128]! +vld1.8 {d4-d5},[r5,: 128]! +vzip.i32 q1,q2 +vld1.8 {d6-d7},[r4,: 128]! +vld1.8 {d8-d9},[r5,: 128]! +vshl.i32 q5,q1,#1 +vzip.i32 q3,q4 +vshl.i32 q6,q2,#1 +vld1.8 {d14},[r4,: 64] +vshl.i32 q8,q3,#1 +vld1.8 {d15},[r5,: 64] +vshl.i32 q9,q4,#1 +vmul.i32 d21,d7,d1 +vtrn.32 d14,d15 +vmul.i32 q11,q4,q0 +vmul.i32 q0,q7,q0 +vmull.s32 q12,d2,d2 +vmlal.s32 q12,d11,d1 +vmlal.s32 q12,d12,d0 +vmlal.s32 q12,d13,d23 +vmlal.s32 q12,d16,d22 +vmlal.s32 q12,d7,d21 +vmull.s32 q10,d2,d11 +vmlal.s32 q10,d4,d1 +vmlal.s32 q10,d13,d0 +vmlal.s32 q10,d6,d23 +vmlal.s32 q10,d17,d22 +vmull.s32 q13,d10,d4 +vmlal.s32 q13,d11,d3 +vmlal.s32 q13,d13,d1 +vmlal.s32 q13,d16,d0 +vmlal.s32 q13,d17,d23 +vmlal.s32 q13,d8,d22 +vmull.s32 q1,d10,d5 +vmlal.s32 q1,d11,d4 +vmlal.s32 q1,d6,d1 +vmlal.s32 q1,d17,d0 +vmlal.s32 q1,d8,d23 +vmull.s32 q14,d10,d6 +vmlal.s32 q14,d11,d13 +vmlal.s32 q14,d4,d4 +vmlal.s32 q14,d17,d1 +vmlal.s32 q14,d18,d0 +vmlal.s32 q14,d9,d23 +vmull.s32 q11,d10,d7 +vmlal.s32 q11,d11,d6 +vmlal.s32 q11,d12,d5 +vmlal.s32 q11,d8,d1 +vmlal.s32 q11,d19,d0 +vmull.s32 q15,d10,d8 +vmlal.s32 q15,d11,d17 +vmlal.s32 q15,d12,d6 +vmlal.s32 q15,d13,d5 +vmlal.s32 q15,d19,d1 +vmlal.s32 q15,d14,d0 +vmull.s32 q2,d10,d9 +vmlal.s32 q2,d11,d8 +vmlal.s32 q2,d12,d7 +vmlal.s32 q2,d13,d6 +vmlal.s32 q2,d14,d1 +vmull.s32 q0,d15,d1 +vmlal.s32 q0,d10,d14 +vmlal.s32 q0,d11,d19 +vmlal.s32 q0,d12,d8 +vmlal.s32 q0,d13,d17 +vmlal.s32 q0,d6,d6 +add r2,sp,#512 +vld1.8 {d18-d19},[r2,: 128] +vmull.s32 q3,d16,d7 +vmlal.s32 q3,d10,d15 +vmlal.s32 q3,d11,d14 +vmlal.s32 q3,d12,d9 +vmlal.s32 q3,d13,d8 +add r2,sp,#528 +vld1.8 {d8-d9},[r2,: 128] +vadd.i64 q5,q12,q9 +vadd.i64 q6,q15,q9 +vshr.s64 q5,q5,#26 +vshr.s64 q6,q6,#26 +vadd.i64 q7,q10,q5 +vshl.i64 q5,q5,#26 +vadd.i64 q8,q7,q4 +vadd.i64 q2,q2,q6 +vshl.i64 q6,q6,#26 +vadd.i64 q10,q2,q4 +vsub.i64 q5,q12,q5 +vshr.s64 q8,q8,#25 +vsub.i64 q6,q15,q6 +vshr.s64 q10,q10,#25 +vadd.i64 q12,q13,q8 +vshl.i64 q8,q8,#25 +vadd.i64 q13,q12,q9 +vadd.i64 q0,q0,q10 +vsub.i64 q7,q7,q8 +vshr.s64 q8,q13,#26 +vshl.i64 q10,q10,#25 +vadd.i64 q13,q0,q9 +vadd.i64 q1,q1,q8 +vshl.i64 q8,q8,#26 +vadd.i64 q15,q1,q4 +vsub.i64 q2,q2,q10 +vshr.s64 q10,q13,#26 +vsub.i64 q8,q12,q8 +vshr.s64 q12,q15,#25 +vadd.i64 q3,q3,q10 +vshl.i64 q10,q10,#26 +vadd.i64 q13,q3,q4 +vadd.i64 q14,q14,q12 +add r2,r3,#288 +vshl.i64 q12,q12,#25 +add r4,r3,#336 +vadd.i64 q15,q14,q9 +add r2,r2,#8 +vsub.i64 q0,q0,q10 +add r4,r4,#8 +vshr.s64 q10,q13,#25 +vsub.i64 q1,q1,q12 +vshr.s64 q12,q15,#26 +vadd.i64 q13,q10,q10 +vadd.i64 q11,q11,q12 +vtrn.32 d16,d2 +vshl.i64 q12,q12,#26 +vtrn.32 d17,d3 +vadd.i64 q1,q11,q4 +vadd.i64 q4,q5,q13 +vst1.8 d16,[r2,: 64]! +vshl.i64 q5,q10,#4 +vst1.8 d17,[r4,: 64]! +vsub.i64 q8,q14,q12 +vshr.s64 q1,q1,#25 +vadd.i64 q4,q4,q5 +vadd.i64 q5,q6,q1 +vshl.i64 q1,q1,#25 +vadd.i64 q6,q5,q9 +vadd.i64 q4,q4,q10 +vshl.i64 q10,q10,#25 +vadd.i64 q9,q4,q9 +vsub.i64 q1,q11,q1 +vshr.s64 q6,q6,#26 +vsub.i64 q3,q3,q10 +vtrn.32 d16,d2 +vshr.s64 q9,q9,#26 +vtrn.32 d17,d3 +vadd.i64 q1,q2,q6 +vst1.8 d16,[r2,: 64] +vshl.i64 q2,q6,#26 +vst1.8 d17,[r4,: 64] +vadd.i64 q6,q7,q9 +vtrn.32 d0,d6 +vshl.i64 q7,q9,#26 +vtrn.32 d1,d7 +vsub.i64 q2,q5,q2 +add r2,r2,#16 +vsub.i64 q3,q4,q7 +vst1.8 d0,[r2,: 64] +add r4,r4,#16 +vst1.8 d1,[r4,: 64] +vtrn.32 d4,d2 +vtrn.32 d5,d3 +sub r2,r2,#8 +sub r4,r4,#8 +vtrn.32 d6,d12 +vtrn.32 d7,d13 +vst1.8 d4,[r2,: 64] +vst1.8 d5,[r4,: 64] +sub r2,r2,#24 +sub r4,r4,#24 +vst1.8 d6,[r2,: 64] +vst1.8 d7,[r4,: 64] +add r2,r3,#240 +add r4,r3,#96 +vld1.8 {d0-d1},[r4,: 128]! +vld1.8 {d2-d3},[r4,: 128]! +vld1.8 {d4},[r4,: 64] +add r4,r3,#144 +vld1.8 {d6-d7},[r4,: 128]! +vtrn.32 q0,q3 +vld1.8 {d8-d9},[r4,: 128]! +vshl.i32 q5,q0,#4 +vtrn.32 q1,q4 +vshl.i32 q6,q3,#4 +vadd.i32 q5,q5,q0 +vadd.i32 q6,q6,q3 +vshl.i32 q7,q1,#4 +vld1.8 {d5},[r4,: 64] +vshl.i32 q8,q4,#4 +vtrn.32 d4,d5 +vadd.i32 q7,q7,q1 +vadd.i32 q8,q8,q4 +vld1.8 {d18-d19},[r2,: 128]! +vshl.i32 q10,q2,#4 +vld1.8 {d22-d23},[r2,: 128]! +vadd.i32 q10,q10,q2 +vld1.8 {d24},[r2,: 64] +vadd.i32 q5,q5,q0 +add r2,r3,#192 +vld1.8 {d26-d27},[r2,: 128]! +vadd.i32 q6,q6,q3 +vld1.8 {d28-d29},[r2,: 128]! +vadd.i32 q8,q8,q4 +vld1.8 {d25},[r2,: 64] +vadd.i32 q10,q10,q2 +vtrn.32 q9,q13 +vadd.i32 q7,q7,q1 +vadd.i32 q5,q5,q0 +vtrn.32 q11,q14 +vadd.i32 q6,q6,q3 +add r2,sp,#560 +vadd.i32 q10,q10,q2 +vtrn.32 d24,d25 +vst1.8 {d12-d13},[r2,: 128] +vshl.i32 q6,q13,#1 +add r2,sp,#576 +vst1.8 {d20-d21},[r2,: 128] +vshl.i32 q10,q14,#1 +add r2,sp,#592 +vst1.8 {d12-d13},[r2,: 128] +vshl.i32 q15,q12,#1 +vadd.i32 q8,q8,q4 +vext.32 d10,d31,d30,#0 +vadd.i32 q7,q7,q1 +add r2,sp,#608 +vst1.8 {d16-d17},[r2,: 128] +vmull.s32 q8,d18,d5 +vmlal.s32 q8,d26,d4 +vmlal.s32 q8,d19,d9 +vmlal.s32 q8,d27,d3 +vmlal.s32 q8,d22,d8 +vmlal.s32 q8,d28,d2 +vmlal.s32 q8,d23,d7 +vmlal.s32 q8,d29,d1 +vmlal.s32 q8,d24,d6 +vmlal.s32 q8,d25,d0 +add r2,sp,#624 +vst1.8 {d14-d15},[r2,: 128] +vmull.s32 q2,d18,d4 +vmlal.s32 q2,d12,d9 +vmlal.s32 q2,d13,d8 +vmlal.s32 q2,d19,d3 +vmlal.s32 q2,d22,d2 +vmlal.s32 q2,d23,d1 +vmlal.s32 q2,d24,d0 +add r2,sp,#640 +vst1.8 {d20-d21},[r2,: 128] +vmull.s32 q7,d18,d9 +vmlal.s32 q7,d26,d3 +vmlal.s32 q7,d19,d8 +vmlal.s32 q7,d27,d2 +vmlal.s32 q7,d22,d7 +vmlal.s32 q7,d28,d1 +vmlal.s32 q7,d23,d6 +vmlal.s32 q7,d29,d0 +add r2,sp,#656 +vst1.8 {d10-d11},[r2,: 128] +vmull.s32 q5,d18,d3 +vmlal.s32 q5,d19,d2 +vmlal.s32 q5,d22,d1 +vmlal.s32 q5,d23,d0 +vmlal.s32 q5,d12,d8 +add r2,sp,#672 +vst1.8 {d16-d17},[r2,: 128] +vmull.s32 q4,d18,d8 +vmlal.s32 q4,d26,d2 +vmlal.s32 q4,d19,d7 +vmlal.s32 q4,d27,d1 +vmlal.s32 q4,d22,d6 +vmlal.s32 q4,d28,d0 +vmull.s32 q8,d18,d7 +vmlal.s32 q8,d26,d1 +vmlal.s32 q8,d19,d6 +vmlal.s32 q8,d27,d0 +add r2,sp,#576 +vld1.8 {d20-d21},[r2,: 128] +vmlal.s32 q7,d24,d21 +vmlal.s32 q7,d25,d20 +vmlal.s32 q4,d23,d21 +vmlal.s32 q4,d29,d20 +vmlal.s32 q8,d22,d21 +vmlal.s32 q8,d28,d20 +vmlal.s32 q5,d24,d20 +add r2,sp,#576 +vst1.8 {d14-d15},[r2,: 128] +vmull.s32 q7,d18,d6 +vmlal.s32 q7,d26,d0 +add r2,sp,#656 +vld1.8 {d30-d31},[r2,: 128] +vmlal.s32 q2,d30,d21 +vmlal.s32 q7,d19,d21 +vmlal.s32 q7,d27,d20 +add r2,sp,#624 +vld1.8 {d26-d27},[r2,: 128] +vmlal.s32 q4,d25,d27 +vmlal.s32 q8,d29,d27 +vmlal.s32 q8,d25,d26 +vmlal.s32 q7,d28,d27 +vmlal.s32 q7,d29,d26 +add r2,sp,#608 +vld1.8 {d28-d29},[r2,: 128] +vmlal.s32 q4,d24,d29 +vmlal.s32 q8,d23,d29 +vmlal.s32 q8,d24,d28 +vmlal.s32 q7,d22,d29 +vmlal.s32 q7,d23,d28 +add r2,sp,#608 +vst1.8 {d8-d9},[r2,: 128] +add r2,sp,#560 +vld1.8 {d8-d9},[r2,: 128] +vmlal.s32 q7,d24,d9 +vmlal.s32 q7,d25,d31 +vmull.s32 q1,d18,d2 +vmlal.s32 q1,d19,d1 +vmlal.s32 q1,d22,d0 +vmlal.s32 q1,d24,d27 +vmlal.s32 q1,d23,d20 +vmlal.s32 q1,d12,d7 +vmlal.s32 q1,d13,d6 +vmull.s32 q6,d18,d1 +vmlal.s32 q6,d19,d0 +vmlal.s32 q6,d23,d27 +vmlal.s32 q6,d22,d20 +vmlal.s32 q6,d24,d26 +vmull.s32 q0,d18,d0 +vmlal.s32 q0,d22,d27 +vmlal.s32 q0,d23,d26 +vmlal.s32 q0,d24,d31 +vmlal.s32 q0,d19,d20 +add r2,sp,#640 +vld1.8 {d18-d19},[r2,: 128] +vmlal.s32 q2,d18,d7 +vmlal.s32 q2,d19,d6 +vmlal.s32 q5,d18,d6 +vmlal.s32 q5,d19,d21 +vmlal.s32 q1,d18,d21 +vmlal.s32 q1,d19,d29 +vmlal.s32 q0,d18,d28 +vmlal.s32 q0,d19,d9 +vmlal.s32 q6,d18,d29 +vmlal.s32 q6,d19,d28 +add r2,sp,#592 +vld1.8 {d18-d19},[r2,: 128] +add r2,sp,#512 +vld1.8 {d22-d23},[r2,: 128] +vmlal.s32 q5,d19,d7 +vmlal.s32 q0,d18,d21 +vmlal.s32 q0,d19,d29 +vmlal.s32 q6,d18,d6 +add r2,sp,#528 +vld1.8 {d6-d7},[r2,: 128] +vmlal.s32 q6,d19,d21 +add r2,sp,#576 +vld1.8 {d18-d19},[r2,: 128] +vmlal.s32 q0,d30,d8 +add r2,sp,#672 +vld1.8 {d20-d21},[r2,: 128] +vmlal.s32 q5,d30,d29 +add r2,sp,#608 +vld1.8 {d24-d25},[r2,: 128] +vmlal.s32 q1,d30,d28 +vadd.i64 q13,q0,q11 +vadd.i64 q14,q5,q11 +vmlal.s32 q6,d30,d9 +vshr.s64 q4,q13,#26 +vshr.s64 q13,q14,#26 +vadd.i64 q7,q7,q4 +vshl.i64 q4,q4,#26 +vadd.i64 q14,q7,q3 +vadd.i64 q9,q9,q13 +vshl.i64 q13,q13,#26 +vadd.i64 q15,q9,q3 +vsub.i64 q0,q0,q4 +vshr.s64 q4,q14,#25 +vsub.i64 q5,q5,q13 +vshr.s64 q13,q15,#25 +vadd.i64 q6,q6,q4 +vshl.i64 q4,q4,#25 +vadd.i64 q14,q6,q11 +vadd.i64 q2,q2,q13 +vsub.i64 q4,q7,q4 +vshr.s64 q7,q14,#26 +vshl.i64 q13,q13,#25 +vadd.i64 q14,q2,q11 +vadd.i64 q8,q8,q7 +vshl.i64 q7,q7,#26 +vadd.i64 q15,q8,q3 +vsub.i64 q9,q9,q13 +vshr.s64 q13,q14,#26 +vsub.i64 q6,q6,q7 +vshr.s64 q7,q15,#25 +vadd.i64 q10,q10,q13 +vshl.i64 q13,q13,#26 +vadd.i64 q14,q10,q3 +vadd.i64 q1,q1,q7 +add r2,r3,#144 +vshl.i64 q7,q7,#25 +add r4,r3,#96 +vadd.i64 q15,q1,q11 +add r2,r2,#8 +vsub.i64 q2,q2,q13 +add r4,r4,#8 +vshr.s64 q13,q14,#25 +vsub.i64 q7,q8,q7 +vshr.s64 q8,q15,#26 +vadd.i64 q14,q13,q13 +vadd.i64 q12,q12,q8 +vtrn.32 d12,d14 +vshl.i64 q8,q8,#26 +vtrn.32 d13,d15 +vadd.i64 q3,q12,q3 +vadd.i64 q0,q0,q14 +vst1.8 d12,[r2,: 64]! +vshl.i64 q7,q13,#4 +vst1.8 d13,[r4,: 64]! +vsub.i64 q1,q1,q8 +vshr.s64 q3,q3,#25 +vadd.i64 q0,q0,q7 +vadd.i64 q5,q5,q3 +vshl.i64 q3,q3,#25 +vadd.i64 q6,q5,q11 +vadd.i64 q0,q0,q13 +vshl.i64 q7,q13,#25 +vadd.i64 q8,q0,q11 +vsub.i64 q3,q12,q3 +vshr.s64 q6,q6,#26 +vsub.i64 q7,q10,q7 +vtrn.32 d2,d6 +vshr.s64 q8,q8,#26 +vtrn.32 d3,d7 +vadd.i64 q3,q9,q6 +vst1.8 d2,[r2,: 64] +vshl.i64 q6,q6,#26 +vst1.8 d3,[r4,: 64] +vadd.i64 q1,q4,q8 +vtrn.32 d4,d14 +vshl.i64 q4,q8,#26 +vtrn.32 d5,d15 +vsub.i64 q5,q5,q6 +add r2,r2,#16 +vsub.i64 q0,q0,q4 +vst1.8 d4,[r2,: 64] +add r4,r4,#16 +vst1.8 d5,[r4,: 64] +vtrn.32 d10,d6 +vtrn.32 d11,d7 +sub r2,r2,#8 +sub r4,r4,#8 +vtrn.32 d0,d2 +vtrn.32 d1,d3 +vst1.8 d10,[r2,: 64] +vst1.8 d11,[r4,: 64] +sub r2,r2,#24 +sub r4,r4,#24 +vst1.8 d0,[r2,: 64] +vst1.8 d1,[r4,: 64] +add r2,r3,#288 +add r4,r3,#336 +vld1.8 {d0-d1},[r2,: 128]! +vld1.8 {d2-d3},[r4,: 128]! +vsub.i32 q0,q0,q1 +vld1.8 {d2-d3},[r2,: 128]! +vld1.8 {d4-d5},[r4,: 128]! +vsub.i32 q1,q1,q2 +add r5,r3,#240 +vld1.8 {d4},[r2,: 64] +vld1.8 {d6},[r4,: 64] +vsub.i32 q2,q2,q3 +vst1.8 {d0-d1},[r5,: 128]! +vst1.8 {d2-d3},[r5,: 128]! +vst1.8 d4,[r5,: 64] +add r2,r3,#144 +add r4,r3,#96 +add r5,r3,#144 +add r6,r3,#192 +vld1.8 {d0-d1},[r2,: 128]! +vld1.8 {d2-d3},[r4,: 128]! +vsub.i32 q2,q0,q1 +vadd.i32 q0,q0,q1 +vld1.8 {d2-d3},[r2,: 128]! +vld1.8 {d6-d7},[r4,: 128]! +vsub.i32 q4,q1,q3 +vadd.i32 q1,q1,q3 +vld1.8 {d6},[r2,: 64] +vld1.8 {d10},[r4,: 64] +vsub.i32 q6,q3,q5 +vadd.i32 q3,q3,q5 +vst1.8 {d4-d5},[r5,: 128]! +vst1.8 {d0-d1},[r6,: 128]! +vst1.8 {d8-d9},[r5,: 128]! +vst1.8 {d2-d3},[r6,: 128]! +vst1.8 d12,[r5,: 64] +vst1.8 d6,[r6,: 64] +add r2,r3,#0 +add r4,r3,#240 +vld1.8 {d0-d1},[r4,: 128]! +vld1.8 {d2-d3},[r4,: 128]! +vld1.8 {d4},[r4,: 64] +add r4,r3,#336 +vld1.8 {d6-d7},[r4,: 128]! +vtrn.32 q0,q3 +vld1.8 {d8-d9},[r4,: 128]! +vshl.i32 q5,q0,#4 +vtrn.32 q1,q4 +vshl.i32 q6,q3,#4 +vadd.i32 q5,q5,q0 +vadd.i32 q6,q6,q3 +vshl.i32 q7,q1,#4 +vld1.8 {d5},[r4,: 64] +vshl.i32 q8,q4,#4 +vtrn.32 d4,d5 +vadd.i32 q7,q7,q1 +vadd.i32 q8,q8,q4 +vld1.8 {d18-d19},[r2,: 128]! +vshl.i32 q10,q2,#4 +vld1.8 {d22-d23},[r2,: 128]! +vadd.i32 q10,q10,q2 +vld1.8 {d24},[r2,: 64] +vadd.i32 q5,q5,q0 +add r2,r3,#288 +vld1.8 {d26-d27},[r2,: 128]! +vadd.i32 q6,q6,q3 +vld1.8 {d28-d29},[r2,: 128]! +vadd.i32 q8,q8,q4 +vld1.8 {d25},[r2,: 64] +vadd.i32 q10,q10,q2 +vtrn.32 q9,q13 +vadd.i32 q7,q7,q1 +vadd.i32 q5,q5,q0 +vtrn.32 q11,q14 +vadd.i32 q6,q6,q3 +add r2,sp,#560 +vadd.i32 q10,q10,q2 +vtrn.32 d24,d25 +vst1.8 {d12-d13},[r2,: 128] +vshl.i32 q6,q13,#1 +add r2,sp,#576 +vst1.8 {d20-d21},[r2,: 128] +vshl.i32 q10,q14,#1 +add r2,sp,#592 +vst1.8 {d12-d13},[r2,: 128] +vshl.i32 q15,q12,#1 +vadd.i32 q8,q8,q4 +vext.32 d10,d31,d30,#0 +vadd.i32 q7,q7,q1 +add r2,sp,#608 +vst1.8 {d16-d17},[r2,: 128] +vmull.s32 q8,d18,d5 +vmlal.s32 q8,d26,d4 +vmlal.s32 q8,d19,d9 +vmlal.s32 q8,d27,d3 +vmlal.s32 q8,d22,d8 +vmlal.s32 q8,d28,d2 +vmlal.s32 q8,d23,d7 +vmlal.s32 q8,d29,d1 +vmlal.s32 q8,d24,d6 +vmlal.s32 q8,d25,d0 +add r2,sp,#624 +vst1.8 {d14-d15},[r2,: 128] +vmull.s32 q2,d18,d4 +vmlal.s32 q2,d12,d9 +vmlal.s32 q2,d13,d8 +vmlal.s32 q2,d19,d3 +vmlal.s32 q2,d22,d2 +vmlal.s32 q2,d23,d1 +vmlal.s32 q2,d24,d0 +add r2,sp,#640 +vst1.8 {d20-d21},[r2,: 128] +vmull.s32 q7,d18,d9 +vmlal.s32 q7,d26,d3 +vmlal.s32 q7,d19,d8 +vmlal.s32 q7,d27,d2 +vmlal.s32 q7,d22,d7 +vmlal.s32 q7,d28,d1 +vmlal.s32 q7,d23,d6 +vmlal.s32 q7,d29,d0 +add r2,sp,#656 +vst1.8 {d10-d11},[r2,: 128] +vmull.s32 q5,d18,d3 +vmlal.s32 q5,d19,d2 +vmlal.s32 q5,d22,d1 +vmlal.s32 q5,d23,d0 +vmlal.s32 q5,d12,d8 +add r2,sp,#672 +vst1.8 {d16-d17},[r2,: 128] +vmull.s32 q4,d18,d8 +vmlal.s32 q4,d26,d2 +vmlal.s32 q4,d19,d7 +vmlal.s32 q4,d27,d1 +vmlal.s32 q4,d22,d6 +vmlal.s32 q4,d28,d0 +vmull.s32 q8,d18,d7 +vmlal.s32 q8,d26,d1 +vmlal.s32 q8,d19,d6 +vmlal.s32 q8,d27,d0 +add r2,sp,#576 +vld1.8 {d20-d21},[r2,: 128] +vmlal.s32 q7,d24,d21 +vmlal.s32 q7,d25,d20 +vmlal.s32 q4,d23,d21 +vmlal.s32 q4,d29,d20 +vmlal.s32 q8,d22,d21 +vmlal.s32 q8,d28,d20 +vmlal.s32 q5,d24,d20 +add r2,sp,#576 +vst1.8 {d14-d15},[r2,: 128] +vmull.s32 q7,d18,d6 +vmlal.s32 q7,d26,d0 +add r2,sp,#656 +vld1.8 {d30-d31},[r2,: 128] +vmlal.s32 q2,d30,d21 +vmlal.s32 q7,d19,d21 +vmlal.s32 q7,d27,d20 +add r2,sp,#624 +vld1.8 {d26-d27},[r2,: 128] +vmlal.s32 q4,d25,d27 +vmlal.s32 q8,d29,d27 +vmlal.s32 q8,d25,d26 +vmlal.s32 q7,d28,d27 +vmlal.s32 q7,d29,d26 +add r2,sp,#608 +vld1.8 {d28-d29},[r2,: 128] +vmlal.s32 q4,d24,d29 +vmlal.s32 q8,d23,d29 +vmlal.s32 q8,d24,d28 +vmlal.s32 q7,d22,d29 +vmlal.s32 q7,d23,d28 +add r2,sp,#608 +vst1.8 {d8-d9},[r2,: 128] +add r2,sp,#560 +vld1.8 {d8-d9},[r2,: 128] +vmlal.s32 q7,d24,d9 +vmlal.s32 q7,d25,d31 +vmull.s32 q1,d18,d2 +vmlal.s32 q1,d19,d1 +vmlal.s32 q1,d22,d0 +vmlal.s32 q1,d24,d27 +vmlal.s32 q1,d23,d20 +vmlal.s32 q1,d12,d7 +vmlal.s32 q1,d13,d6 +vmull.s32 q6,d18,d1 +vmlal.s32 q6,d19,d0 +vmlal.s32 q6,d23,d27 +vmlal.s32 q6,d22,d20 +vmlal.s32 q6,d24,d26 +vmull.s32 q0,d18,d0 +vmlal.s32 q0,d22,d27 +vmlal.s32 q0,d23,d26 +vmlal.s32 q0,d24,d31 +vmlal.s32 q0,d19,d20 +add r2,sp,#640 +vld1.8 {d18-d19},[r2,: 128] +vmlal.s32 q2,d18,d7 +vmlal.s32 q2,d19,d6 +vmlal.s32 q5,d18,d6 +vmlal.s32 q5,d19,d21 +vmlal.s32 q1,d18,d21 +vmlal.s32 q1,d19,d29 +vmlal.s32 q0,d18,d28 +vmlal.s32 q0,d19,d9 +vmlal.s32 q6,d18,d29 +vmlal.s32 q6,d19,d28 +add r2,sp,#592 +vld1.8 {d18-d19},[r2,: 128] +add r2,sp,#512 +vld1.8 {d22-d23},[r2,: 128] +vmlal.s32 q5,d19,d7 +vmlal.s32 q0,d18,d21 +vmlal.s32 q0,d19,d29 +vmlal.s32 q6,d18,d6 +add r2,sp,#528 +vld1.8 {d6-d7},[r2,: 128] +vmlal.s32 q6,d19,d21 +add r2,sp,#576 +vld1.8 {d18-d19},[r2,: 128] +vmlal.s32 q0,d30,d8 +add r2,sp,#672 +vld1.8 {d20-d21},[r2,: 128] +vmlal.s32 q5,d30,d29 +add r2,sp,#608 +vld1.8 {d24-d25},[r2,: 128] +vmlal.s32 q1,d30,d28 +vadd.i64 q13,q0,q11 +vadd.i64 q14,q5,q11 +vmlal.s32 q6,d30,d9 +vshr.s64 q4,q13,#26 +vshr.s64 q13,q14,#26 +vadd.i64 q7,q7,q4 +vshl.i64 q4,q4,#26 +vadd.i64 q14,q7,q3 +vadd.i64 q9,q9,q13 +vshl.i64 q13,q13,#26 +vadd.i64 q15,q9,q3 +vsub.i64 q0,q0,q4 +vshr.s64 q4,q14,#25 +vsub.i64 q5,q5,q13 +vshr.s64 q13,q15,#25 +vadd.i64 q6,q6,q4 +vshl.i64 q4,q4,#25 +vadd.i64 q14,q6,q11 +vadd.i64 q2,q2,q13 +vsub.i64 q4,q7,q4 +vshr.s64 q7,q14,#26 +vshl.i64 q13,q13,#25 +vadd.i64 q14,q2,q11 +vadd.i64 q8,q8,q7 +vshl.i64 q7,q7,#26 +vadd.i64 q15,q8,q3 +vsub.i64 q9,q9,q13 +vshr.s64 q13,q14,#26 +vsub.i64 q6,q6,q7 +vshr.s64 q7,q15,#25 +vadd.i64 q10,q10,q13 +vshl.i64 q13,q13,#26 +vadd.i64 q14,q10,q3 +vadd.i64 q1,q1,q7 +add r2,r3,#288 +vshl.i64 q7,q7,#25 +add r4,r3,#96 +vadd.i64 q15,q1,q11 +add r2,r2,#8 +vsub.i64 q2,q2,q13 +add r4,r4,#8 +vshr.s64 q13,q14,#25 +vsub.i64 q7,q8,q7 +vshr.s64 q8,q15,#26 +vadd.i64 q14,q13,q13 +vadd.i64 q12,q12,q8 +vtrn.32 d12,d14 +vshl.i64 q8,q8,#26 +vtrn.32 d13,d15 +vadd.i64 q3,q12,q3 +vadd.i64 q0,q0,q14 +vst1.8 d12,[r2,: 64]! +vshl.i64 q7,q13,#4 +vst1.8 d13,[r4,: 64]! +vsub.i64 q1,q1,q8 +vshr.s64 q3,q3,#25 +vadd.i64 q0,q0,q7 +vadd.i64 q5,q5,q3 +vshl.i64 q3,q3,#25 +vadd.i64 q6,q5,q11 +vadd.i64 q0,q0,q13 +vshl.i64 q7,q13,#25 +vadd.i64 q8,q0,q11 +vsub.i64 q3,q12,q3 +vshr.s64 q6,q6,#26 +vsub.i64 q7,q10,q7 +vtrn.32 d2,d6 +vshr.s64 q8,q8,#26 +vtrn.32 d3,d7 +vadd.i64 q3,q9,q6 +vst1.8 d2,[r2,: 64] +vshl.i64 q6,q6,#26 +vst1.8 d3,[r4,: 64] +vadd.i64 q1,q4,q8 +vtrn.32 d4,d14 +vshl.i64 q4,q8,#26 +vtrn.32 d5,d15 +vsub.i64 q5,q5,q6 +add r2,r2,#16 +vsub.i64 q0,q0,q4 +vst1.8 d4,[r2,: 64] +add r4,r4,#16 +vst1.8 d5,[r4,: 64] +vtrn.32 d10,d6 +vtrn.32 d11,d7 +sub r2,r2,#8 +sub r4,r4,#8 +vtrn.32 d0,d2 +vtrn.32 d1,d3 +vst1.8 d10,[r2,: 64] +vst1.8 d11,[r4,: 64] +sub r2,r2,#24 +sub r4,r4,#24 +vst1.8 d0,[r2,: 64] +vst1.8 d1,[r4,: 64] +add r2,sp,#544 +add r4,r3,#144 +add r5,r3,#192 +vld1.8 {d0-d1},[r2,: 128] +vld1.8 {d2-d3},[r4,: 128]! +vld1.8 {d4-d5},[r5,: 128]! +vzip.i32 q1,q2 +vld1.8 {d6-d7},[r4,: 128]! +vld1.8 {d8-d9},[r5,: 128]! +vshl.i32 q5,q1,#1 +vzip.i32 q3,q4 +vshl.i32 q6,q2,#1 +vld1.8 {d14},[r4,: 64] +vshl.i32 q8,q3,#1 +vld1.8 {d15},[r5,: 64] +vshl.i32 q9,q4,#1 +vmul.i32 d21,d7,d1 +vtrn.32 d14,d15 +vmul.i32 q11,q4,q0 +vmul.i32 q0,q7,q0 +vmull.s32 q12,d2,d2 +vmlal.s32 q12,d11,d1 +vmlal.s32 q12,d12,d0 +vmlal.s32 q12,d13,d23 +vmlal.s32 q12,d16,d22 +vmlal.s32 q12,d7,d21 +vmull.s32 q10,d2,d11 +vmlal.s32 q10,d4,d1 +vmlal.s32 q10,d13,d0 +vmlal.s32 q10,d6,d23 +vmlal.s32 q10,d17,d22 +vmull.s32 q13,d10,d4 +vmlal.s32 q13,d11,d3 +vmlal.s32 q13,d13,d1 +vmlal.s32 q13,d16,d0 +vmlal.s32 q13,d17,d23 +vmlal.s32 q13,d8,d22 +vmull.s32 q1,d10,d5 +vmlal.s32 q1,d11,d4 +vmlal.s32 q1,d6,d1 +vmlal.s32 q1,d17,d0 +vmlal.s32 q1,d8,d23 +vmull.s32 q14,d10,d6 +vmlal.s32 q14,d11,d13 +vmlal.s32 q14,d4,d4 +vmlal.s32 q14,d17,d1 +vmlal.s32 q14,d18,d0 +vmlal.s32 q14,d9,d23 +vmull.s32 q11,d10,d7 +vmlal.s32 q11,d11,d6 +vmlal.s32 q11,d12,d5 +vmlal.s32 q11,d8,d1 +vmlal.s32 q11,d19,d0 +vmull.s32 q15,d10,d8 +vmlal.s32 q15,d11,d17 +vmlal.s32 q15,d12,d6 +vmlal.s32 q15,d13,d5 +vmlal.s32 q15,d19,d1 +vmlal.s32 q15,d14,d0 +vmull.s32 q2,d10,d9 +vmlal.s32 q2,d11,d8 +vmlal.s32 q2,d12,d7 +vmlal.s32 q2,d13,d6 +vmlal.s32 q2,d14,d1 +vmull.s32 q0,d15,d1 +vmlal.s32 q0,d10,d14 +vmlal.s32 q0,d11,d19 +vmlal.s32 q0,d12,d8 +vmlal.s32 q0,d13,d17 +vmlal.s32 q0,d6,d6 +add r2,sp,#512 +vld1.8 {d18-d19},[r2,: 128] +vmull.s32 q3,d16,d7 +vmlal.s32 q3,d10,d15 +vmlal.s32 q3,d11,d14 +vmlal.s32 q3,d12,d9 +vmlal.s32 q3,d13,d8 +add r2,sp,#528 +vld1.8 {d8-d9},[r2,: 128] +vadd.i64 q5,q12,q9 +vadd.i64 q6,q15,q9 +vshr.s64 q5,q5,#26 +vshr.s64 q6,q6,#26 +vadd.i64 q7,q10,q5 +vshl.i64 q5,q5,#26 +vadd.i64 q8,q7,q4 +vadd.i64 q2,q2,q6 +vshl.i64 q6,q6,#26 +vadd.i64 q10,q2,q4 +vsub.i64 q5,q12,q5 +vshr.s64 q8,q8,#25 +vsub.i64 q6,q15,q6 +vshr.s64 q10,q10,#25 +vadd.i64 q12,q13,q8 +vshl.i64 q8,q8,#25 +vadd.i64 q13,q12,q9 +vadd.i64 q0,q0,q10 +vsub.i64 q7,q7,q8 +vshr.s64 q8,q13,#26 +vshl.i64 q10,q10,#25 +vadd.i64 q13,q0,q9 +vadd.i64 q1,q1,q8 +vshl.i64 q8,q8,#26 +vadd.i64 q15,q1,q4 +vsub.i64 q2,q2,q10 +vshr.s64 q10,q13,#26 +vsub.i64 q8,q12,q8 +vshr.s64 q12,q15,#25 +vadd.i64 q3,q3,q10 +vshl.i64 q10,q10,#26 +vadd.i64 q13,q3,q4 +vadd.i64 q14,q14,q12 +add r2,r3,#144 +vshl.i64 q12,q12,#25 +add r4,r3,#192 +vadd.i64 q15,q14,q9 +add r2,r2,#8 +vsub.i64 q0,q0,q10 +add r4,r4,#8 +vshr.s64 q10,q13,#25 +vsub.i64 q1,q1,q12 +vshr.s64 q12,q15,#26 +vadd.i64 q13,q10,q10 +vadd.i64 q11,q11,q12 +vtrn.32 d16,d2 +vshl.i64 q12,q12,#26 +vtrn.32 d17,d3 +vadd.i64 q1,q11,q4 +vadd.i64 q4,q5,q13 +vst1.8 d16,[r2,: 64]! +vshl.i64 q5,q10,#4 +vst1.8 d17,[r4,: 64]! +vsub.i64 q8,q14,q12 +vshr.s64 q1,q1,#25 +vadd.i64 q4,q4,q5 +vadd.i64 q5,q6,q1 +vshl.i64 q1,q1,#25 +vadd.i64 q6,q5,q9 +vadd.i64 q4,q4,q10 +vshl.i64 q10,q10,#25 +vadd.i64 q9,q4,q9 +vsub.i64 q1,q11,q1 +vshr.s64 q6,q6,#26 +vsub.i64 q3,q3,q10 +vtrn.32 d16,d2 +vshr.s64 q9,q9,#26 +vtrn.32 d17,d3 +vadd.i64 q1,q2,q6 +vst1.8 d16,[r2,: 64] +vshl.i64 q2,q6,#26 +vst1.8 d17,[r4,: 64] +vadd.i64 q6,q7,q9 +vtrn.32 d0,d6 +vshl.i64 q7,q9,#26 +vtrn.32 d1,d7 +vsub.i64 q2,q5,q2 +add r2,r2,#16 +vsub.i64 q3,q4,q7 +vst1.8 d0,[r2,: 64] +add r4,r4,#16 +vst1.8 d1,[r4,: 64] +vtrn.32 d4,d2 +vtrn.32 d5,d3 +sub r2,r2,#8 +sub r4,r4,#8 +vtrn.32 d6,d12 +vtrn.32 d7,d13 +vst1.8 d4,[r2,: 64] +vst1.8 d5,[r4,: 64] +sub r2,r2,#24 +sub r4,r4,#24 +vst1.8 d6,[r2,: 64] +vst1.8 d7,[r4,: 64] +add r2,r3,#336 +add r4,r3,#288 +vld1.8 {d0-d1},[r2,: 128]! +vld1.8 {d2-d3},[r4,: 128]! +vadd.i32 q0,q0,q1 +vld1.8 {d2-d3},[r2,: 128]! +vld1.8 {d4-d5},[r4,: 128]! +vadd.i32 q1,q1,q2 +add r5,r3,#288 +vld1.8 {d4},[r2,: 64] +vld1.8 {d6},[r4,: 64] +vadd.i32 q2,q2,q3 +vst1.8 {d0-d1},[r5,: 128]! +vst1.8 {d2-d3},[r5,: 128]! +vst1.8 d4,[r5,: 64] +add r2,r3,#48 +add r4,r3,#144 +vld1.8 {d0-d1},[r4,: 128]! +vld1.8 {d2-d3},[r4,: 128]! +vld1.8 {d4},[r4,: 64] +add r4,r3,#288 +vld1.8 {d6-d7},[r4,: 128]! +vtrn.32 q0,q3 +vld1.8 {d8-d9},[r4,: 128]! +vshl.i32 q5,q0,#4 +vtrn.32 q1,q4 +vshl.i32 q6,q3,#4 +vadd.i32 q5,q5,q0 +vadd.i32 q6,q6,q3 +vshl.i32 q7,q1,#4 +vld1.8 {d5},[r4,: 64] +vshl.i32 q8,q4,#4 +vtrn.32 d4,d5 +vadd.i32 q7,q7,q1 +vadd.i32 q8,q8,q4 +vld1.8 {d18-d19},[r2,: 128]! +vshl.i32 q10,q2,#4 +vld1.8 {d22-d23},[r2,: 128]! +vadd.i32 q10,q10,q2 +vld1.8 {d24},[r2,: 64] +vadd.i32 q5,q5,q0 +add r2,r3,#240 +vld1.8 {d26-d27},[r2,: 128]! +vadd.i32 q6,q6,q3 +vld1.8 {d28-d29},[r2,: 128]! +vadd.i32 q8,q8,q4 +vld1.8 {d25},[r2,: 64] +vadd.i32 q10,q10,q2 +vtrn.32 q9,q13 +vadd.i32 q7,q7,q1 +vadd.i32 q5,q5,q0 +vtrn.32 q11,q14 +vadd.i32 q6,q6,q3 +add r2,sp,#560 +vadd.i32 q10,q10,q2 +vtrn.32 d24,d25 +vst1.8 {d12-d13},[r2,: 128] +vshl.i32 q6,q13,#1 +add r2,sp,#576 +vst1.8 {d20-d21},[r2,: 128] +vshl.i32 q10,q14,#1 +add r2,sp,#592 +vst1.8 {d12-d13},[r2,: 128] +vshl.i32 q15,q12,#1 +vadd.i32 q8,q8,q4 +vext.32 d10,d31,d30,#0 +vadd.i32 q7,q7,q1 +add r2,sp,#608 +vst1.8 {d16-d17},[r2,: 128] +vmull.s32 q8,d18,d5 +vmlal.s32 q8,d26,d4 +vmlal.s32 q8,d19,d9 +vmlal.s32 q8,d27,d3 +vmlal.s32 q8,d22,d8 +vmlal.s32 q8,d28,d2 +vmlal.s32 q8,d23,d7 +vmlal.s32 q8,d29,d1 +vmlal.s32 q8,d24,d6 +vmlal.s32 q8,d25,d0 +add r2,sp,#624 +vst1.8 {d14-d15},[r2,: 128] +vmull.s32 q2,d18,d4 +vmlal.s32 q2,d12,d9 +vmlal.s32 q2,d13,d8 +vmlal.s32 q2,d19,d3 +vmlal.s32 q2,d22,d2 +vmlal.s32 q2,d23,d1 +vmlal.s32 q2,d24,d0 +add r2,sp,#640 +vst1.8 {d20-d21},[r2,: 128] +vmull.s32 q7,d18,d9 +vmlal.s32 q7,d26,d3 +vmlal.s32 q7,d19,d8 +vmlal.s32 q7,d27,d2 +vmlal.s32 q7,d22,d7 +vmlal.s32 q7,d28,d1 +vmlal.s32 q7,d23,d6 +vmlal.s32 q7,d29,d0 +add r2,sp,#656 +vst1.8 {d10-d11},[r2,: 128] +vmull.s32 q5,d18,d3 +vmlal.s32 q5,d19,d2 +vmlal.s32 q5,d22,d1 +vmlal.s32 q5,d23,d0 +vmlal.s32 q5,d12,d8 +add r2,sp,#672 +vst1.8 {d16-d17},[r2,: 128] +vmull.s32 q4,d18,d8 +vmlal.s32 q4,d26,d2 +vmlal.s32 q4,d19,d7 +vmlal.s32 q4,d27,d1 +vmlal.s32 q4,d22,d6 +vmlal.s32 q4,d28,d0 +vmull.s32 q8,d18,d7 +vmlal.s32 q8,d26,d1 +vmlal.s32 q8,d19,d6 +vmlal.s32 q8,d27,d0 +add r2,sp,#576 +vld1.8 {d20-d21},[r2,: 128] +vmlal.s32 q7,d24,d21 +vmlal.s32 q7,d25,d20 +vmlal.s32 q4,d23,d21 +vmlal.s32 q4,d29,d20 +vmlal.s32 q8,d22,d21 +vmlal.s32 q8,d28,d20 +vmlal.s32 q5,d24,d20 +add r2,sp,#576 +vst1.8 {d14-d15},[r2,: 128] +vmull.s32 q7,d18,d6 +vmlal.s32 q7,d26,d0 +add r2,sp,#656 +vld1.8 {d30-d31},[r2,: 128] +vmlal.s32 q2,d30,d21 +vmlal.s32 q7,d19,d21 +vmlal.s32 q7,d27,d20 +add r2,sp,#624 +vld1.8 {d26-d27},[r2,: 128] +vmlal.s32 q4,d25,d27 +vmlal.s32 q8,d29,d27 +vmlal.s32 q8,d25,d26 +vmlal.s32 q7,d28,d27 +vmlal.s32 q7,d29,d26 +add r2,sp,#608 +vld1.8 {d28-d29},[r2,: 128] +vmlal.s32 q4,d24,d29 +vmlal.s32 q8,d23,d29 +vmlal.s32 q8,d24,d28 +vmlal.s32 q7,d22,d29 +vmlal.s32 q7,d23,d28 +add r2,sp,#608 +vst1.8 {d8-d9},[r2,: 128] +add r2,sp,#560 +vld1.8 {d8-d9},[r2,: 128] +vmlal.s32 q7,d24,d9 +vmlal.s32 q7,d25,d31 +vmull.s32 q1,d18,d2 +vmlal.s32 q1,d19,d1 +vmlal.s32 q1,d22,d0 +vmlal.s32 q1,d24,d27 +vmlal.s32 q1,d23,d20 +vmlal.s32 q1,d12,d7 +vmlal.s32 q1,d13,d6 +vmull.s32 q6,d18,d1 +vmlal.s32 q6,d19,d0 +vmlal.s32 q6,d23,d27 +vmlal.s32 q6,d22,d20 +vmlal.s32 q6,d24,d26 +vmull.s32 q0,d18,d0 +vmlal.s32 q0,d22,d27 +vmlal.s32 q0,d23,d26 +vmlal.s32 q0,d24,d31 +vmlal.s32 q0,d19,d20 +add r2,sp,#640 +vld1.8 {d18-d19},[r2,: 128] +vmlal.s32 q2,d18,d7 +vmlal.s32 q2,d19,d6 +vmlal.s32 q5,d18,d6 +vmlal.s32 q5,d19,d21 +vmlal.s32 q1,d18,d21 +vmlal.s32 q1,d19,d29 +vmlal.s32 q0,d18,d28 +vmlal.s32 q0,d19,d9 +vmlal.s32 q6,d18,d29 +vmlal.s32 q6,d19,d28 +add r2,sp,#592 +vld1.8 {d18-d19},[r2,: 128] +add r2,sp,#512 +vld1.8 {d22-d23},[r2,: 128] +vmlal.s32 q5,d19,d7 +vmlal.s32 q0,d18,d21 +vmlal.s32 q0,d19,d29 +vmlal.s32 q6,d18,d6 +add r2,sp,#528 +vld1.8 {d6-d7},[r2,: 128] +vmlal.s32 q6,d19,d21 +add r2,sp,#576 +vld1.8 {d18-d19},[r2,: 128] +vmlal.s32 q0,d30,d8 +add r2,sp,#672 +vld1.8 {d20-d21},[r2,: 128] +vmlal.s32 q5,d30,d29 +add r2,sp,#608 +vld1.8 {d24-d25},[r2,: 128] +vmlal.s32 q1,d30,d28 +vadd.i64 q13,q0,q11 +vadd.i64 q14,q5,q11 +vmlal.s32 q6,d30,d9 +vshr.s64 q4,q13,#26 +vshr.s64 q13,q14,#26 +vadd.i64 q7,q7,q4 +vshl.i64 q4,q4,#26 +vadd.i64 q14,q7,q3 +vadd.i64 q9,q9,q13 +vshl.i64 q13,q13,#26 +vadd.i64 q15,q9,q3 +vsub.i64 q0,q0,q4 +vshr.s64 q4,q14,#25 +vsub.i64 q5,q5,q13 +vshr.s64 q13,q15,#25 +vadd.i64 q6,q6,q4 +vshl.i64 q4,q4,#25 +vadd.i64 q14,q6,q11 +vadd.i64 q2,q2,q13 +vsub.i64 q4,q7,q4 +vshr.s64 q7,q14,#26 +vshl.i64 q13,q13,#25 +vadd.i64 q14,q2,q11 +vadd.i64 q8,q8,q7 +vshl.i64 q7,q7,#26 +vadd.i64 q15,q8,q3 +vsub.i64 q9,q9,q13 +vshr.s64 q13,q14,#26 +vsub.i64 q6,q6,q7 +vshr.s64 q7,q15,#25 +vadd.i64 q10,q10,q13 +vshl.i64 q13,q13,#26 +vadd.i64 q14,q10,q3 +vadd.i64 q1,q1,q7 +add r2,r3,#240 +vshl.i64 q7,q7,#25 +add r4,r3,#144 +vadd.i64 q15,q1,q11 +add r2,r2,#8 +vsub.i64 q2,q2,q13 +add r4,r4,#8 +vshr.s64 q13,q14,#25 +vsub.i64 q7,q8,q7 +vshr.s64 q8,q15,#26 +vadd.i64 q14,q13,q13 +vadd.i64 q12,q12,q8 +vtrn.32 d12,d14 +vshl.i64 q8,q8,#26 +vtrn.32 d13,d15 +vadd.i64 q3,q12,q3 +vadd.i64 q0,q0,q14 +vst1.8 d12,[r2,: 64]! +vshl.i64 q7,q13,#4 +vst1.8 d13,[r4,: 64]! +vsub.i64 q1,q1,q8 +vshr.s64 q3,q3,#25 +vadd.i64 q0,q0,q7 +vadd.i64 q5,q5,q3 +vshl.i64 q3,q3,#25 +vadd.i64 q6,q5,q11 +vadd.i64 q0,q0,q13 +vshl.i64 q7,q13,#25 +vadd.i64 q8,q0,q11 +vsub.i64 q3,q12,q3 +vshr.s64 q6,q6,#26 +vsub.i64 q7,q10,q7 +vtrn.32 d2,d6 +vshr.s64 q8,q8,#26 +vtrn.32 d3,d7 +vadd.i64 q3,q9,q6 +vst1.8 d2,[r2,: 64] +vshl.i64 q6,q6,#26 +vst1.8 d3,[r4,: 64] +vadd.i64 q1,q4,q8 +vtrn.32 d4,d14 +vshl.i64 q4,q8,#26 +vtrn.32 d5,d15 +vsub.i64 q5,q5,q6 +add r2,r2,#16 +vsub.i64 q0,q0,q4 +vst1.8 d4,[r2,: 64] +add r4,r4,#16 +vst1.8 d5,[r4,: 64] +vtrn.32 d10,d6 +vtrn.32 d11,d7 +sub r2,r2,#8 +sub r4,r4,#8 +vtrn.32 d0,d2 +vtrn.32 d1,d3 +vst1.8 d10,[r2,: 64] +vst1.8 d11,[r4,: 64] +sub r2,r2,#24 +sub r4,r4,#24 +vst1.8 d0,[r2,: 64] +vst1.8 d1,[r4,: 64] +ldr r2,[sp,#488] +ldr r4,[sp,#492] +subs r5,r2,#1 +bge ._mainloop +add r1,r3,#144 +add r2,r3,#336 +vld1.8 {d0-d1},[r1,: 128]! +vld1.8 {d2-d3},[r1,: 128]! +vld1.8 {d4},[r1,: 64] +vst1.8 {d0-d1},[r2,: 128]! +vst1.8 {d2-d3},[r2,: 128]! +vst1.8 d4,[r2,: 64] +ldr r1,=0 +._invertloop: +add r2,r3,#144 +ldr r4,=0 +ldr r5,=2 +cmp r1,#1 +ldreq r5,=1 +addeq r2,r3,#336 +addeq r4,r3,#48 +cmp r1,#2 +ldreq r5,=1 +addeq r2,r3,#48 +cmp r1,#3 +ldreq r5,=5 +addeq r4,r3,#336 +cmp r1,#4 +ldreq r5,=10 +cmp r1,#5 +ldreq r5,=20 +cmp r1,#6 +ldreq r5,=10 +addeq r2,r3,#336 +addeq r4,r3,#336 +cmp r1,#7 +ldreq r5,=50 +cmp r1,#8 +ldreq r5,=100 +cmp r1,#9 +ldreq r5,=50 +addeq r2,r3,#336 +cmp r1,#10 +ldreq r5,=5 +addeq r2,r3,#48 +cmp r1,#11 +ldreq r5,=0 +addeq r2,r3,#96 +add r6,r3,#144 +add r7,r3,#288 +vld1.8 {d0-d1},[r6,: 128]! +vld1.8 {d2-d3},[r6,: 128]! +vld1.8 {d4},[r6,: 64] +vst1.8 {d0-d1},[r7,: 128]! +vst1.8 {d2-d3},[r7,: 128]! +vst1.8 d4,[r7,: 64] +cmp r5,#0 +beq ._skipsquaringloop +._squaringloop: +add r6,r3,#288 +add r7,r3,#288 +add r8,r3,#288 +vmov.i32 q0,#19 +vmov.i32 q1,#0 +vmov.i32 q2,#1 +vzip.i32 q1,q2 +vld1.8 {d4-d5},[r7,: 128]! +vld1.8 {d6-d7},[r7,: 128]! +vld1.8 {d9},[r7,: 64] +vld1.8 {d10-d11},[r6,: 128]! +add r7,sp,#416 +vld1.8 {d12-d13},[r6,: 128]! +vmul.i32 q7,q2,q0 +vld1.8 {d8},[r6,: 64] +vext.32 d17,d11,d10,#1 +vmul.i32 q9,q3,q0 +vext.32 d16,d10,d8,#1 +vshl.u32 q10,q5,q1 +vext.32 d22,d14,d4,#1 +vext.32 d24,d18,d6,#1 +vshl.u32 q13,q6,q1 +vshl.u32 d28,d8,d2 +vrev64.i32 d22,d22 +vmul.i32 d1,d9,d1 +vrev64.i32 d24,d24 +vext.32 d29,d8,d13,#1 +vext.32 d0,d1,d9,#1 +vrev64.i32 d0,d0 +vext.32 d2,d9,d1,#1 +vext.32 d23,d15,d5,#1 +vmull.s32 q4,d20,d4 +vrev64.i32 d23,d23 +vmlal.s32 q4,d21,d1 +vrev64.i32 d2,d2 +vmlal.s32 q4,d26,d19 +vext.32 d3,d5,d15,#1 +vmlal.s32 q4,d27,d18 +vrev64.i32 d3,d3 +vmlal.s32 q4,d28,d15 +vext.32 d14,d12,d11,#1 +vmull.s32 q5,d16,d23 +vext.32 d15,d13,d12,#1 +vmlal.s32 q5,d17,d4 +vst1.8 d8,[r7,: 64]! +vmlal.s32 q5,d14,d1 +vext.32 d12,d9,d8,#0 +vmlal.s32 q5,d15,d19 +vmov.i64 d13,#0 +vmlal.s32 q5,d29,d18 +vext.32 d25,d19,d7,#1 +vmlal.s32 q6,d20,d5 +vrev64.i32 d25,d25 +vmlal.s32 q6,d21,d4 +vst1.8 d11,[r7,: 64]! +vmlal.s32 q6,d26,d1 +vext.32 d9,d10,d10,#0 +vmlal.s32 q6,d27,d19 +vmov.i64 d8,#0 +vmlal.s32 q6,d28,d18 +vmlal.s32 q4,d16,d24 +vmlal.s32 q4,d17,d5 +vmlal.s32 q4,d14,d4 +vst1.8 d12,[r7,: 64]! +vmlal.s32 q4,d15,d1 +vext.32 d10,d13,d12,#0 +vmlal.s32 q4,d29,d19 +vmov.i64 d11,#0 +vmlal.s32 q5,d20,d6 +vmlal.s32 q5,d21,d5 +vmlal.s32 q5,d26,d4 +vext.32 d13,d8,d8,#0 +vmlal.s32 q5,d27,d1 +vmov.i64 d12,#0 +vmlal.s32 q5,d28,d19 +vst1.8 d9,[r7,: 64]! +vmlal.s32 q6,d16,d25 +vmlal.s32 q6,d17,d6 +vst1.8 d10,[r7,: 64] +vmlal.s32 q6,d14,d5 +vext.32 d8,d11,d10,#0 +vmlal.s32 q6,d15,d4 +vmov.i64 d9,#0 +vmlal.s32 q6,d29,d1 +vmlal.s32 q4,d20,d7 +vmlal.s32 q4,d21,d6 +vmlal.s32 q4,d26,d5 +vext.32 d11,d12,d12,#0 +vmlal.s32 q4,d27,d4 +vmov.i64 d10,#0 +vmlal.s32 q4,d28,d1 +vmlal.s32 q5,d16,d0 +sub r6,r7,#32 +vmlal.s32 q5,d17,d7 +vmlal.s32 q5,d14,d6 +vext.32 d30,d9,d8,#0 +vmlal.s32 q5,d15,d5 +vld1.8 {d31},[r6,: 64]! +vmlal.s32 q5,d29,d4 +vmlal.s32 q15,d20,d0 +vext.32 d0,d6,d18,#1 +vmlal.s32 q15,d21,d25 +vrev64.i32 d0,d0 +vmlal.s32 q15,d26,d24 +vext.32 d1,d7,d19,#1 +vext.32 d7,d10,d10,#0 +vmlal.s32 q15,d27,d23 +vrev64.i32 d1,d1 +vld1.8 {d6},[r6,: 64] +vmlal.s32 q15,d28,d22 +vmlal.s32 q3,d16,d4 +add r6,r6,#24 +vmlal.s32 q3,d17,d2 +vext.32 d4,d31,d30,#0 +vmov d17,d11 +vmlal.s32 q3,d14,d1 +vext.32 d11,d13,d13,#0 +vext.32 d13,d30,d30,#0 +vmlal.s32 q3,d15,d0 +vext.32 d1,d8,d8,#0 +vmlal.s32 q3,d29,d3 +vld1.8 {d5},[r6,: 64] +sub r6,r6,#16 +vext.32 d10,d6,d6,#0 +vmov.i32 q1,#0xffffffff +vshl.i64 q4,q1,#25 +add r7,sp,#512 +vld1.8 {d14-d15},[r7,: 128] +vadd.i64 q9,q2,q7 +vshl.i64 q1,q1,#26 +vshr.s64 q10,q9,#26 +vld1.8 {d0},[r6,: 64]! +vadd.i64 q5,q5,q10 +vand q9,q9,q1 +vld1.8 {d16},[r6,: 64]! +add r6,sp,#528 +vld1.8 {d20-d21},[r6,: 128] +vadd.i64 q11,q5,q10 +vsub.i64 q2,q2,q9 +vshr.s64 q9,q11,#25 +vext.32 d12,d5,d4,#0 +vand q11,q11,q4 +vadd.i64 q0,q0,q9 +vmov d19,d7 +vadd.i64 q3,q0,q7 +vsub.i64 q5,q5,q11 +vshr.s64 q11,q3,#26 +vext.32 d18,d11,d10,#0 +vand q3,q3,q1 +vadd.i64 q8,q8,q11 +vadd.i64 q11,q8,q10 +vsub.i64 q0,q0,q3 +vshr.s64 q3,q11,#25 +vand q11,q11,q4 +vadd.i64 q3,q6,q3 +vadd.i64 q6,q3,q7 +vsub.i64 q8,q8,q11 +vshr.s64 q11,q6,#26 +vand q6,q6,q1 +vadd.i64 q9,q9,q11 +vadd.i64 d25,d19,d21 +vsub.i64 q3,q3,q6 +vshr.s64 d23,d25,#25 +vand q4,q12,q4 +vadd.i64 d21,d23,d23 +vshl.i64 d25,d23,#4 +vadd.i64 d21,d21,d23 +vadd.i64 d25,d25,d21 +vadd.i64 d4,d4,d25 +vzip.i32 q0,q8 +vadd.i64 d12,d4,d14 +add r6,r8,#8 +vst1.8 d0,[r6,: 64] +vsub.i64 d19,d19,d9 +add r6,r6,#16 +vst1.8 d16,[r6,: 64] +vshr.s64 d22,d12,#26 +vand q0,q6,q1 +vadd.i64 d10,d10,d22 +vzip.i32 q3,q9 +vsub.i64 d4,d4,d0 +sub r6,r6,#8 +vst1.8 d6,[r6,: 64] +add r6,r6,#16 +vst1.8 d18,[r6,: 64] +vzip.i32 q2,q5 +sub r6,r6,#32 +vst1.8 d4,[r6,: 64] +subs r5,r5,#1 +bhi ._squaringloop +._skipsquaringloop: +mov r2,r2 +add r5,r3,#288 +add r6,r3,#144 +vmov.i32 q0,#19 +vmov.i32 q1,#0 +vmov.i32 q2,#1 +vzip.i32 q1,q2 +vld1.8 {d4-d5},[r5,: 128]! +vld1.8 {d6-d7},[r5,: 128]! +vld1.8 {d9},[r5,: 64] +vld1.8 {d10-d11},[r2,: 128]! +add r5,sp,#416 +vld1.8 {d12-d13},[r2,: 128]! +vmul.i32 q7,q2,q0 +vld1.8 {d8},[r2,: 64] +vext.32 d17,d11,d10,#1 +vmul.i32 q9,q3,q0 +vext.32 d16,d10,d8,#1 +vshl.u32 q10,q5,q1 +vext.32 d22,d14,d4,#1 +vext.32 d24,d18,d6,#1 +vshl.u32 q13,q6,q1 +vshl.u32 d28,d8,d2 +vrev64.i32 d22,d22 +vmul.i32 d1,d9,d1 +vrev64.i32 d24,d24 +vext.32 d29,d8,d13,#1 +vext.32 d0,d1,d9,#1 +vrev64.i32 d0,d0 +vext.32 d2,d9,d1,#1 +vext.32 d23,d15,d5,#1 +vmull.s32 q4,d20,d4 +vrev64.i32 d23,d23 +vmlal.s32 q4,d21,d1 +vrev64.i32 d2,d2 +vmlal.s32 q4,d26,d19 +vext.32 d3,d5,d15,#1 +vmlal.s32 q4,d27,d18 +vrev64.i32 d3,d3 +vmlal.s32 q4,d28,d15 +vext.32 d14,d12,d11,#1 +vmull.s32 q5,d16,d23 +vext.32 d15,d13,d12,#1 +vmlal.s32 q5,d17,d4 +vst1.8 d8,[r5,: 64]! +vmlal.s32 q5,d14,d1 +vext.32 d12,d9,d8,#0 +vmlal.s32 q5,d15,d19 +vmov.i64 d13,#0 +vmlal.s32 q5,d29,d18 +vext.32 d25,d19,d7,#1 +vmlal.s32 q6,d20,d5 +vrev64.i32 d25,d25 +vmlal.s32 q6,d21,d4 +vst1.8 d11,[r5,: 64]! +vmlal.s32 q6,d26,d1 +vext.32 d9,d10,d10,#0 +vmlal.s32 q6,d27,d19 +vmov.i64 d8,#0 +vmlal.s32 q6,d28,d18 +vmlal.s32 q4,d16,d24 +vmlal.s32 q4,d17,d5 +vmlal.s32 q4,d14,d4 +vst1.8 d12,[r5,: 64]! +vmlal.s32 q4,d15,d1 +vext.32 d10,d13,d12,#0 +vmlal.s32 q4,d29,d19 +vmov.i64 d11,#0 +vmlal.s32 q5,d20,d6 +vmlal.s32 q5,d21,d5 +vmlal.s32 q5,d26,d4 +vext.32 d13,d8,d8,#0 +vmlal.s32 q5,d27,d1 +vmov.i64 d12,#0 +vmlal.s32 q5,d28,d19 +vst1.8 d9,[r5,: 64]! +vmlal.s32 q6,d16,d25 +vmlal.s32 q6,d17,d6 +vst1.8 d10,[r5,: 64] +vmlal.s32 q6,d14,d5 +vext.32 d8,d11,d10,#0 +vmlal.s32 q6,d15,d4 +vmov.i64 d9,#0 +vmlal.s32 q6,d29,d1 +vmlal.s32 q4,d20,d7 +vmlal.s32 q4,d21,d6 +vmlal.s32 q4,d26,d5 +vext.32 d11,d12,d12,#0 +vmlal.s32 q4,d27,d4 +vmov.i64 d10,#0 +vmlal.s32 q4,d28,d1 +vmlal.s32 q5,d16,d0 +sub r2,r5,#32 +vmlal.s32 q5,d17,d7 +vmlal.s32 q5,d14,d6 +vext.32 d30,d9,d8,#0 +vmlal.s32 q5,d15,d5 +vld1.8 {d31},[r2,: 64]! +vmlal.s32 q5,d29,d4 +vmlal.s32 q15,d20,d0 +vext.32 d0,d6,d18,#1 +vmlal.s32 q15,d21,d25 +vrev64.i32 d0,d0 +vmlal.s32 q15,d26,d24 +vext.32 d1,d7,d19,#1 +vext.32 d7,d10,d10,#0 +vmlal.s32 q15,d27,d23 +vrev64.i32 d1,d1 +vld1.8 {d6},[r2,: 64] +vmlal.s32 q15,d28,d22 +vmlal.s32 q3,d16,d4 +add r2,r2,#24 +vmlal.s32 q3,d17,d2 +vext.32 d4,d31,d30,#0 +vmov d17,d11 +vmlal.s32 q3,d14,d1 +vext.32 d11,d13,d13,#0 +vext.32 d13,d30,d30,#0 +vmlal.s32 q3,d15,d0 +vext.32 d1,d8,d8,#0 +vmlal.s32 q3,d29,d3 +vld1.8 {d5},[r2,: 64] +sub r2,r2,#16 +vext.32 d10,d6,d6,#0 +vmov.i32 q1,#0xffffffff +vshl.i64 q4,q1,#25 +add r5,sp,#512 +vld1.8 {d14-d15},[r5,: 128] +vadd.i64 q9,q2,q7 +vshl.i64 q1,q1,#26 +vshr.s64 q10,q9,#26 +vld1.8 {d0},[r2,: 64]! +vadd.i64 q5,q5,q10 +vand q9,q9,q1 +vld1.8 {d16},[r2,: 64]! +add r2,sp,#528 +vld1.8 {d20-d21},[r2,: 128] +vadd.i64 q11,q5,q10 +vsub.i64 q2,q2,q9 +vshr.s64 q9,q11,#25 +vext.32 d12,d5,d4,#0 +vand q11,q11,q4 +vadd.i64 q0,q0,q9 +vmov d19,d7 +vadd.i64 q3,q0,q7 +vsub.i64 q5,q5,q11 +vshr.s64 q11,q3,#26 +vext.32 d18,d11,d10,#0 +vand q3,q3,q1 +vadd.i64 q8,q8,q11 +vadd.i64 q11,q8,q10 +vsub.i64 q0,q0,q3 +vshr.s64 q3,q11,#25 +vand q11,q11,q4 +vadd.i64 q3,q6,q3 +vadd.i64 q6,q3,q7 +vsub.i64 q8,q8,q11 +vshr.s64 q11,q6,#26 +vand q6,q6,q1 +vadd.i64 q9,q9,q11 +vadd.i64 d25,d19,d21 +vsub.i64 q3,q3,q6 +vshr.s64 d23,d25,#25 +vand q4,q12,q4 +vadd.i64 d21,d23,d23 +vshl.i64 d25,d23,#4 +vadd.i64 d21,d21,d23 +vadd.i64 d25,d25,d21 +vadd.i64 d4,d4,d25 +vzip.i32 q0,q8 +vadd.i64 d12,d4,d14 +add r2,r6,#8 +vst1.8 d0,[r2,: 64] +vsub.i64 d19,d19,d9 +add r2,r2,#16 +vst1.8 d16,[r2,: 64] +vshr.s64 d22,d12,#26 +vand q0,q6,q1 +vadd.i64 d10,d10,d22 +vzip.i32 q3,q9 +vsub.i64 d4,d4,d0 +sub r2,r2,#8 +vst1.8 d6,[r2,: 64] +add r2,r2,#16 +vst1.8 d18,[r2,: 64] +vzip.i32 q2,q5 +sub r2,r2,#32 +vst1.8 d4,[r2,: 64] +cmp r4,#0 +beq ._skippostcopy +add r2,r3,#144 +mov r4,r4 +vld1.8 {d0-d1},[r2,: 128]! +vld1.8 {d2-d3},[r2,: 128]! +vld1.8 {d4},[r2,: 64] +vst1.8 {d0-d1},[r4,: 128]! +vst1.8 {d2-d3},[r4,: 128]! +vst1.8 d4,[r4,: 64] +._skippostcopy: +cmp r1,#1 +bne ._skipfinalcopy +add r2,r3,#288 +add r4,r3,#144 +vld1.8 {d0-d1},[r2,: 128]! +vld1.8 {d2-d3},[r2,: 128]! +vld1.8 {d4},[r2,: 64] +vst1.8 {d0-d1},[r4,: 128]! +vst1.8 {d2-d3},[r4,: 128]! +vst1.8 d4,[r4,: 64] +._skipfinalcopy: +add r1,r1,#1 +cmp r1,#12 +blo ._invertloop +add r1,r3,#144 +ldr r2,[r1],#4 +ldr r3,[r1],#4 +ldr r4,[r1],#4 +ldr r5,[r1],#4 +ldr r6,[r1],#4 +ldr r7,[r1],#4 +ldr r8,[r1],#4 +ldr r9,[r1],#4 +ldr r10,[r1],#4 +ldr r1,[r1] +add r11,r1,r1,LSL #4 +add r11,r11,r1,LSL #1 +add r11,r11,#16777216 +mov r11,r11,ASR #25 +add r11,r11,r2 +mov r11,r11,ASR #26 +add r11,r11,r3 +mov r11,r11,ASR #25 +add r11,r11,r4 +mov r11,r11,ASR #26 +add r11,r11,r5 +mov r11,r11,ASR #25 +add r11,r11,r6 +mov r11,r11,ASR #26 +add r11,r11,r7 +mov r11,r11,ASR #25 +add r11,r11,r8 +mov r11,r11,ASR #26 +add r11,r11,r9 +mov r11,r11,ASR #25 +add r11,r11,r10 +mov r11,r11,ASR #26 +add r11,r11,r1 +mov r11,r11,ASR #25 +add r2,r2,r11 +add r2,r2,r11,LSL #1 +add r2,r2,r11,LSL #4 +mov r11,r2,ASR #26 +add r3,r3,r11 +sub r2,r2,r11,LSL #26 +mov r11,r3,ASR #25 +add r4,r4,r11 +sub r3,r3,r11,LSL #25 +mov r11,r4,ASR #26 +add r5,r5,r11 +sub r4,r4,r11,LSL #26 +mov r11,r5,ASR #25 +add r6,r6,r11 +sub r5,r5,r11,LSL #25 +mov r11,r6,ASR #26 +add r7,r7,r11 +sub r6,r6,r11,LSL #26 +mov r11,r7,ASR #25 +add r8,r8,r11 +sub r7,r7,r11,LSL #25 +mov r11,r8,ASR #26 +add r9,r9,r11 +sub r8,r8,r11,LSL #26 +mov r11,r9,ASR #25 +add r10,r10,r11 +sub r9,r9,r11,LSL #25 +mov r11,r10,ASR #26 +add r1,r1,r11 +sub r10,r10,r11,LSL #26 +mov r11,r1,ASR #25 +sub r1,r1,r11,LSL #25 +add r2,r2,r3,LSL #26 +mov r3,r3,LSR #6 +add r3,r3,r4,LSL #19 +mov r4,r4,LSR #13 +add r4,r4,r5,LSL #13 +mov r5,r5,LSR #19 +add r5,r5,r6,LSL #6 +add r6,r7,r8,LSL #25 +mov r7,r8,LSR #7 +add r7,r7,r9,LSL #19 +mov r8,r9,LSR #13 +add r8,r8,r10,LSL #12 +mov r9,r10,LSR #20 +add r1,r9,r1,LSL #6 +str r2,[r0],#4 +str r3,[r0],#4 +str r4,[r0],#4 +str r5,[r0],#4 +str r6,[r0],#4 +str r7,[r0],#4 +str r8,[r0],#4 +str r1,[r0] +ldrd r4,[sp,#0] +ldrd r6,[sp,#8] +ldrd r8,[sp,#16] +ldrd r10,[sp,#24] +ldr r12,[sp,#480] +ldr r14,[sp,#484] +ldr r0,=0 +mov sp,r12 +vpop {q4,q5,q6,q7} +bx lr + +#endif /* __arm__ */ +#endif /* !OPENSSL_NO_ASM */ diff --git a/test-generator/cbits/asm/x25519-asm-x86_64.S b/test-generator/cbits/asm/x25519-asm-x86_64.S new file mode 100644 index 0000000..f43be46 --- /dev/null +++ b/test-generator/cbits/asm/x25519-asm-x86_64.S @@ -0,0 +1,1921 @@ +/* Copyright (c) 2015, Google Inc. + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY + * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION + * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN + * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ + +/* This file is adapted from crypto_scalarmult/curve25519/amd64-51/ in + * SUPERCOP 20141124 (http://bench.cr.yp.to/supercop.html). That code is public + * domain licensed but the standard ISC license is included above to keep + * licensing simple. */ + +#if !defined(OPENSSL_NO_ASM) +#if defined(__x86_64__) + +.data +.p2align 4 + +#if defined(__APPLE__) +/* OS X's C ABI prefixes functions with underscore. */ +#define C_ABI(x) _ ## x +#define HIDDEN .private_extern +#elif defined(__MINGW32__) || defined(__MINGW64__) +#define C_ABI(x) x +#define HIDDEN .globl +#else +#define C_ABI(x) x +#define HIDDEN .hidden +#endif + +x25519_x86_64_REDMASK51: .quad 0x0007FFFFFFFFFFFF +x25519_x86_64_121666_213: .quad 996687872 +x25519_x86_64_2P0: .quad 0xFFFFFFFFFFFDA +x25519_x86_64_2P1234: .quad 0xFFFFFFFFFFFFE +x25519_x86_64_4P0: .quad 0x1FFFFFFFFFFFB4 +x25519_x86_64_4P1234: .quad 0x1FFFFFFFFFFFFC +x25519_x86_64_MU0: .quad 0xED9CE5A30A2C131B +x25519_x86_64_MU1: .quad 0x2106215D086329A7 +x25519_x86_64_MU2: .quad 0xFFFFFFFFFFFFFFEB +x25519_x86_64_MU3: .quad 0xFFFFFFFFFFFFFFFF +x25519_x86_64_MU4: .quad 0x000000000000000F +x25519_x86_64_ORDER0: .quad 0x5812631A5CF5D3ED +x25519_x86_64_ORDER1: .quad 0x14DEF9DEA2F79CD6 +x25519_x86_64_ORDER2: .quad 0x0000000000000000 +x25519_x86_64_ORDER3: .quad 0x1000000000000000 +x25519_x86_64_EC2D0: .quad 1859910466990425 +x25519_x86_64_EC2D1: .quad 932731440258426 +x25519_x86_64_EC2D2: .quad 1072319116312658 +x25519_x86_64_EC2D3: .quad 1815898335770999 +x25519_x86_64_EC2D4: .quad 633789495995903 +x25519_x86_64__38: .quad 38 + +.text +.p2align 5 + +.globl C_ABI(GFp_x25519_x86_64_freeze) +HIDDEN C_ABI(GFp_x25519_x86_64_freeze) +C_ABI(GFp_x25519_x86_64_freeze): +.cfi_startproc +/* This is a leaf function and uses the redzone for saving registers. */ +movq %r12,-8(%rsp) +.cfi_rel_offset r12, -8 +movq 0(%rdi),%rsi +movq 8(%rdi),%rdx +movq 16(%rdi),%rcx +movq 24(%rdi),%r8 +movq 32(%rdi),%r9 +movq x25519_x86_64_REDMASK51(%rip),%rax +mov %rax,%r10 +sub $18,%r10 +mov $3,%r11 +._reduceloop: +mov %rsi,%r12 +shr $51,%r12 +and %rax,%rsi +add %r12,%rdx +mov %rdx,%r12 +shr $51,%r12 +and %rax,%rdx +add %r12,%rcx +mov %rcx,%r12 +shr $51,%r12 +and %rax,%rcx +add %r12,%r8 +mov %r8,%r12 +shr $51,%r12 +and %rax,%r8 +add %r12,%r9 +mov %r9,%r12 +shr $51,%r12 +and %rax,%r9 +imulq $19,%r12,%r12 +add %r12,%rsi +sub $1,%r11 +ja ._reduceloop +mov $1,%r12 +cmp %r10,%rsi +cmovl %r11,%r12 +cmp %rax,%rdx +cmovne %r11,%r12 +cmp %rax,%rcx +cmovne %r11,%r12 +cmp %rax,%r8 +cmovne %r11,%r12 +cmp %rax,%r9 +cmovne %r11,%r12 +neg %r12 +and %r12,%rax +and %r12,%r10 +sub %r10,%rsi +sub %rax,%rdx +sub %rax,%rcx +sub %rax,%r8 +sub %rax,%r9 +movq %rsi,0(%rdi) +movq %rdx,8(%rdi) +movq %rcx,16(%rdi) +movq %r8,24(%rdi) +movq %r9,32(%rdi) +movq -8(%rsp),%r12 +ret +.cfi_endproc + +.p2align 5 +.globl C_ABI(GFp_x25519_x86_64_mul) +HIDDEN C_ABI(GFp_x25519_x86_64_mul) +C_ABI(GFp_x25519_x86_64_mul): +.cfi_startproc +/* This is a leaf function and uses the redzone for saving registers. */ +movq %r12,-8(%rsp) +.cfi_rel_offset r12, -8 +movq %r13,-16(%rsp) +.cfi_rel_offset r13, -16 +movq %r14,-24(%rsp) +.cfi_rel_offset r14, -24 +movq %r15,-32(%rsp) +.cfi_rel_offset r15, -32 +movq %rbx,-40(%rsp) +.cfi_rel_offset rbx, -40 +movq %rbp,-48(%rsp) +.cfi_rel_offset rbp, -48 +mov %rdx,%rcx +movq 24(%rsi),%rdx +imulq $19,%rdx,%rax +movq %rax,-64(%rsp) +mulq 16(%rcx) +mov %rax,%r8 +mov %rdx,%r9 +movq 32(%rsi),%rdx +imulq $19,%rdx,%rax +movq %rax,-72(%rsp) +mulq 8(%rcx) +add %rax,%r8 +adc %rdx,%r9 +movq 0(%rsi),%rax +mulq 0(%rcx) +add %rax,%r8 +adc %rdx,%r9 +movq 0(%rsi),%rax +mulq 8(%rcx) +mov %rax,%r10 +mov %rdx,%r11 +movq 0(%rsi),%rax +mulq 16(%rcx) +mov %rax,%r12 +mov %rdx,%r13 +movq 0(%rsi),%rax +mulq 24(%rcx) +mov %rax,%r14 +mov %rdx,%r15 +movq 0(%rsi),%rax +mulq 32(%rcx) +mov %rax,%rbx +mov %rdx,%rbp +movq 8(%rsi),%rax +mulq 0(%rcx) +add %rax,%r10 +adc %rdx,%r11 +movq 8(%rsi),%rax +mulq 8(%rcx) +add %rax,%r12 +adc %rdx,%r13 +movq 8(%rsi),%rax +mulq 16(%rcx) +add %rax,%r14 +adc %rdx,%r15 +movq 8(%rsi),%rax +mulq 24(%rcx) +add %rax,%rbx +adc %rdx,%rbp +movq 8(%rsi),%rdx +imulq $19,%rdx,%rax +mulq 32(%rcx) +add %rax,%r8 +adc %rdx,%r9 +movq 16(%rsi),%rax +mulq 0(%rcx) +add %rax,%r12 +adc %rdx,%r13 +movq 16(%rsi),%rax +mulq 8(%rcx) +add %rax,%r14 +adc %rdx,%r15 +movq 16(%rsi),%rax +mulq 16(%rcx) +add %rax,%rbx +adc %rdx,%rbp +movq 16(%rsi),%rdx +imulq $19,%rdx,%rax +mulq 24(%rcx) +add %rax,%r8 +adc %rdx,%r9 +movq 16(%rsi),%rdx +imulq $19,%rdx,%rax +mulq 32(%rcx) +add %rax,%r10 +adc %rdx,%r11 +movq 24(%rsi),%rax +mulq 0(%rcx) +add %rax,%r14 +adc %rdx,%r15 +movq 24(%rsi),%rax +mulq 8(%rcx) +add %rax,%rbx +adc %rdx,%rbp +movq -64(%rsp),%rax +mulq 24(%rcx) +add %rax,%r10 +adc %rdx,%r11 +movq -64(%rsp),%rax +mulq 32(%rcx) +add %rax,%r12 +adc %rdx,%r13 +movq 32(%rsi),%rax +mulq 0(%rcx) +add %rax,%rbx +adc %rdx,%rbp +movq -72(%rsp),%rax +mulq 16(%rcx) +add %rax,%r10 +adc %rdx,%r11 +movq -72(%rsp),%rax +mulq 24(%rcx) +add %rax,%r12 +adc %rdx,%r13 +movq -72(%rsp),%rax +mulq 32(%rcx) +add %rax,%r14 +adc %rdx,%r15 +movq x25519_x86_64_REDMASK51(%rip),%rsi +shld $13,%r8,%r9 +and %rsi,%r8 +shld $13,%r10,%r11 +and %rsi,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rsi,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rsi,%r14 +add %r13,%r14 +shld $13,%rbx,%rbp +and %rsi,%rbx +add %r15,%rbx +imulq $19,%rbp,%rdx +add %rdx,%r8 +mov %r8,%rdx +shr $51,%rdx +add %r10,%rdx +mov %rdx,%rcx +shr $51,%rdx +and %rsi,%r8 +add %r12,%rdx +mov %rdx,%r9 +shr $51,%rdx +and %rsi,%rcx +add %r14,%rdx +mov %rdx,%rax +shr $51,%rdx +and %rsi,%r9 +add %rbx,%rdx +mov %rdx,%r10 +shr $51,%rdx +and %rsi,%rax +imulq $19,%rdx,%rdx +add %rdx,%r8 +and %rsi,%r10 +movq %r8,0(%rdi) +movq %rcx,8(%rdi) +movq %r9,16(%rdi) +movq %rax,24(%rdi) +movq %r10,32(%rdi) +movq -8(%rsp),%r12 +movq -16(%rsp),%r13 +movq -24(%rsp),%r14 +movq -32(%rsp),%r15 +movq -40(%rsp),%rbx +movq -48(%rsp),%rbp +ret +.cfi_endproc + +.p2align 5 +.globl C_ABI(GFp_x25519_x86_64_square) +HIDDEN C_ABI(GFp_x25519_x86_64_square) +C_ABI(GFp_x25519_x86_64_square): +.cfi_startproc +/* This is a leaf function and uses the redzone for saving registers. */ +movq %r12,-8(%rsp) +.cfi_rel_offset r12, -8 +movq %r13,-16(%rsp) +.cfi_rel_offset r13, -16 +movq %r14,-24(%rsp) +.cfi_rel_offset r14, -24 +movq %r15,-32(%rsp) +.cfi_rel_offset r15, -32 +movq %rbx,-40(%rsp) +.cfi_rel_offset rbx, -40 +movq 0(%rsi),%rax +mulq 0(%rsi) +mov %rax,%rcx +mov %rdx,%r8 +movq 0(%rsi),%rax +shl $1,%rax +mulq 8(%rsi) +mov %rax,%r9 +mov %rdx,%r10 +movq 0(%rsi),%rax +shl $1,%rax +mulq 16(%rsi) +mov %rax,%r11 +mov %rdx,%r12 +movq 0(%rsi),%rax +shl $1,%rax +mulq 24(%rsi) +mov %rax,%r13 +mov %rdx,%r14 +movq 0(%rsi),%rax +shl $1,%rax +mulq 32(%rsi) +mov %rax,%r15 +mov %rdx,%rbx +movq 8(%rsi),%rax +mulq 8(%rsi) +add %rax,%r11 +adc %rdx,%r12 +movq 8(%rsi),%rax +shl $1,%rax +mulq 16(%rsi) +add %rax,%r13 +adc %rdx,%r14 +movq 8(%rsi),%rax +shl $1,%rax +mulq 24(%rsi) +add %rax,%r15 +adc %rdx,%rbx +movq 8(%rsi),%rdx +imulq $38,%rdx,%rax +mulq 32(%rsi) +add %rax,%rcx +adc %rdx,%r8 +movq 16(%rsi),%rax +mulq 16(%rsi) +add %rax,%r15 +adc %rdx,%rbx +movq 16(%rsi),%rdx +imulq $38,%rdx,%rax +mulq 24(%rsi) +add %rax,%rcx +adc %rdx,%r8 +movq 16(%rsi),%rdx +imulq $38,%rdx,%rax +mulq 32(%rsi) +add %rax,%r9 +adc %rdx,%r10 +movq 24(%rsi),%rdx +imulq $19,%rdx,%rax +mulq 24(%rsi) +add %rax,%r9 +adc %rdx,%r10 +movq 24(%rsi),%rdx +imulq $38,%rdx,%rax +mulq 32(%rsi) +add %rax,%r11 +adc %rdx,%r12 +movq 32(%rsi),%rdx +imulq $19,%rdx,%rax +mulq 32(%rsi) +add %rax,%r13 +adc %rdx,%r14 +movq x25519_x86_64_REDMASK51(%rip),%rsi +shld $13,%rcx,%r8 +and %rsi,%rcx +shld $13,%r9,%r10 +and %rsi,%r9 +add %r8,%r9 +shld $13,%r11,%r12 +and %rsi,%r11 +add %r10,%r11 +shld $13,%r13,%r14 +and %rsi,%r13 +add %r12,%r13 +shld $13,%r15,%rbx +and %rsi,%r15 +add %r14,%r15 +imulq $19,%rbx,%rdx +add %rdx,%rcx +mov %rcx,%rdx +shr $51,%rdx +add %r9,%rdx +and %rsi,%rcx +mov %rdx,%r8 +shr $51,%rdx +add %r11,%rdx +and %rsi,%r8 +mov %rdx,%r9 +shr $51,%rdx +add %r13,%rdx +and %rsi,%r9 +mov %rdx,%rax +shr $51,%rdx +add %r15,%rdx +and %rsi,%rax +mov %rdx,%r10 +shr $51,%rdx +imulq $19,%rdx,%rdx +add %rdx,%rcx +and %rsi,%r10 +movq %rcx,0(%rdi) +movq %r8,8(%rdi) +movq %r9,16(%rdi) +movq %rax,24(%rdi) +movq %r10,32(%rdi) +movq -8(%rsp),%r12 +movq -16(%rsp),%r13 +movq -24(%rsp),%r14 +movq -32(%rsp),%r15 +movq -40(%rsp),%rbx +ret +.cfi_endproc + +.p2align 5 +.globl C_ABI(GFp_x25519_x86_64_ladderstep) +HIDDEN C_ABI(GFp_x25519_x86_64_ladderstep) +C_ABI(GFp_x25519_x86_64_ladderstep): +.cfi_startproc +sub $344,%rsp +.cfi_adjust_cfa_offset 344 +movq %r12,296(%rsp) +.cfi_rel_offset r12, 296 +movq %r13,304(%rsp) +.cfi_rel_offset r13, 304 +movq %r14,312(%rsp) +.cfi_rel_offset r14, 312 +movq %r15,320(%rsp) +.cfi_rel_offset r15, 320 +movq %rbx,328(%rsp) +.cfi_rel_offset rbx, 328 +movq %rbp,336(%rsp) +.cfi_rel_offset rbp, 336 +movq 40(%rdi),%rsi +movq 48(%rdi),%rdx +movq 56(%rdi),%rcx +movq 64(%rdi),%r8 +movq 72(%rdi),%r9 +mov %rsi,%rax +mov %rdx,%r10 +mov %rcx,%r11 +mov %r8,%r12 +mov %r9,%r13 +add x25519_x86_64_2P0(%rip),%rax +add x25519_x86_64_2P1234(%rip),%r10 +add x25519_x86_64_2P1234(%rip),%r11 +add x25519_x86_64_2P1234(%rip),%r12 +add x25519_x86_64_2P1234(%rip),%r13 +addq 80(%rdi),%rsi +addq 88(%rdi),%rdx +addq 96(%rdi),%rcx +addq 104(%rdi),%r8 +addq 112(%rdi),%r9 +subq 80(%rdi),%rax +subq 88(%rdi),%r10 +subq 96(%rdi),%r11 +subq 104(%rdi),%r12 +subq 112(%rdi),%r13 +movq %rsi,0(%rsp) +movq %rdx,8(%rsp) +movq %rcx,16(%rsp) +movq %r8,24(%rsp) +movq %r9,32(%rsp) +movq %rax,40(%rsp) +movq %r10,48(%rsp) +movq %r11,56(%rsp) +movq %r12,64(%rsp) +movq %r13,72(%rsp) +movq 40(%rsp),%rax +mulq 40(%rsp) +mov %rax,%rsi +mov %rdx,%rcx +movq 40(%rsp),%rax +shl $1,%rax +mulq 48(%rsp) +mov %rax,%r8 +mov %rdx,%r9 +movq 40(%rsp),%rax +shl $1,%rax +mulq 56(%rsp) +mov %rax,%r10 +mov %rdx,%r11 +movq 40(%rsp),%rax +shl $1,%rax +mulq 64(%rsp) +mov %rax,%r12 +mov %rdx,%r13 +movq 40(%rsp),%rax +shl $1,%rax +mulq 72(%rsp) +mov %rax,%r14 +mov %rdx,%r15 +movq 48(%rsp),%rax +mulq 48(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 48(%rsp),%rax +shl $1,%rax +mulq 56(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 48(%rsp),%rax +shl $1,%rax +mulq 64(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 48(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 72(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 56(%rsp),%rax +mulq 56(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 56(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 64(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 56(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 72(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 64(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 64(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 64(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 72(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 72(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 72(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +and %rdx,%rsi +mov %rcx,%r8 +shr $51,%rcx +add %r10,%rcx +and %rdx,%r8 +mov %rcx,%r9 +shr $51,%rcx +add %r12,%rcx +and %rdx,%r9 +mov %rcx,%rax +shr $51,%rcx +add %r14,%rcx +and %rdx,%rax +mov %rcx,%r10 +shr $51,%rcx +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,80(%rsp) +movq %r8,88(%rsp) +movq %r9,96(%rsp) +movq %rax,104(%rsp) +movq %r10,112(%rsp) +movq 0(%rsp),%rax +mulq 0(%rsp) +mov %rax,%rsi +mov %rdx,%rcx +movq 0(%rsp),%rax +shl $1,%rax +mulq 8(%rsp) +mov %rax,%r8 +mov %rdx,%r9 +movq 0(%rsp),%rax +shl $1,%rax +mulq 16(%rsp) +mov %rax,%r10 +mov %rdx,%r11 +movq 0(%rsp),%rax +shl $1,%rax +mulq 24(%rsp) +mov %rax,%r12 +mov %rdx,%r13 +movq 0(%rsp),%rax +shl $1,%rax +mulq 32(%rsp) +mov %rax,%r14 +mov %rdx,%r15 +movq 8(%rsp),%rax +mulq 8(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 8(%rsp),%rax +shl $1,%rax +mulq 16(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 8(%rsp),%rax +shl $1,%rax +mulq 24(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 8(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 32(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 16(%rsp),%rax +mulq 16(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 16(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 24(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 16(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 32(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 24(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 24(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 24(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 32(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 32(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 32(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +and %rdx,%rsi +mov %rcx,%r8 +shr $51,%rcx +add %r10,%rcx +and %rdx,%r8 +mov %rcx,%r9 +shr $51,%rcx +add %r12,%rcx +and %rdx,%r9 +mov %rcx,%rax +shr $51,%rcx +add %r14,%rcx +and %rdx,%rax +mov %rcx,%r10 +shr $51,%rcx +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,120(%rsp) +movq %r8,128(%rsp) +movq %r9,136(%rsp) +movq %rax,144(%rsp) +movq %r10,152(%rsp) +mov %rsi,%rsi +mov %r8,%rdx +mov %r9,%rcx +mov %rax,%r8 +mov %r10,%r9 +add x25519_x86_64_2P0(%rip),%rsi +add x25519_x86_64_2P1234(%rip),%rdx +add x25519_x86_64_2P1234(%rip),%rcx +add x25519_x86_64_2P1234(%rip),%r8 +add x25519_x86_64_2P1234(%rip),%r9 +subq 80(%rsp),%rsi +subq 88(%rsp),%rdx +subq 96(%rsp),%rcx +subq 104(%rsp),%r8 +subq 112(%rsp),%r9 +movq %rsi,160(%rsp) +movq %rdx,168(%rsp) +movq %rcx,176(%rsp) +movq %r8,184(%rsp) +movq %r9,192(%rsp) +movq 120(%rdi),%rsi +movq 128(%rdi),%rdx +movq 136(%rdi),%rcx +movq 144(%rdi),%r8 +movq 152(%rdi),%r9 +mov %rsi,%rax +mov %rdx,%r10 +mov %rcx,%r11 +mov %r8,%r12 +mov %r9,%r13 +add x25519_x86_64_2P0(%rip),%rax +add x25519_x86_64_2P1234(%rip),%r10 +add x25519_x86_64_2P1234(%rip),%r11 +add x25519_x86_64_2P1234(%rip),%r12 +add x25519_x86_64_2P1234(%rip),%r13 +addq 160(%rdi),%rsi +addq 168(%rdi),%rdx +addq 176(%rdi),%rcx +addq 184(%rdi),%r8 +addq 192(%rdi),%r9 +subq 160(%rdi),%rax +subq 168(%rdi),%r10 +subq 176(%rdi),%r11 +subq 184(%rdi),%r12 +subq 192(%rdi),%r13 +movq %rsi,200(%rsp) +movq %rdx,208(%rsp) +movq %rcx,216(%rsp) +movq %r8,224(%rsp) +movq %r9,232(%rsp) +movq %rax,240(%rsp) +movq %r10,248(%rsp) +movq %r11,256(%rsp) +movq %r12,264(%rsp) +movq %r13,272(%rsp) +movq 224(%rsp),%rsi +imulq $19,%rsi,%rax +movq %rax,280(%rsp) +mulq 56(%rsp) +mov %rax,%rsi +mov %rdx,%rcx +movq 232(%rsp),%rdx +imulq $19,%rdx,%rax +movq %rax,288(%rsp) +mulq 48(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 200(%rsp),%rax +mulq 40(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 200(%rsp),%rax +mulq 48(%rsp) +mov %rax,%r8 +mov %rdx,%r9 +movq 200(%rsp),%rax +mulq 56(%rsp) +mov %rax,%r10 +mov %rdx,%r11 +movq 200(%rsp),%rax +mulq 64(%rsp) +mov %rax,%r12 +mov %rdx,%r13 +movq 200(%rsp),%rax +mulq 72(%rsp) +mov %rax,%r14 +mov %rdx,%r15 +movq 208(%rsp),%rax +mulq 40(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 208(%rsp),%rax +mulq 48(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 208(%rsp),%rax +mulq 56(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 208(%rsp),%rax +mulq 64(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 208(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 72(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 216(%rsp),%rax +mulq 40(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 216(%rsp),%rax +mulq 48(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 216(%rsp),%rax +mulq 56(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 216(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 64(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 216(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 72(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 224(%rsp),%rax +mulq 40(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 224(%rsp),%rax +mulq 48(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 280(%rsp),%rax +mulq 64(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 280(%rsp),%rax +mulq 72(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 232(%rsp),%rax +mulq 40(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 288(%rsp),%rax +mulq 56(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 288(%rsp),%rax +mulq 64(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 288(%rsp),%rax +mulq 72(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +mov %rcx,%r8 +shr $51,%rcx +and %rdx,%rsi +add %r10,%rcx +mov %rcx,%r9 +shr $51,%rcx +and %rdx,%r8 +add %r12,%rcx +mov %rcx,%rax +shr $51,%rcx +and %rdx,%r9 +add %r14,%rcx +mov %rcx,%r10 +shr $51,%rcx +and %rdx,%rax +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,40(%rsp) +movq %r8,48(%rsp) +movq %r9,56(%rsp) +movq %rax,64(%rsp) +movq %r10,72(%rsp) +movq 264(%rsp),%rsi +imulq $19,%rsi,%rax +movq %rax,200(%rsp) +mulq 16(%rsp) +mov %rax,%rsi +mov %rdx,%rcx +movq 272(%rsp),%rdx +imulq $19,%rdx,%rax +movq %rax,208(%rsp) +mulq 8(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 240(%rsp),%rax +mulq 0(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 240(%rsp),%rax +mulq 8(%rsp) +mov %rax,%r8 +mov %rdx,%r9 +movq 240(%rsp),%rax +mulq 16(%rsp) +mov %rax,%r10 +mov %rdx,%r11 +movq 240(%rsp),%rax +mulq 24(%rsp) +mov %rax,%r12 +mov %rdx,%r13 +movq 240(%rsp),%rax +mulq 32(%rsp) +mov %rax,%r14 +mov %rdx,%r15 +movq 248(%rsp),%rax +mulq 0(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 248(%rsp),%rax +mulq 8(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 248(%rsp),%rax +mulq 16(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 248(%rsp),%rax +mulq 24(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 248(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 32(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 256(%rsp),%rax +mulq 0(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 256(%rsp),%rax +mulq 8(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 256(%rsp),%rax +mulq 16(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 256(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 24(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 256(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 32(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 264(%rsp),%rax +mulq 0(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 264(%rsp),%rax +mulq 8(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 200(%rsp),%rax +mulq 24(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 200(%rsp),%rax +mulq 32(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 272(%rsp),%rax +mulq 0(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 208(%rsp),%rax +mulq 16(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 208(%rsp),%rax +mulq 24(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 208(%rsp),%rax +mulq 32(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +mov %rcx,%r8 +shr $51,%rcx +and %rdx,%rsi +add %r10,%rcx +mov %rcx,%r9 +shr $51,%rcx +and %rdx,%r8 +add %r12,%rcx +mov %rcx,%rax +shr $51,%rcx +and %rdx,%r9 +add %r14,%rcx +mov %rcx,%r10 +shr $51,%rcx +and %rdx,%rax +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +mov %rsi,%rdx +mov %r8,%rcx +mov %r9,%r11 +mov %rax,%r12 +mov %r10,%r13 +add x25519_x86_64_2P0(%rip),%rdx +add x25519_x86_64_2P1234(%rip),%rcx +add x25519_x86_64_2P1234(%rip),%r11 +add x25519_x86_64_2P1234(%rip),%r12 +add x25519_x86_64_2P1234(%rip),%r13 +addq 40(%rsp),%rsi +addq 48(%rsp),%r8 +addq 56(%rsp),%r9 +addq 64(%rsp),%rax +addq 72(%rsp),%r10 +subq 40(%rsp),%rdx +subq 48(%rsp),%rcx +subq 56(%rsp),%r11 +subq 64(%rsp),%r12 +subq 72(%rsp),%r13 +movq %rsi,120(%rdi) +movq %r8,128(%rdi) +movq %r9,136(%rdi) +movq %rax,144(%rdi) +movq %r10,152(%rdi) +movq %rdx,160(%rdi) +movq %rcx,168(%rdi) +movq %r11,176(%rdi) +movq %r12,184(%rdi) +movq %r13,192(%rdi) +movq 120(%rdi),%rax +mulq 120(%rdi) +mov %rax,%rsi +mov %rdx,%rcx +movq 120(%rdi),%rax +shl $1,%rax +mulq 128(%rdi) +mov %rax,%r8 +mov %rdx,%r9 +movq 120(%rdi),%rax +shl $1,%rax +mulq 136(%rdi) +mov %rax,%r10 +mov %rdx,%r11 +movq 120(%rdi),%rax +shl $1,%rax +mulq 144(%rdi) +mov %rax,%r12 +mov %rdx,%r13 +movq 120(%rdi),%rax +shl $1,%rax +mulq 152(%rdi) +mov %rax,%r14 +mov %rdx,%r15 +movq 128(%rdi),%rax +mulq 128(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 128(%rdi),%rax +shl $1,%rax +mulq 136(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq 128(%rdi),%rax +shl $1,%rax +mulq 144(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 128(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 152(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 136(%rdi),%rax +mulq 136(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 136(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 144(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 136(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 152(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 144(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 144(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 144(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 152(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 152(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 152(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +and %rdx,%rsi +mov %rcx,%r8 +shr $51,%rcx +add %r10,%rcx +and %rdx,%r8 +mov %rcx,%r9 +shr $51,%rcx +add %r12,%rcx +and %rdx,%r9 +mov %rcx,%rax +shr $51,%rcx +add %r14,%rcx +and %rdx,%rax +mov %rcx,%r10 +shr $51,%rcx +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,120(%rdi) +movq %r8,128(%rdi) +movq %r9,136(%rdi) +movq %rax,144(%rdi) +movq %r10,152(%rdi) +movq 160(%rdi),%rax +mulq 160(%rdi) +mov %rax,%rsi +mov %rdx,%rcx +movq 160(%rdi),%rax +shl $1,%rax +mulq 168(%rdi) +mov %rax,%r8 +mov %rdx,%r9 +movq 160(%rdi),%rax +shl $1,%rax +mulq 176(%rdi) +mov %rax,%r10 +mov %rdx,%r11 +movq 160(%rdi),%rax +shl $1,%rax +mulq 184(%rdi) +mov %rax,%r12 +mov %rdx,%r13 +movq 160(%rdi),%rax +shl $1,%rax +mulq 192(%rdi) +mov %rax,%r14 +mov %rdx,%r15 +movq 168(%rdi),%rax +mulq 168(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 168(%rdi),%rax +shl $1,%rax +mulq 176(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq 168(%rdi),%rax +shl $1,%rax +mulq 184(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 168(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 192(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 176(%rdi),%rax +mulq 176(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 176(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 184(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 176(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 192(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 184(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 184(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 184(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 192(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 192(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 192(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +and %rdx,%rsi +mov %rcx,%r8 +shr $51,%rcx +add %r10,%rcx +and %rdx,%r8 +mov %rcx,%r9 +shr $51,%rcx +add %r12,%rcx +and %rdx,%r9 +mov %rcx,%rax +shr $51,%rcx +add %r14,%rcx +and %rdx,%rax +mov %rcx,%r10 +shr $51,%rcx +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,160(%rdi) +movq %r8,168(%rdi) +movq %r9,176(%rdi) +movq %rax,184(%rdi) +movq %r10,192(%rdi) +movq 184(%rdi),%rsi +imulq $19,%rsi,%rax +movq %rax,0(%rsp) +mulq 16(%rdi) +mov %rax,%rsi +mov %rdx,%rcx +movq 192(%rdi),%rdx +imulq $19,%rdx,%rax +movq %rax,8(%rsp) +mulq 8(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 160(%rdi),%rax +mulq 0(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 160(%rdi),%rax +mulq 8(%rdi) +mov %rax,%r8 +mov %rdx,%r9 +movq 160(%rdi),%rax +mulq 16(%rdi) +mov %rax,%r10 +mov %rdx,%r11 +movq 160(%rdi),%rax +mulq 24(%rdi) +mov %rax,%r12 +mov %rdx,%r13 +movq 160(%rdi),%rax +mulq 32(%rdi) +mov %rax,%r14 +mov %rdx,%r15 +movq 168(%rdi),%rax +mulq 0(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 168(%rdi),%rax +mulq 8(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 168(%rdi),%rax +mulq 16(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq 168(%rdi),%rax +mulq 24(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 168(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 32(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 176(%rdi),%rax +mulq 0(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 176(%rdi),%rax +mulq 8(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq 176(%rdi),%rax +mulq 16(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 176(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 24(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 176(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 32(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 184(%rdi),%rax +mulq 0(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq 184(%rdi),%rax +mulq 8(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 0(%rsp),%rax +mulq 24(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 0(%rsp),%rax +mulq 32(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 192(%rdi),%rax +mulq 0(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 8(%rsp),%rax +mulq 16(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 8(%rsp),%rax +mulq 24(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 8(%rsp),%rax +mulq 32(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +mov %rcx,%r8 +shr $51,%rcx +and %rdx,%rsi +add %r10,%rcx +mov %rcx,%r9 +shr $51,%rcx +and %rdx,%r8 +add %r12,%rcx +mov %rcx,%rax +shr $51,%rcx +and %rdx,%r9 +add %r14,%rcx +mov %rcx,%r10 +shr $51,%rcx +and %rdx,%rax +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,160(%rdi) +movq %r8,168(%rdi) +movq %r9,176(%rdi) +movq %rax,184(%rdi) +movq %r10,192(%rdi) +movq 144(%rsp),%rsi +imulq $19,%rsi,%rax +movq %rax,0(%rsp) +mulq 96(%rsp) +mov %rax,%rsi +mov %rdx,%rcx +movq 152(%rsp),%rdx +imulq $19,%rdx,%rax +movq %rax,8(%rsp) +mulq 88(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 120(%rsp),%rax +mulq 80(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 120(%rsp),%rax +mulq 88(%rsp) +mov %rax,%r8 +mov %rdx,%r9 +movq 120(%rsp),%rax +mulq 96(%rsp) +mov %rax,%r10 +mov %rdx,%r11 +movq 120(%rsp),%rax +mulq 104(%rsp) +mov %rax,%r12 +mov %rdx,%r13 +movq 120(%rsp),%rax +mulq 112(%rsp) +mov %rax,%r14 +mov %rdx,%r15 +movq 128(%rsp),%rax +mulq 80(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 128(%rsp),%rax +mulq 88(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 128(%rsp),%rax +mulq 96(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 128(%rsp),%rax +mulq 104(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 128(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 112(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 136(%rsp),%rax +mulq 80(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 136(%rsp),%rax +mulq 88(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 136(%rsp),%rax +mulq 96(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 136(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 104(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 136(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 112(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 144(%rsp),%rax +mulq 80(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 144(%rsp),%rax +mulq 88(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 0(%rsp),%rax +mulq 104(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 0(%rsp),%rax +mulq 112(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 152(%rsp),%rax +mulq 80(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 8(%rsp),%rax +mulq 96(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 8(%rsp),%rax +mulq 104(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 8(%rsp),%rax +mulq 112(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +mov %rcx,%r8 +shr $51,%rcx +and %rdx,%rsi +add %r10,%rcx +mov %rcx,%r9 +shr $51,%rcx +and %rdx,%r8 +add %r12,%rcx +mov %rcx,%rax +shr $51,%rcx +and %rdx,%r9 +add %r14,%rcx +mov %rcx,%r10 +shr $51,%rcx +and %rdx,%rax +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,40(%rdi) +movq %r8,48(%rdi) +movq %r9,56(%rdi) +movq %rax,64(%rdi) +movq %r10,72(%rdi) +movq 160(%rsp),%rax +mulq x25519_x86_64_121666_213(%rip) +shr $13,%rax +mov %rax,%rsi +mov %rdx,%rcx +movq 168(%rsp),%rax +mulq x25519_x86_64_121666_213(%rip) +shr $13,%rax +add %rax,%rcx +mov %rdx,%r8 +movq 176(%rsp),%rax +mulq x25519_x86_64_121666_213(%rip) +shr $13,%rax +add %rax,%r8 +mov %rdx,%r9 +movq 184(%rsp),%rax +mulq x25519_x86_64_121666_213(%rip) +shr $13,%rax +add %rax,%r9 +mov %rdx,%r10 +movq 192(%rsp),%rax +mulq x25519_x86_64_121666_213(%rip) +shr $13,%rax +add %rax,%r10 +imulq $19,%rdx,%rdx +add %rdx,%rsi +addq 80(%rsp),%rsi +addq 88(%rsp),%rcx +addq 96(%rsp),%r8 +addq 104(%rsp),%r9 +addq 112(%rsp),%r10 +movq %rsi,80(%rdi) +movq %rcx,88(%rdi) +movq %r8,96(%rdi) +movq %r9,104(%rdi) +movq %r10,112(%rdi) +movq 104(%rdi),%rsi +imulq $19,%rsi,%rax +movq %rax,0(%rsp) +mulq 176(%rsp) +mov %rax,%rsi +mov %rdx,%rcx +movq 112(%rdi),%rdx +imulq $19,%rdx,%rax +movq %rax,8(%rsp) +mulq 168(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 80(%rdi),%rax +mulq 160(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 80(%rdi),%rax +mulq 168(%rsp) +mov %rax,%r8 +mov %rdx,%r9 +movq 80(%rdi),%rax +mulq 176(%rsp) +mov %rax,%r10 +mov %rdx,%r11 +movq 80(%rdi),%rax +mulq 184(%rsp) +mov %rax,%r12 +mov %rdx,%r13 +movq 80(%rdi),%rax +mulq 192(%rsp) +mov %rax,%r14 +mov %rdx,%r15 +movq 88(%rdi),%rax +mulq 160(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 88(%rdi),%rax +mulq 168(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 88(%rdi),%rax +mulq 176(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 88(%rdi),%rax +mulq 184(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 88(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 192(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 96(%rdi),%rax +mulq 160(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 96(%rdi),%rax +mulq 168(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 96(%rdi),%rax +mulq 176(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 96(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 184(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 96(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 192(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 104(%rdi),%rax +mulq 160(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 104(%rdi),%rax +mulq 168(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 0(%rsp),%rax +mulq 184(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 0(%rsp),%rax +mulq 192(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 112(%rdi),%rax +mulq 160(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 8(%rsp),%rax +mulq 176(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 8(%rsp),%rax +mulq 184(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 8(%rsp),%rax +mulq 192(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +mov %rcx,%r8 +shr $51,%rcx +and %rdx,%rsi +add %r10,%rcx +mov %rcx,%r9 +shr $51,%rcx +and %rdx,%r8 +add %r12,%rcx +mov %rcx,%rax +shr $51,%rcx +and %rdx,%r9 +add %r14,%rcx +mov %rcx,%r10 +shr $51,%rcx +and %rdx,%rax +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,80(%rdi) +movq %r8,88(%rdi) +movq %r9,96(%rdi) +movq %rax,104(%rdi) +movq %r10,112(%rdi) +movq 296(%rsp),%r12 +movq 304(%rsp),%r13 +movq 312(%rsp),%r14 +movq 320(%rsp),%r15 +movq 328(%rsp),%rbx +movq 336(%rsp),%rbp +add $344,%rsp +.cfi_adjust_cfa_offset -344 +ret +.cfi_endproc + +.p2align 5 +.globl C_ABI(GFp_x25519_x86_64_work_cswap) +HIDDEN C_ABI(GFp_x25519_x86_64_work_cswap) +C_ABI(GFp_x25519_x86_64_work_cswap): +.cfi_startproc +cmp $1,%rsi +movq 0(%rdi),%rsi +movq 80(%rdi),%rdx +movq 8(%rdi),%rcx +movq 88(%rdi),%r8 +mov %rsi,%r9 +cmove %rdx,%rsi +cmove %r9,%rdx +mov %rcx,%r9 +cmove %r8,%rcx +cmove %r9,%r8 +movq %rsi,0(%rdi) +movq %rdx,80(%rdi) +movq %rcx,8(%rdi) +movq %r8,88(%rdi) +movq 16(%rdi),%rsi +movq 96(%rdi),%rdx +movq 24(%rdi),%rcx +movq 104(%rdi),%r8 +mov %rsi,%r9 +cmove %rdx,%rsi +cmove %r9,%rdx +mov %rcx,%r9 +cmove %r8,%rcx +cmove %r9,%r8 +movq %rsi,16(%rdi) +movq %rdx,96(%rdi) +movq %rcx,24(%rdi) +movq %r8,104(%rdi) +movq 32(%rdi),%rsi +movq 112(%rdi),%rdx +movq 40(%rdi),%rcx +movq 120(%rdi),%r8 +mov %rsi,%r9 +cmove %rdx,%rsi +cmove %r9,%rdx +mov %rcx,%r9 +cmove %r8,%rcx +cmove %r9,%r8 +movq %rsi,32(%rdi) +movq %rdx,112(%rdi) +movq %rcx,40(%rdi) +movq %r8,120(%rdi) +movq 48(%rdi),%rsi +movq 128(%rdi),%rdx +movq 56(%rdi),%rcx +movq 136(%rdi),%r8 +mov %rsi,%r9 +cmove %rdx,%rsi +cmove %r9,%rdx +mov %rcx,%r9 +cmove %r8,%rcx +cmove %r9,%r8 +movq %rsi,48(%rdi) +movq %rdx,128(%rdi) +movq %rcx,56(%rdi) +movq %r8,136(%rdi) +movq 64(%rdi),%rsi +movq 144(%rdi),%rdx +movq 72(%rdi),%rcx +movq 152(%rdi),%r8 +mov %rsi,%r9 +cmove %rdx,%rsi +cmove %r9,%rdx +mov %rcx,%r9 +cmove %r8,%rcx +cmove %r9,%r8 +movq %rsi,64(%rdi) +movq %rdx,144(%rdi) +movq %rcx,72(%rdi) +movq %r8,152(%rdi) +mov %rdi,%rax +mov %rsi,%rdx +ret +.cfi_endproc + +#endif /* __x86_64__ */ +#endif /* !OPENSSL_NO_ASM */ diff --git a/test-generator/cbits/curve25519.c b/test-generator/cbits/curve25519.c new file mode 100644 index 0000000..1528915 --- /dev/null +++ b/test-generator/cbits/curve25519.c @@ -0,0 +1,4726 @@ +/* Copyright (c) 2015, Google Inc. + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY + * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION + * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN + * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ + +/* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP + * 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as + * public domain but this file has the ISC license just to keep licencing + * simple. + * + * The field functions are shared by Ed25519 and X25519 where possible. */ + +#include + +#include +#include + +#include "internal2.h" +#include "internal.h" + + +/* Prevent -Wmissing-prototypes warnings. */ +void GFp_curve25519_scalar_mask(uint8_t a[32]); +void GFp_fe_invert(fe out, const fe z); +uint8_t GFp_fe_isnegative(const fe f); +void GFp_fe_mul(fe h, const fe f, const fe g); +void GFp_fe_tobytes(uint8_t *s, const fe h); +void GFp_ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, + const ge_p3 *A, const uint8_t *b); +int GFp_x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s); +void GFp_x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]); +void GFp_x25519_sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b, + const uint8_t *c); +void GFp_x25519_sc_reduce(uint8_t *s); +void GFp_x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], + const uint8_t point[32]); + +static const int64_t kBottom25Bits = INT64_C(0x1ffffff); +static const int64_t kBottom26Bits = INT64_C(0x3ffffff); +static const int64_t kTop39Bits = INT64_C(0xfffffffffe000000); +static const int64_t kTop38Bits = INT64_C(0xfffffffffc000000); + +uint64_t load_3(const uint8_t *in) { + uint64_t result; + result = (uint64_t)in[0]; + result |= ((uint64_t)in[1]) << 8; + result |= ((uint64_t)in[2]) << 16; + return result; +} + +uint64_t load_4(const uint8_t *in) { + uint64_t result; + result = (uint64_t)in[0]; + result |= ((uint64_t)in[1]) << 8; + result |= ((uint64_t)in[2]) << 16; + result |= ((uint64_t)in[3]) << 24; + return result; +} + +void fe_frombytes(fe h, const uint8_t *s) { + /* Ignores top bit of h. */ + int64_t h0 = load_4(s); + int64_t h1 = load_3(s + 4) << 6; + int64_t h2 = load_3(s + 7) << 5; + int64_t h3 = load_3(s + 10) << 3; + int64_t h4 = load_3(s + 13) << 2; + int64_t h5 = load_4(s + 16); + int64_t h6 = load_3(s + 20) << 7; + int64_t h7 = load_3(s + 23) << 5; + int64_t h8 = load_3(s + 26) << 4; + int64_t h9 = (load_3(s + 29) & 8388607) << 2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + h[0] = (int32_t)h0; + h[1] = (int32_t)h1; + h[2] = (int32_t)h2; + h[3] = (int32_t)h3; + h[4] = (int32_t)h4; + h[5] = (int32_t)h5; + h[6] = (int32_t)h6; + h[7] = (int32_t)h7; + h[8] = (int32_t)h8; + h[9] = (int32_t)h9; +} + +/* Preconditions: + * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + * + * Write p=2^255-19; q=floor(h/p). + * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). + * + * Proof: + * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. + * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. + * + * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). + * Then 0> 25; + q = (h0 + q) >> 26; + q = (h1 + q) >> 25; + q = (h2 + q) >> 26; + q = (h3 + q) >> 25; + q = (h4 + q) >> 26; + q = (h5 + q) >> 25; + q = (h6 + q) >> 26; + q = (h7 + q) >> 25; + q = (h8 + q) >> 26; + q = (h9 + q) >> 25; + + /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ + h0 += 19 * q; + /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ + + h1 += h0 >> 26; h0 &= kBottom26Bits; + h2 += h1 >> 25; h1 &= kBottom25Bits; + h3 += h2 >> 26; h2 &= kBottom26Bits; + h4 += h3 >> 25; h3 &= kBottom25Bits; + h5 += h4 >> 26; h4 &= kBottom26Bits; + h6 += h5 >> 25; h5 &= kBottom25Bits; + h7 += h6 >> 26; h6 &= kBottom26Bits; + h8 += h7 >> 25; h7 &= kBottom25Bits; + h9 += h8 >> 26; h8 &= kBottom26Bits; + h9 &= kBottom25Bits; + /* h10 = carry9 */ + + /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. + * Have h0+...+2^230 h9 between 0 and 2^255-1; + * evidently 2^255 h10-2^255 q = 0. + * Goal: Output h0+...+2^230 h9. */ + + s[0] = (uint8_t)(h0 >> 0); + s[1] = (uint8_t)(h0 >> 8); + s[2] = (uint8_t)(h0 >> 16); + s[3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2)); + s[4] = (uint8_t)(h1 >> 6); + s[5] = (uint8_t)(h1 >> 14); + s[6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3)); + s[7] = (uint8_t)(h2 >> 5); + s[8] = (uint8_t)(h2 >> 13); + s[9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5)); + s[10] = (uint8_t)(h3 >> 3); + s[11] = (uint8_t)(h3 >> 11); + s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6)); + s[13] = (uint8_t)(h4 >> 2); + s[14] = (uint8_t)(h4 >> 10); + s[15] = (uint8_t)(h4 >> 18); + s[16] = (uint8_t)(h5 >> 0); + s[17] = (uint8_t)(h5 >> 8); + s[18] = (uint8_t)(h5 >> 16); + s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1)); + s[20] = (uint8_t)(h6 >> 7); + s[21] = (uint8_t)(h6 >> 15); + s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3)); + s[23] = (uint8_t)(h7 >> 5); + s[24] = (uint8_t)(h7 >> 13); + s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4)); + s[26] = (uint8_t)(h8 >> 4); + s[27] = (uint8_t)(h8 >> 12); + s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6)); + s[29] = (uint8_t)(h9 >> 2); + s[30] = (uint8_t)(h9 >> 10); + s[31] = (uint8_t)(h9 >> 18); +} + +/* h = f */ +static void fe_copy(fe h, const fe f) { + memmove(h, f, sizeof(int32_t) * 10); +} + +/* h = 0 */ +static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); } + +/* h = 1 */ +static void fe_1(fe h) { + memset(h, 0, sizeof(int32_t) * 10); + h[0] = 1; +} + +/* h = f + g + * Can overlap h with f or g. + * + * Preconditions: + * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + * Postconditions: + * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ +void fe_add(fe h, const fe f, const fe g) { + unsigned i; + for (i = 0; i < 10; i++) { + h[i] = f[i] + g[i]; + } +} + +/* h = f - g + * Can overlap h with f or g. + * + * Preconditions: + * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + * Postconditions: + * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ +void fe_sub(fe h, const fe f, const fe g) { + unsigned i; + for (i = 0; i < 10; i++) { + h[i] = f[i] - g[i]; + } +} + +/* h = f * g + * Can overlap h with f or g. + * + * Preconditions: + * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + * Postconditions: + * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. + * + * Notes on implementation strategy: + * + * Using schoolbook multiplication. + * Karatsuba would save a little in some cost models. + * + * Most multiplications by 2 and 19 are 32-bit precomputations; + * cheaper than 64-bit postcomputations. + * + * There is one remaining multiplication by 19 in the carry chain; + * one *19 precomputation can be merged into this, + * but the resulting data flow is considerably less clean. + * + * There are 12 carries below. + * 10 of them are 2-way parallelizable and vectorizable. + * Can get away with 11 carries, but then data flow is much deeper. + * + * With tighter constraints on inputs can squeeze carries into int32. */ +void GFp_fe_mul(fe h, const fe f, const fe g) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ + int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ + int32_t g3_19 = 19 * g3; + int32_t g4_19 = 19 * g4; + int32_t g5_19 = 19 * g5; + int32_t g6_19 = 19 * g6; + int32_t g7_19 = 19 * g7; + int32_t g8_19 = 19 * g8; + int32_t g9_19 = 19 * g9; + int32_t f1_2 = 2 * f1; + int32_t f3_2 = 2 * f3; + int32_t f5_2 = 2 * f5; + int32_t f7_2 = 2 * f7; + int32_t f9_2 = 2 * f9; + int64_t f0g0 = f0 * (int64_t) g0; + int64_t f0g1 = f0 * (int64_t) g1; + int64_t f0g2 = f0 * (int64_t) g2; + int64_t f0g3 = f0 * (int64_t) g3; + int64_t f0g4 = f0 * (int64_t) g4; + int64_t f0g5 = f0 * (int64_t) g5; + int64_t f0g6 = f0 * (int64_t) g6; + int64_t f0g7 = f0 * (int64_t) g7; + int64_t f0g8 = f0 * (int64_t) g8; + int64_t f0g9 = f0 * (int64_t) g9; + int64_t f1g0 = f1 * (int64_t) g0; + int64_t f1g1_2 = f1_2 * (int64_t) g1; + int64_t f1g2 = f1 * (int64_t) g2; + int64_t f1g3_2 = f1_2 * (int64_t) g3; + int64_t f1g4 = f1 * (int64_t) g4; + int64_t f1g5_2 = f1_2 * (int64_t) g5; + int64_t f1g6 = f1 * (int64_t) g6; + int64_t f1g7_2 = f1_2 * (int64_t) g7; + int64_t f1g8 = f1 * (int64_t) g8; + int64_t f1g9_38 = f1_2 * (int64_t) g9_19; + int64_t f2g0 = f2 * (int64_t) g0; + int64_t f2g1 = f2 * (int64_t) g1; + int64_t f2g2 = f2 * (int64_t) g2; + int64_t f2g3 = f2 * (int64_t) g3; + int64_t f2g4 = f2 * (int64_t) g4; + int64_t f2g5 = f2 * (int64_t) g5; + int64_t f2g6 = f2 * (int64_t) g6; + int64_t f2g7 = f2 * (int64_t) g7; + int64_t f2g8_19 = f2 * (int64_t) g8_19; + int64_t f2g9_19 = f2 * (int64_t) g9_19; + int64_t f3g0 = f3 * (int64_t) g0; + int64_t f3g1_2 = f3_2 * (int64_t) g1; + int64_t f3g2 = f3 * (int64_t) g2; + int64_t f3g3_2 = f3_2 * (int64_t) g3; + int64_t f3g4 = f3 * (int64_t) g4; + int64_t f3g5_2 = f3_2 * (int64_t) g5; + int64_t f3g6 = f3 * (int64_t) g6; + int64_t f3g7_38 = f3_2 * (int64_t) g7_19; + int64_t f3g8_19 = f3 * (int64_t) g8_19; + int64_t f3g9_38 = f3_2 * (int64_t) g9_19; + int64_t f4g0 = f4 * (int64_t) g0; + int64_t f4g1 = f4 * (int64_t) g1; + int64_t f4g2 = f4 * (int64_t) g2; + int64_t f4g3 = f4 * (int64_t) g3; + int64_t f4g4 = f4 * (int64_t) g4; + int64_t f4g5 = f4 * (int64_t) g5; + int64_t f4g6_19 = f4 * (int64_t) g6_19; + int64_t f4g7_19 = f4 * (int64_t) g7_19; + int64_t f4g8_19 = f4 * (int64_t) g8_19; + int64_t f4g9_19 = f4 * (int64_t) g9_19; + int64_t f5g0 = f5 * (int64_t) g0; + int64_t f5g1_2 = f5_2 * (int64_t) g1; + int64_t f5g2 = f5 * (int64_t) g2; + int64_t f5g3_2 = f5_2 * (int64_t) g3; + int64_t f5g4 = f5 * (int64_t) g4; + int64_t f5g5_38 = f5_2 * (int64_t) g5_19; + int64_t f5g6_19 = f5 * (int64_t) g6_19; + int64_t f5g7_38 = f5_2 * (int64_t) g7_19; + int64_t f5g8_19 = f5 * (int64_t) g8_19; + int64_t f5g9_38 = f5_2 * (int64_t) g9_19; + int64_t f6g0 = f6 * (int64_t) g0; + int64_t f6g1 = f6 * (int64_t) g1; + int64_t f6g2 = f6 * (int64_t) g2; + int64_t f6g3 = f6 * (int64_t) g3; + int64_t f6g4_19 = f6 * (int64_t) g4_19; + int64_t f6g5_19 = f6 * (int64_t) g5_19; + int64_t f6g6_19 = f6 * (int64_t) g6_19; + int64_t f6g7_19 = f6 * (int64_t) g7_19; + int64_t f6g8_19 = f6 * (int64_t) g8_19; + int64_t f6g9_19 = f6 * (int64_t) g9_19; + int64_t f7g0 = f7 * (int64_t) g0; + int64_t f7g1_2 = f7_2 * (int64_t) g1; + int64_t f7g2 = f7 * (int64_t) g2; + int64_t f7g3_38 = f7_2 * (int64_t) g3_19; + int64_t f7g4_19 = f7 * (int64_t) g4_19; + int64_t f7g5_38 = f7_2 * (int64_t) g5_19; + int64_t f7g6_19 = f7 * (int64_t) g6_19; + int64_t f7g7_38 = f7_2 * (int64_t) g7_19; + int64_t f7g8_19 = f7 * (int64_t) g8_19; + int64_t f7g9_38 = f7_2 * (int64_t) g9_19; + int64_t f8g0 = f8 * (int64_t) g0; + int64_t f8g1 = f8 * (int64_t) g1; + int64_t f8g2_19 = f8 * (int64_t) g2_19; + int64_t f8g3_19 = f8 * (int64_t) g3_19; + int64_t f8g4_19 = f8 * (int64_t) g4_19; + int64_t f8g5_19 = f8 * (int64_t) g5_19; + int64_t f8g6_19 = f8 * (int64_t) g6_19; + int64_t f8g7_19 = f8 * (int64_t) g7_19; + int64_t f8g8_19 = f8 * (int64_t) g8_19; + int64_t f8g9_19 = f8 * (int64_t) g9_19; + int64_t f9g0 = f9 * (int64_t) g0; + int64_t f9g1_38 = f9_2 * (int64_t) g1_19; + int64_t f9g2_19 = f9 * (int64_t) g2_19; + int64_t f9g3_38 = f9_2 * (int64_t) g3_19; + int64_t f9g4_19 = f9 * (int64_t) g4_19; + int64_t f9g5_38 = f9_2 * (int64_t) g5_19; + int64_t f9g6_19 = f9 * (int64_t) g6_19; + int64_t f9g7_38 = f9_2 * (int64_t) g7_19; + int64_t f9g8_19 = f9 * (int64_t) g8_19; + int64_t f9g9_38 = f9_2 * (int64_t) g9_19; + int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; + int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; + int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; + int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; + int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; + int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; + int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; + int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; + int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; + int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) + * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 + * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) + * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + /* |h0| <= 2^25 */ + /* |h4| <= 2^25 */ + /* |h1| <= 1.71*2^59 */ + /* |h5| <= 1.71*2^59 */ + + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + /* |h1| <= 2^24; from now on fits into int32 */ + /* |h5| <= 2^24; from now on fits into int32 */ + /* |h2| <= 1.41*2^60 */ + /* |h6| <= 1.41*2^60 */ + + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + /* |h2| <= 2^25; from now on fits into int32 unchanged */ + /* |h6| <= 2^25; from now on fits into int32 unchanged */ + /* |h3| <= 1.71*2^59 */ + /* |h7| <= 1.71*2^59 */ + + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + /* |h3| <= 2^24; from now on fits into int32 unchanged */ + /* |h7| <= 2^24; from now on fits into int32 unchanged */ + /* |h4| <= 1.72*2^34 */ + /* |h8| <= 1.41*2^60 */ + + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + /* |h4| <= 2^25; from now on fits into int32 unchanged */ + /* |h8| <= 2^25; from now on fits into int32 unchanged */ + /* |h5| <= 1.01*2^24 */ + /* |h9| <= 1.71*2^59 */ + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + /* |h9| <= 2^24; from now on fits into int32 unchanged */ + /* |h0| <= 1.1*2^39 */ + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + /* |h0| <= 2^25; from now on fits into int32 unchanged */ + /* |h1| <= 1.01*2^24 */ + + h[0] = (int32_t)h0; + h[1] = (int32_t)h1; + h[2] = (int32_t)h2; + h[3] = (int32_t)h3; + h[4] = (int32_t)h4; + h[5] = (int32_t)h5; + h[6] = (int32_t)h6; + h[7] = (int32_t)h7; + h[8] = (int32_t)h8; + h[9] = (int32_t)h9; +} + +/* h = f * f + * Can overlap h with f. + * + * Preconditions: + * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + * Postconditions: + * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ +void fe_sq(fe h, const fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t f0_2 = 2 * f0; + int32_t f1_2 = 2 * f1; + int32_t f2_2 = 2 * f2; + int32_t f3_2 = 2 * f3; + int32_t f4_2 = 2 * f4; + int32_t f5_2 = 2 * f5; + int32_t f6_2 = 2 * f6; + int32_t f7_2 = 2 * f7; + int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + int64_t f0f0 = f0 * (int64_t) f0; + int64_t f0f1_2 = f0_2 * (int64_t) f1; + int64_t f0f2_2 = f0_2 * (int64_t) f2; + int64_t f0f3_2 = f0_2 * (int64_t) f3; + int64_t f0f4_2 = f0_2 * (int64_t) f4; + int64_t f0f5_2 = f0_2 * (int64_t) f5; + int64_t f0f6_2 = f0_2 * (int64_t) f6; + int64_t f0f7_2 = f0_2 * (int64_t) f7; + int64_t f0f8_2 = f0_2 * (int64_t) f8; + int64_t f0f9_2 = f0_2 * (int64_t) f9; + int64_t f1f1_2 = f1_2 * (int64_t) f1; + int64_t f1f2_2 = f1_2 * (int64_t) f2; + int64_t f1f3_4 = f1_2 * (int64_t) f3_2; + int64_t f1f4_2 = f1_2 * (int64_t) f4; + int64_t f1f5_4 = f1_2 * (int64_t) f5_2; + int64_t f1f6_2 = f1_2 * (int64_t) f6; + int64_t f1f7_4 = f1_2 * (int64_t) f7_2; + int64_t f1f8_2 = f1_2 * (int64_t) f8; + int64_t f1f9_76 = f1_2 * (int64_t) f9_38; + int64_t f2f2 = f2 * (int64_t) f2; + int64_t f2f3_2 = f2_2 * (int64_t) f3; + int64_t f2f4_2 = f2_2 * (int64_t) f4; + int64_t f2f5_2 = f2_2 * (int64_t) f5; + int64_t f2f6_2 = f2_2 * (int64_t) f6; + int64_t f2f7_2 = f2_2 * (int64_t) f7; + int64_t f2f8_38 = f2_2 * (int64_t) f8_19; + int64_t f2f9_38 = f2 * (int64_t) f9_38; + int64_t f3f3_2 = f3_2 * (int64_t) f3; + int64_t f3f4_2 = f3_2 * (int64_t) f4; + int64_t f3f5_4 = f3_2 * (int64_t) f5_2; + int64_t f3f6_2 = f3_2 * (int64_t) f6; + int64_t f3f7_76 = f3_2 * (int64_t) f7_38; + int64_t f3f8_38 = f3_2 * (int64_t) f8_19; + int64_t f3f9_76 = f3_2 * (int64_t) f9_38; + int64_t f4f4 = f4 * (int64_t) f4; + int64_t f4f5_2 = f4_2 * (int64_t) f5; + int64_t f4f6_38 = f4_2 * (int64_t) f6_19; + int64_t f4f7_38 = f4 * (int64_t) f7_38; + int64_t f4f8_38 = f4_2 * (int64_t) f8_19; + int64_t f4f9_38 = f4 * (int64_t) f9_38; + int64_t f5f5_38 = f5 * (int64_t) f5_38; + int64_t f5f6_38 = f5_2 * (int64_t) f6_19; + int64_t f5f7_76 = f5_2 * (int64_t) f7_38; + int64_t f5f8_38 = f5_2 * (int64_t) f8_19; + int64_t f5f9_76 = f5_2 * (int64_t) f9_38; + int64_t f6f6_19 = f6 * (int64_t) f6_19; + int64_t f6f7_38 = f6 * (int64_t) f7_38; + int64_t f6f8_38 = f6_2 * (int64_t) f8_19; + int64_t f6f9_38 = f6 * (int64_t) f9_38; + int64_t f7f7_38 = f7 * (int64_t) f7_38; + int64_t f7f8_38 = f7_2 * (int64_t) f8_19; + int64_t f7f9_76 = f7_2 * (int64_t) f9_38; + int64_t f8f8_19 = f8 * (int64_t) f8_19; + int64_t f8f9_38 = f8 * (int64_t) f9_38; + int64_t f9f9_38 = f9 * (int64_t) f9_38; + int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; + int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; + int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; + int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; + int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; + int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; + int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; + int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; + int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; + int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + + h[0] = (int32_t)h0; + h[1] = (int32_t)h1; + h[2] = (int32_t)h2; + h[3] = (int32_t)h3; + h[4] = (int32_t)h4; + h[5] = (int32_t)h5; + h[6] = (int32_t)h6; + h[7] = (int32_t)h7; + h[8] = (int32_t)h8; + h[9] = (int32_t)h9; +} + +void GFp_fe_invert(fe out, const fe z) { + fe t0; + fe t1; + fe t2; + fe t3; + int i; + + fe_sq(t0, z); + fe_sq(t1, t0); + for (i = 1; i < 2; ++i) { + fe_sq(t1, t1); + } + GFp_fe_mul(t1, z, t1); + GFp_fe_mul(t0, t0, t1); + fe_sq(t2, t0); + GFp_fe_mul(t1, t1, t2); + fe_sq(t2, t1); + for (i = 1; i < 5; ++i) { + fe_sq(t2, t2); + } + GFp_fe_mul(t1, t2, t1); + fe_sq(t2, t1); + for (i = 1; i < 10; ++i) { + fe_sq(t2, t2); + } + GFp_fe_mul(t2, t2, t1); + fe_sq(t3, t2); + for (i = 1; i < 20; ++i) { + fe_sq(t3, t3); + } + GFp_fe_mul(t2, t3, t2); + fe_sq(t2, t2); + for (i = 1; i < 10; ++i) { + fe_sq(t2, t2); + } + GFp_fe_mul(t1, t2, t1); + fe_sq(t2, t1); + for (i = 1; i < 50; ++i) { + fe_sq(t2, t2); + } + GFp_fe_mul(t2, t2, t1); + fe_sq(t3, t2); + for (i = 1; i < 100; ++i) { + fe_sq(t3, t3); + } + GFp_fe_mul(t2, t3, t2); + fe_sq(t2, t2); + for (i = 1; i < 50; ++i) { + fe_sq(t2, t2); + } + GFp_fe_mul(t1, t2, t1); + fe_sq(t1, t1); + for (i = 1; i < 5; ++i) { + fe_sq(t1, t1); + } + GFp_fe_mul(out, t1, t0); +} + +/* h = -f + * + * Preconditions: + * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + * Postconditions: + * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ +void fe_neg(fe h, const fe f) { + unsigned i; + for (i = 0; i < 10; i++) { + h[i] = -f[i]; + } +} + +/* Replace (f,g) with (g,g) if b == 1; + * replace (f,g) with (f,g) if b == 0. + * + * Preconditions: b in {0,1}. */ +void fe_cmov(fe f, const fe g, unsigned b) { + b = 0-b; + unsigned i; + for (i = 0; i < 10; i++) { + int32_t x = f[i] ^ g[i]; + x &= b; + f[i] ^= x; + } +} + +/* return 0 if f == 0 + * return 1 if f != 0 + * + * Preconditions: + * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ +int fe_isnonzero(const fe f) { + uint8_t s[32]; + GFp_fe_tobytes(s, f); + + static const uint8_t zero[32] = {0}; + return memcmp(s, zero, sizeof(zero)) != 0; +} + +/* return 1 if f is in {1,3,5,...,q-2} + * return 0 if f is in {0,2,4,...,q-1} + * + * Preconditions: + * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ +uint8_t GFp_fe_isnegative(const fe f) { + uint8_t s[32]; + GFp_fe_tobytes(s, f); + return s[0] & 1; +} + +/* h = 2 * f * f + * Can overlap h with f. + * + * Preconditions: + * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + * Postconditions: + * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ +void fe_sq2(fe h, const fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t f0_2 = 2 * f0; + int32_t f1_2 = 2 * f1; + int32_t f2_2 = 2 * f2; + int32_t f3_2 = 2 * f3; + int32_t f4_2 = 2 * f4; + int32_t f5_2 = 2 * f5; + int32_t f6_2 = 2 * f6; + int32_t f7_2 = 2 * f7; + int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + int64_t f0f0 = f0 * (int64_t) f0; + int64_t f0f1_2 = f0_2 * (int64_t) f1; + int64_t f0f2_2 = f0_2 * (int64_t) f2; + int64_t f0f3_2 = f0_2 * (int64_t) f3; + int64_t f0f4_2 = f0_2 * (int64_t) f4; + int64_t f0f5_2 = f0_2 * (int64_t) f5; + int64_t f0f6_2 = f0_2 * (int64_t) f6; + int64_t f0f7_2 = f0_2 * (int64_t) f7; + int64_t f0f8_2 = f0_2 * (int64_t) f8; + int64_t f0f9_2 = f0_2 * (int64_t) f9; + int64_t f1f1_2 = f1_2 * (int64_t) f1; + int64_t f1f2_2 = f1_2 * (int64_t) f2; + int64_t f1f3_4 = f1_2 * (int64_t) f3_2; + int64_t f1f4_2 = f1_2 * (int64_t) f4; + int64_t f1f5_4 = f1_2 * (int64_t) f5_2; + int64_t f1f6_2 = f1_2 * (int64_t) f6; + int64_t f1f7_4 = f1_2 * (int64_t) f7_2; + int64_t f1f8_2 = f1_2 * (int64_t) f8; + int64_t f1f9_76 = f1_2 * (int64_t) f9_38; + int64_t f2f2 = f2 * (int64_t) f2; + int64_t f2f3_2 = f2_2 * (int64_t) f3; + int64_t f2f4_2 = f2_2 * (int64_t) f4; + int64_t f2f5_2 = f2_2 * (int64_t) f5; + int64_t f2f6_2 = f2_2 * (int64_t) f6; + int64_t f2f7_2 = f2_2 * (int64_t) f7; + int64_t f2f8_38 = f2_2 * (int64_t) f8_19; + int64_t f2f9_38 = f2 * (int64_t) f9_38; + int64_t f3f3_2 = f3_2 * (int64_t) f3; + int64_t f3f4_2 = f3_2 * (int64_t) f4; + int64_t f3f5_4 = f3_2 * (int64_t) f5_2; + int64_t f3f6_2 = f3_2 * (int64_t) f6; + int64_t f3f7_76 = f3_2 * (int64_t) f7_38; + int64_t f3f8_38 = f3_2 * (int64_t) f8_19; + int64_t f3f9_76 = f3_2 * (int64_t) f9_38; + int64_t f4f4 = f4 * (int64_t) f4; + int64_t f4f5_2 = f4_2 * (int64_t) f5; + int64_t f4f6_38 = f4_2 * (int64_t) f6_19; + int64_t f4f7_38 = f4 * (int64_t) f7_38; + int64_t f4f8_38 = f4_2 * (int64_t) f8_19; + int64_t f4f9_38 = f4 * (int64_t) f9_38; + int64_t f5f5_38 = f5 * (int64_t) f5_38; + int64_t f5f6_38 = f5_2 * (int64_t) f6_19; + int64_t f5f7_76 = f5_2 * (int64_t) f7_38; + int64_t f5f8_38 = f5_2 * (int64_t) f8_19; + int64_t f5f9_76 = f5_2 * (int64_t) f9_38; + int64_t f6f6_19 = f6 * (int64_t) f6_19; + int64_t f6f7_38 = f6 * (int64_t) f7_38; + int64_t f6f8_38 = f6_2 * (int64_t) f8_19; + int64_t f6f9_38 = f6 * (int64_t) f9_38; + int64_t f7f7_38 = f7 * (int64_t) f7_38; + int64_t f7f8_38 = f7_2 * (int64_t) f8_19; + int64_t f7f9_76 = f7_2 * (int64_t) f9_38; + int64_t f8f8_19 = f8 * (int64_t) f8_19; + int64_t f8f9_38 = f8 * (int64_t) f9_38; + int64_t f9f9_38 = f9 * (int64_t) f9_38; + int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; + int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; + int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; + int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; + int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; + int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; + int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; + int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; + int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; + int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + h0 += h0; + h1 += h1; + h2 += h2; + h3 += h3; + h4 += h4; + h5 += h5; + h6 += h6; + h7 += h7; + h8 += h8; + h9 += h9; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + + h[0] = (int32_t)h0; + h[1] = (int32_t)h1; + h[2] = (int32_t)h2; + h[3] = (int32_t)h3; + h[4] = (int32_t)h4; + h[5] = (int32_t)h5; + h[6] = (int32_t)h6; + h[7] = (int32_t)h7; + h[8] = (int32_t)h8; + h[9] = (int32_t)h9; +} + +void fe_pow22523(fe out, const fe z) { + fe t0; + fe t1; + fe t2; + int i; + + fe_sq(t0, z); + fe_sq(t1, t0); + for (i = 1; i < 2; ++i) { + fe_sq(t1, t1); + } + GFp_fe_mul(t1, z, t1); + GFp_fe_mul(t0, t0, t1); + fe_sq(t0, t0); + GFp_fe_mul(t0, t1, t0); + fe_sq(t1, t0); + for (i = 1; i < 5; ++i) { + fe_sq(t1, t1); + } + GFp_fe_mul(t0, t1, t0); + fe_sq(t1, t0); + for (i = 1; i < 10; ++i) { + fe_sq(t1, t1); + } + GFp_fe_mul(t1, t1, t0); + fe_sq(t2, t1); + for (i = 1; i < 20; ++i) { + fe_sq(t2, t2); + } + GFp_fe_mul(t1, t2, t1); + fe_sq(t1, t1); + for (i = 1; i < 10; ++i) { + fe_sq(t1, t1); + } + GFp_fe_mul(t0, t1, t0); + fe_sq(t1, t0); + for (i = 1; i < 50; ++i) { + fe_sq(t1, t1); + } + GFp_fe_mul(t1, t1, t0); + fe_sq(t2, t1); + for (i = 1; i < 100; ++i) { + fe_sq(t2, t2); + } + GFp_fe_mul(t1, t2, t1); + fe_sq(t1, t1); + for (i = 1; i < 50; ++i) { + fe_sq(t1, t1); + } + GFp_fe_mul(t0, t1, t0); + fe_sq(t0, t0); + for (i = 1; i < 2; ++i) { + fe_sq(t0, t0); + } + GFp_fe_mul(out, t0, z); +} + +static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729, + -8787816, -6275908, -3247719, -18696448, -12055116}; + +static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472, + -272473, -25146209, -2005654, 326686, 11406482}; + +int GFp_x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) { + fe u; + fe v; + fe v3; + fe vxx; + fe check; + + fe_frombytes(h->Y, s); + fe_1(h->Z); + fe_sq(u, h->Y); + GFp_fe_mul(v, u, d); + fe_sub(u, u, h->Z); /* u = y^2-1 */ + fe_add(v, v, h->Z); /* v = dy^2+1 */ + + fe_sq(v3, v); + GFp_fe_mul(v3, v3, v); /* v3 = v^3 */ + fe_sq(h->X, v3); + GFp_fe_mul(h->X, h->X, v); + GFp_fe_mul(h->X, h->X, u); /* x = uv^7 */ + + fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ + GFp_fe_mul(h->X, h->X, v3); + GFp_fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ + + fe_sq(vxx, h->X); + GFp_fe_mul(vxx, vxx, v); + fe_sub(check, vxx, u); /* vx^2-u */ + if (fe_isnonzero(check)) { + fe_add(check, vxx, u); /* vx^2+u */ + if (fe_isnonzero(check)) { + return 0; + } + GFp_fe_mul(h->X, h->X, sqrtm1); + } + + if (GFp_fe_isnegative(h->X) != (s[31] >> 7)) { + fe_neg(h->X, h->X); + } + + GFp_fe_mul(h->T, h->X, h->Y); + return 1; +} + +static void ge_p2_0(ge_p2 *h) { + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); +} + +static void ge_p3_0(ge_p3 *h) { + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); + fe_0(h->T); +} + +static void ge_precomp_0(ge_precomp *h) { + fe_1(h->yplusx); + fe_1(h->yminusx); + fe_0(h->xy2d); +} + +/* r = p */ +void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { + fe_copy(r->X, p->X); + fe_copy(r->Y, p->Y); + fe_copy(r->Z, p->Z); +} + +static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458, + 15978800, -12551817, -6495438, 29715968, 9444199}; + +/* r = p */ +void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) { + fe_add(r->YplusX, p->Y, p->X); + fe_sub(r->YminusX, p->Y, p->X); + fe_copy(r->Z, p->Z); + GFp_fe_mul(r->T2d, p->T, d2); +} + +/* r = p */ +void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { + GFp_fe_mul(r->X, p->X, p->T); + GFp_fe_mul(r->Y, p->Y, p->Z); + GFp_fe_mul(r->Z, p->Z, p->T); +} + +/* r = p */ +void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { + GFp_fe_mul(r->X, p->X, p->T); + GFp_fe_mul(r->Y, p->Y, p->Z); + GFp_fe_mul(r->Z, p->Z, p->T); + GFp_fe_mul(r->T, p->X, p->Y); +} + +/* r = 2 * p */ +void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { + fe t0; + + fe_sq(r->X, p->X); + fe_sq(r->Z, p->Y); + fe_sq2(r->T, p->Z); + fe_add(r->Y, p->X, p->Y); + fe_sq(t0, r->Y); + fe_add(r->Y, r->Z, r->X); + fe_sub(r->Z, r->Z, r->X); + fe_sub(r->X, t0, r->Y); + fe_sub(r->T, r->T, r->Z); +} + +/* r = 2 * p */ +void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { + ge_p2 q; + ge_p3_to_p2(&q, p); + ge_p2_dbl(r, &q); +} + +/* r = p + q */ +void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { + fe t0; + + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + GFp_fe_mul(r->Z, r->X, q->yplusx); + GFp_fe_mul(r->Y, r->Y, q->yminusx); + GFp_fe_mul(r->T, q->xy2d, p->T); + fe_add(t0, p->Z, p->Z); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_add(r->Z, t0, r->T); + fe_sub(r->T, t0, r->T); +} + +/* r = p - q */ +void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { + fe t0; + + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + GFp_fe_mul(r->Z, r->X, q->yminusx); + GFp_fe_mul(r->Y, r->Y, q->yplusx); + GFp_fe_mul(r->T, q->xy2d, p->T); + fe_add(t0, p->Z, p->Z); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_sub(r->Z, t0, r->T); + fe_add(r->T, t0, r->T); +} + +/* r = p + q */ +void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { + fe t0; + + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + GFp_fe_mul(r->Z, r->X, q->YplusX); + GFp_fe_mul(r->Y, r->Y, q->YminusX); + GFp_fe_mul(r->T, q->T2d, p->T); + GFp_fe_mul(r->X, p->Z, q->Z); + fe_add(t0, r->X, r->X); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_add(r->Z, t0, r->T); + fe_sub(r->T, t0, r->T); +} + +/* r = p - q */ +void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { + fe t0; + + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + GFp_fe_mul(r->Z, r->X, q->YminusX); + GFp_fe_mul(r->Y, r->Y, q->YplusX); + GFp_fe_mul(r->T, q->T2d, p->T); + GFp_fe_mul(r->X, p->Z, q->Z); + fe_add(t0, r->X, r->X); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_sub(r->Z, t0, r->T); + fe_add(r->T, t0, r->T); +} + +static uint8_t equal(signed char b, signed char c) { + uint8_t ub = b; + uint8_t uc = c; + uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */ + uint32_t y = x; /* 0: yes; 1..255: no */ + y -= 1; /* 4294967295: yes; 0..254: no */ + y >>= 31; /* 1: yes; 0: no */ + return (uint8_t)y; +} + +static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) { + fe_cmov(t->yplusx, u->yplusx, b); + fe_cmov(t->yminusx, u->yminusx, b); + fe_cmov(t->xy2d, u->xy2d, b); +} + +#if defined(OPENSSL_SMALL) + +static void x25519_ge_scalarmult_small_precomp( + ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]) { + /* precomp_table is first expanded into matching |ge_precomp| + * elements. */ + ge_precomp multiples[15]; + + unsigned i; + for (i = 0; i < 15; i++) { + const uint8_t *bytes = &precomp_table[i*(2 * 32)]; + fe x, y; + fe_frombytes(x, bytes); + fe_frombytes(y, bytes + 32); + + ge_precomp *out = &multiples[i]; + fe_add(out->yplusx, y, x); + fe_sub(out->yminusx, y, x); + GFp_fe_mul(out->xy2d, x, y); + GFp_fe_mul(out->xy2d, out->xy2d, d2); + } + + /* See the comment above |k25519SmallPrecomp| about the structure of the + * precomputed elements. This loop does 64 additions and 64 doublings to + * calculate the result. */ + ge_p3_0(h); + + for (i = 63; i < 64; i--) { + unsigned j; + signed char index = 0; + + for (j = 0; j < 4; j++) { + const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7)); + index |= (bit << j); + } + + ge_precomp e; + ge_precomp_0(&e); + + for (j = 1; j < 16; j++) { + cmov(&e, &multiples[j-1], equal(index, j)); + } + + ge_cached cached; + ge_p1p1 r; + x25519_ge_p3_to_cached(&cached, h); + x25519_ge_add(&r, h, &cached); + x25519_ge_p1p1_to_p3(h, &r); + + ge_madd(&r, h, &e); + x25519_ge_p1p1_to_p3(h, &r); + } +} + +/* This block of code replaces the standard base-point table with a much smaller + * one. The standard table is 30,720 bytes while this one is just 960. + * + * This table contains 15 pairs of group elements, (x, y), where each field + * element is serialised with |GFp_fe_tobytes|. If |i| is the index of the group + * element then consider i+1 as a four-bit number: (i_0, i_1, i_2, i_3) where + * i_0 is the most significant bit). The value of the group element is then + * (i_x2^192 + i_1x2^128 + i_2x2^64 + i_3)G, where G is the generator. */ +static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = { + 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95, + 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0, + 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66, + 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, + 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, + 0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e, + 0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4, + 0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62, + 0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba, + 0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd, + 0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61, + 0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c, + 0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c, + 0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5, + 0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3, + 0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18, + 0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2, + 0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95, + 0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b, + 0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90, + 0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52, + 0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb, + 0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c, + 0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e, + 0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e, + 0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a, + 0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43, + 0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53, + 0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8, + 0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89, + 0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef, + 0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60, + 0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a, + 0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8, + 0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54, + 0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b, + 0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd, + 0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb, + 0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c, + 0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b, + 0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63, + 0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a, + 0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07, + 0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa, + 0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a, + 0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84, + 0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc, + 0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42, + 0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0, + 0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0, + 0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a, + 0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5, + 0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c, + 0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27, + 0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31, + 0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c, + 0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87, + 0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0, + 0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23, + 0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2, + 0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87, + 0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d, + 0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b, + 0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d, + 0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6, + 0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84, + 0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04, + 0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19, + 0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b, + 0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a, + 0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea, + 0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30, + 0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7, + 0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa, + 0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5, + 0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71, + 0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab, + 0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb, + 0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c, + 0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25, +}; + +void GFp_x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) { + x25519_ge_scalarmult_small_precomp(h, a, k25519SmallPrecomp); +} + +#else + +/* k25519Precomp[i][j] = (j+1)*256^i*B */ +static const ge_precomp k25519Precomp[32][8] = { + { + { + {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, + 27544626, -11754271, -6079156, 2047605}, + {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, + 5043384, 19500929, -15469378}, + {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, + 29287919, 11864899, -24514362, -4438546}, + }, + { + {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, + -11717903, -3814571, -358445, -10211303}, + {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, + -15616551, 11189268, -26829678, -5319081}, + {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, + -3128826, -9541118, -15472047, -4166697}, + }, + { + {15636291, -9688557, 24204773, -7912398, 616977, -16685262, + 27787600, -14772189, 28944400, -1550024}, + {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, + 16354577, -11775962, 7689662, 11199574}, + {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, + 7512774, 10017326, -17749093, -9920357}, + }, + { + {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, + -28926210, 15006023, 3284568, -6276540}, + {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, + 7464579, 9656445, 13059162, 10374397}, + {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, + -3839045, -641708, -101325}, + }, + { + {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, + 32867885, 14515107, -15438304, 10819380}, + {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, + 12483688, -12668491, 5581306}, + {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, + 28542350, 13850243, -23678021, -15815942}, + }, + { + {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, + -19188627, -15224819, -9818940, -12085777}, + {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, + -15689887, 1762328, 14866737}, + {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, + -28236412, 3959421, 27914454, 4383652}, + }, + { + {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, + 5230134, -23952439, -15175766}, + {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, + 20654025, 16520125, 30598449, 7715701}, + {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, + -31400660, 1370708, 29794553, -1409300}, + }, + { + {14499471, -2729599, -33191113, -4254652, 28494862, 14271267, + 30290735, 10876454, -33154098, 2381726}, + {-7195431, -2655363, -14730155, 462251, -27724326, 3941372, + -6236617, 3696005, -32300832, 15351955}, + {27431194, 8222322, 16448760, -3907995, -18707002, 11938355, + -32961401, -2970515, 29551813, 10109425}, + }, + }, + { + { + {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, + -2378284, -1627556, 10092783, -4764171}, + {27939166, 14210322, 4677035, 16277044, -22964462, -12398139, + -32508754, 12005538, -17810127, 12803510}, + {17228999, -15661624, -1233527, 300140, -1224870, -11714777, + 30364213, -9038194, 18016357, 4397660}, + }, + { + {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, + -26619106, 14544525, -17477504, 982639}, + {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, + -4120128, -21047696, 9934963}, + {5793303, 16271923, -24131614, -10116404, 29188560, 1206517, + -14747930, 4559895, -30123922, -10897950}, + }, + { + {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, + 24191034, 4541697, -13338309, 5500568}, + {12650548, -1497113, 9052871, 11355358, -17680037, -8400164, + -17430592, 12264343, 10874051, 13524335}, + {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, + 5080568, -22528059, 5376628}, + }, + { + {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, + -22321305, -9447443, 4535768, 1569007}, + {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, + -30494562, 3044290, 31848280, 12543772}, + {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, + -27377195, -2062731, 7718482, 14474653}, + }, + { + {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, + -7236665, 24316168, -5253567}, + {13741529, 10911568, -33233417, -8603737, -20177830, -1033297, + 33040651, -13424532, -20729456, 8321686}, + {21060490, -2212744, 15712757, -4336099, 1639040, 10656336, + 23845965, -11874838, -9984458, 608372}, + }, + { + {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, + 1123968, -6780577, 27229399, 23887}, + {-23244140, -294205, -11744728, 14712571, -29465699, -2029617, + 12797024, -6440308, -1633405, 16678954}, + {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, + -1508144, -4795045, -17169265, 4904953}, + }, + { + {24059557, 14617003, 19037157, -15039908, 19766093, -14906429, + 5169211, 16191880, 2128236, -4326833}, + {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, + -29806336, 916033, -6882542, -2986532}, + {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, + 285431, 2763829, 15736322, 4143876}, + }, + { + {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, + -14594663, 23527084, -16458268}, + {33431127, -11130478, -17838966, -15626900, 8909499, 8376530, + -32625340, 4087881, -15188911, -14416214}, + {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, + 4357868, -4774191, -16323038}, + }, + }, + { + { + {6721966, 13833823, -23523388, -1551314, 26354293, -11863321, + 23365147, -3949732, 7390890, 2759800}, + {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, + -4264057, 1244380, -12919645}, + {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, + 9208236, 15886429, 16489664}, + }, + { + {1996075, 10375649, 14346367, 13311202, -6874135, -16438411, + -13693198, 398369, -30606455, -712933}, + {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, + 13348553, 12076947, -30836462, 5113182}, + {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, + -30341101, -7336386, 13847711, 5387222}, + }, + { + {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, + 8763061, 3617786, -19600662, 10370991}, + {20246567, -14369378, 22358229, -543712, 18507283, -10413996, + 14554437, -8746092, 32232924, 16763880}, + {9648505, 10094563, 26416693, 14745928, -30374318, -6472621, + 11094161, 15689506, 3140038, -16510092}, + }, + { + {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, + -27224800, 9448613, -28774454, 366295}, + {19153450, 11523972, -11096490, -6503142, -24647631, 5420647, + 28344573, 8041113, 719605, 11671788}, + {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, + -15266516, 27000813, -10195553}, + }, + { + {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, + 5336097, 6750977, -14521026}, + {11836410, -3979488, 26297894, 16080799, 23455045, 15735944, + 1695823, -8819122, 8169720, 16220347}, + {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, + -11144307, -2627664, -5990708, -14166033}, + }, + { + {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, + 27884329, 2847284, 2655861, 1738395}, + {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, + 21651608, -3239336, -19087449, -11005278}, + {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, + 5821408, 10478196, 8544890}, + }, + { + {32173121, -16129311, 24896207, 3921497, 22579056, -3410854, + 19270449, 12217473, 17789017, -3395995}, + {-30552961, -2228401, -15578829, -10147201, 13243889, 517024, + 15479401, -3853233, 30460520, 1052596}, + {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, + 27491595, -4612359, 3179268, -9478891}, + }, + { + {31947069, -14366651, -4640583, -15339921, -15125977, -6039709, + -14756777, -16411740, 19072640, -9511060}, + {11685058, 11822410, 3158003, -13952594, 33402194, -4165066, + 5977896, -5215017, 473099, 5040608}, + {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, + 28326862, 1721092, -19558642, -3131606}, + }, + }, + { + { + {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, + 8076149, -27868496, 11538389}, + {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, + 8754525, 7446702, -5676054, 5797016}, + {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, + 2014099, -9050574, -2369172, -5877341}, + }, + { + {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, + 1192730, -3714199, 15123619, 10811505}, + {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, + 15776356, -28886779, -11974553}, + {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, + -20654173, -16484855, 4714547, -9600655}, + }, + { + {15200332, 8368572, 19679101, 15970074, -31872674, 1959451, + 24611599, -4543832, -11745876, 12340220}, + {12876937, -10480056, 33134381, 6590940, -6307776, 14872440, + 9613953, 8241152, 15370987, 9608631}, + {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, + 15866074, -28210621, -8814099}, + }, + { + {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, + 858697, 20571223, 8420556}, + {14620715, 13067227, -15447274, 8264467, 14106269, 15080814, + 33531827, 12516406, -21574435, -12476749}, + {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, + 7256740, 8791136, 15069930}, + }, + { + {1276410, -9371918, 22949635, -16322807, -23493039, -5702186, + 14711875, 4874229, -30663140, -2331391}, + {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, + -7912378, -33069337, 9234253}, + {20590503, -9018988, 31529744, -7352666, -2706834, 10650548, + 31559055, -11609587, 18979186, 13396066}, + }, + { + {24474287, 4968103, 22267082, 4407354, 24063882, -8325180, + -18816887, 13594782, 33514650, 7021958}, + {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, + -25948728, -3916677, -21480480, 12868082}, + {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, + -21446107, 2244500, -12455797, -8089383}, + }, + { + {-30595528, 13793479, -5852820, 319136, -25723172, -6263899, + 33086546, 8957937, -15233648, 5540521}, + {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, + -23710744, -1568984, -16128528, -14962807}, + {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, + 892185, -11513277, -15205948}, + }, + { + {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, + 4763127, -19179614, 5867134}, + {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, + 27846559, 5931263, -29749703, -16108455}, + {27461885, -2977536, 22380810, 1815854, -23033753, -3031938, + 7283490, -15148073, -19526700, 7734629}, + }, + }, + { + { + {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, + 7585295, -3176626, 18549497, 15302069}, + {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, + 10458790, -6418461, -8872242, 8424746}, + {24687205, 8613276, -30667046, -3233545, 1863892, -1830544, + 19206234, 7134917, -11284482, -828919}, + }, + { + {11334899, -9218022, 8025293, 12707519, 17523892, -10476071, + 10243738, -14685461, -5066034, 16498837}, + {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, + -14124238, 6536641, 10543906}, + {-28946384, 15479763, -17466835, 568876, -1497683, 11223454, + -2669190, -16625574, -27235709, 8876771}, + }, + { + {-25742899, -12566864, -15649966, -846607, -33026686, -796288, + -33481822, 15824474, -604426, -9039817}, + {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, + -4890037, 1657394, 3084098}, + {10477963, -7470260, 12119566, -13250805, 29016247, -5365589, + 31280319, 14396151, -30233575, 15272409}, + }, + { + {-12288309, 3169463, 28813183, 16658753, 25116432, -5630466, + -25173957, -12636138, -25014757, 1950504}, + {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630, + -8384306, -8767532, 15341279, 8373727}, + {28685821, 7759505, -14378516, -12002860, -31971820, 4079242, + 298136, -10232602, -2878207, 15190420}, + }, + { + {-32932876, 13806336, -14337485, -15794431, -24004620, 10940928, + 8669718, 2742393, -26033313, -6875003}, + {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854, + 9291594, -16247779, -12154742, 6048605}, + {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163, + 13934231, 5128323, 11213262, 9168384}, + }, + { + {-26280513, 11007847, 19408960, -940758, -18592965, -4328580, + -5088060, -11105150, 20470157, -16398701}, + {-23136053, 9282192, 14855179, -15390078, -7362815, -14408560, + -22783952, 14461608, 14042978, 5230683}, + {29969567, -2741594, -16711867, -8552442, 9175486, -2468974, + 21556951, 3506042, -5933891, -12449708}, + }, + { + {-3144746, 8744661, 19704003, 4581278, -20430686, 6830683, + -21284170, 8971513, -28539189, 15326563}, + {-19464629, 10110288, -17262528, -3503892, -23500387, 1355669, + -15523050, 15300988, -20514118, 9168260}, + {-5353335, 4488613, -23803248, 16314347, 7780487, -15638939, + -28948358, 9601605, 33087103, -9011387}, + }, + { + {-19443170, -15512900, -20797467, -12445323, -29824447, 10229461, + -27444329, -15000531, -5996870, 15664672}, + {23294591, -16632613, -22650781, -8470978, 27844204, 11461195, + 13099750, -2460356, 18151676, 13417686}, + {-24722913, -4176517, -31150679, 5988919, -26858785, 6685065, + 1661597, -12551441, 15271676, -15452665}, + }, + }, + { + { + {11433042, -13228665, 8239631, -5279517, -1985436, -725718, + -18698764, 2167544, -6921301, -13440182}, + {-31436171, 15575146, 30436815, 12192228, -22463353, 9395379, + -9917708, -8638997, 12215110, 12028277}, + {14098400, 6555944, 23007258, 5757252, -15427832, -12950502, + 30123440, 4617780, -16900089, -655628}, + }, + { + {-4026201, -15240835, 11893168, 13718664, -14809462, 1847385, + -15819999, 10154009, 23973261, -12684474}, + {-26531820, -3695990, -1908898, 2534301, -31870557, 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31088447, -7764523, -11356529, 728112}, + }, + { + {26047220, -11751471, -6900323, -16521798, 24092068, 9158119, + -4273545, -12555558, -29365436, -5498272}, + {17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, + 12327945, 10750447, 10014012}, + {-10312768, 3936952, 9156313, -8897683, 16498692, -994647, + -27481051, -666732, 3424691, 7540221}, + }, + { + {30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, + -16317219, -9244265, 15258046}, + {13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, + 2711395, 1062915, -5136345}, + {-19240248, -11254599, -29509029, -7499965, -5835763, 13005411, + -6066489, 12194497, 32960380, 1459310}, + }, + }, + { + { + {19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, + -6101885, 18638003, -11174937}, + {31395534, 15098109, 26581030, 8030562, -16527914, -5007134, + 9012486, -7584354, -6643087, -5442636}, + {-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, + 9677543, -32294889, -6456008}, + }, + { + {-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, + -7839692, -7852844, -8138429}, + {-15236356, -15433509, 7766470, 746860, 26346930, -10221762, + -27333451, 10754588, -9431476, 5203576}, + {31834314, 14135496, -770007, 5159118, 20917671, -16768096, + -7467973, -7337524, 31809243, 7347066}, + }, + { + {-9606723, -11874240, 20414459, 13033986, 13716524, -11691881, + 19797970, -12211255, 15192876, -2087490}, + {-12663563, -2181719, 1168162, -3804809, 26747877, -14138091, + 10609330, 12694420, 33473243, -13382104}, + {33184999, 11180355, 15832085, -11385430, -1633671, 225884, + 15089336, -11023903, -6135662, 14480053}, + }, + { + {31308717, -5619998, 31030840, -1897099, 15674547, -6582883, + 5496208, 13685227, 27595050, 8737275}, + {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, + -31008351, -12610604, 26498114, 66511}, + {22644454, -8761729, -16671776, 4884562, -3105614, -13559366, + 30540766, -4286747, -13327787, -7515095}, + }, + { + {-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, + 8205540, 13585437, -17127465, 15115439}, + {23711543, -672915, 31206561, -8362711, 6164647, -9709987, + -33535882, -1426096, 8236921, 16492939}, + {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, + 19574902, 10071562, 6708380, -6222424}, + }, + { + {2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, + 9328700, 29955601, -11678310}, + {3096359, 9271816, -21620864, -15521844, -14847996, -7592937, + -25892142, -12635595, -9917575, 6216608}, + {-32615849, 338663, -25195611, 2510422, -29213566, -13820213, + 24822830, -6146567, -26767480, 7525079}, + }, + { + {-23066649, -13985623, 16133487, -7896178, -3389565, 778788, + -910336, -2782495, -19386633, 11994101}, + {21691500, -13624626, -641331, -14367021, 3285881, -3483596, + -25064666, 9718258, -7477437, 13381418}, + {18445390, -4202236, 14979846, 11622458, -1727110, -3582980, + 23111648, -6375247, 28535282, 15779576}, + }, + { + {30098053, 3089662, -9234387, 16662135, -21306940, 11308411, + -14068454, 12021730, 9955285, -16303356}, + {9734894, -14576830, -7473633, -9138735, 2060392, 11313496, + -18426029, 9924399, 20194861, 13380996}, + {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, + -1984914, 15707771, 26342023, 10146099}, + }, + }, + { + { + {-26016874, -219943, 21339191, -41388, 19745256, -2878700, + -29637280, 2227040, 21612326, -545728}, + {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, + 25764461, 12243797, -20856566, 11649658}, + {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, + 6114064, 33514190, 2333242}, + }, + { + {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, + -6679750, -12670638, 24350578, -13450001}, + {-4116307, -11271533, -23886186, 4843615, -30088339, 690623, + -31536088, -10406836, 8317860, 12352766}, + {18200138, -14475911, -33087759, -2696619, -23702521, -9102511, + -23552096, -2287550, 20712163, 6719373}, + }, + { + {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, + -3763210, 26224235, -3297458}, + {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, + 21728352, 9493610, 18620611, -16428628}, + {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, + -5269471, -9725556, -30701573, -16479657}, + }, + { + {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, + 12248509, -5240639, 13735342, 1934062}, + {25089769, 6742589, 17081145, -13406266, 21909293, -16067981, + -15136294, -3765346, -21277997, 5473616}, + {31883677, -7961101, 1083432, -11572403, 22828471, 13290673, + -7125085, 12469656, 29111212, -5451014}, + }, + { + {24244947, -15050407, -26262976, 2791540, -14997599, 16666678, + 24367466, 6388839, -10295587, 452383}, + {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, + -24236251, -5915248, 15766062, 8407814}, + {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, + -8917023, -4388953, -8067909, 2276718}, + }, + { + {30157918, 12924066, -17712050, 9245753, 19895028, 3368142, + -23827587, 5096219, 22740376, -7303417}, + {2041139, -14256350, 7783687, 13876377, -25946985, -13352459, + 24051124, 13742383, -15637599, 13295222}, + {33338237, -8505733, 12532113, 7977527, 9106186, -1715251, + -17720195, -4612972, -4451357, -14669444}, + }, + { + {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, + -2469266, -4141880, 7770569, 9620597}, + {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, + -1694323, -33502340, -14767970}, + {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, + 1220118, 30494170, -11440799}, + }, + { + {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, + -26739026, 926050, -1684339, -13333647}, + {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, + 9021034, 9078865, 3353509, 4033511}, + {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, + 23161163, 8839127, 27485041, 7356032}, + }, + }, + { + { + {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, + 2625015, 28431036, -16771834}, + {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, + -22545972, 14150565, 15970762, 4099461}, + {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, + 13617293, -9937143, 11465739, 8317062}, + }, + { + {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, + 14898637, 3848455, 20969334, -5157516}, + {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, + -21610826, -3649888, 11177095, 14989547}, + {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, + 13515641, 2581286, -28487508, 9930240}, + }, + { + {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, + 18345767, -13403753, 16291481, -5314038}, + {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, + 6957617, 4368891, 9788741}, + {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, + -21722536, -8613148, 16250552, -11111103}, + }, + { + {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, + 10604807, -30190403, 4782747}, + {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, + -9981571, 4383045, 22546403, 437323}, + {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, + 27343084, 2786261, -30633590, -14097016}, + }, + { + {-14467279, -683715, -33374107, 7448552, 19294360, 14334329, + -19690631, 2355319, -19284671, -6114373}, + {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, + 18952177, 15496498, -29380133, 11754228}, + {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, + 7141596, 11724556, 22761615, -10134141}, + }, + { + {16918416, 11729663, -18083579, 3022987, -31015732, -13339659, + -28741185, -12227393, 32851222, 11717399}, + {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, + 31474879, 3483633, -1193175, -4030831}, + {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, + 33142652, 6546660, -19985279, -3948376}, + }, + { + {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, + -8537131, -12833048, -30772034, -15486313}, + {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, + -31135347, -16049879, 10928917, 3011958}, + {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, + -30831056, -12805180, 18008031, 10258577}, + }, + { + {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, + -1853465, 1367120, 25127874, 6671743}, + {29701166, -14373934, -10878120, 9279288, -17568, 13127210, + 21382910, 11042292, 25838796, 4642684}, + {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, + 30468147, -13900640, 18423289, 4177476}, + }, + }, +}; + +static uint8_t negative(signed char b) { + uint32_t x = b; + x >>= 31; /* 1: yes; 0: no */ + return (uint8_t)x; +} + +static void table_select(ge_precomp *t, int pos, signed char b) { + ge_precomp minust; + uint8_t bnegative = negative(b); + uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); + + ge_precomp_0(t); + cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); + cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); + cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); + cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); + cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); + cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); + cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); + cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); + fe_copy(minust.yplusx, t->yminusx); + fe_copy(minust.yminusx, t->yplusx); + fe_neg(minust.xy2d, t->xy2d); + cmov(t, &minust, bnegative); +} + +/* h = a * B + * where a = a[0]+256*a[1]+...+256^31 a[31] + * B is the Ed25519 base point (x,4/5) with x positive. + * + * Preconditions: + * a[31] <= 127 */ +void GFp_x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t *a) { + signed char e[64]; + signed char carry; + ge_p1p1 r; + ge_p2 s; + ge_precomp t; + int i; + + for (i = 0; i < 32; ++i) { + e[2 * i + 0] = (a[i] >> 0) & 15; + e[2 * i + 1] = (a[i] >> 4) & 15; + } + /* each e[i] is between 0 and 15 */ + /* e[63] is between 0 and 7 */ + + carry = 0; + for (i = 0; i < 63; ++i) { + e[i] += carry; + carry = e[i] + 8; + carry >>= 4; + e[i] -= carry << 4; + } + e[63] += carry; + /* each e[i] is between -8 and 8 */ + + ge_p3_0(h); + for (i = 1; i < 64; i += 2) { + table_select(&t, i / 2, e[i]); + ge_madd(&r, h, &t); + x25519_ge_p1p1_to_p3(h, &r); + } + + ge_p3_dbl(&r, h); + x25519_ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); + x25519_ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); + x25519_ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); + x25519_ge_p1p1_to_p3(h, &r); + + for (i = 0; i < 64; i += 2) { + table_select(&t, i / 2, e[i]); + ge_madd(&r, h, &t); + x25519_ge_p1p1_to_p3(h, &r); + } +} + +#endif + +void slide(signed char *r, const uint8_t *a) { + int i; + int b; + int k; + + for (i = 0; i < 256; ++i) { + r[i] = 1 & (a[i >> 3] >> (i & 7)); + } + + for (i = 0; i < 256; ++i) { + if (r[i]) { + for (b = 1; b <= 6 && i + b < 256; ++b) { + if (r[i + b]) { + if (r[i] + (r[i + b] << b) <= 15) { + r[i] += r[i + b] << b; + r[i + b] = 0; + } else if (r[i] - (r[i + b] << b) >= -15) { + r[i] -= r[i + b] << b; + for (k = i + b; k < 256; ++k) { + if (!r[k]) { + r[k] = 1; + break; + } + r[k] = 0; + } + } else { + break; + } + } + } + } + } +} + +static const ge_precomp Bi[8] = { + { + {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, + -11754271, -6079156, 2047605}, + {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, + 5043384, 19500929, -15469378}, + {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, + 11864899, -24514362, -4438546}, + }, + { + {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, + -14772189, 28944400, -1550024}, + {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, + -11775962, 7689662, 11199574}, + {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, + 10017326, -17749093, -9920357}, + }, + { + {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, + 14515107, -15438304, 10819380}, + {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, + 12483688, -12668491, 5581306}, + {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, + 13850243, -23678021, -15815942}, + }, + { + {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, + 5230134, -23952439, -15175766}, + {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, + 16520125, 30598449, 7715701}, + {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, + 1370708, 29794553, -1409300}, + }, + { + {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, + -1361450, -13062696, 13821877}, + {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, + -7212327, 18853322, -14220951}, + {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, + -10431137, 2207753, -3209784}, + }, + { + {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, + -663000, -31111463, -16132436}, + {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, + 15725684, 171356, 6466918}, + {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, + -14088058, -30714912, 16193877}, + }, + { + {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, + 4729455, -18074513, 9256800}, + {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, + 9761698, -19827198, 630305}, + {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, + -15960994, -2449256, -14291300}, + }, + { + {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, + 15033784, 25105118, -7894876}, + {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, + 1573892, -2625887, 2198790, -15804619}, + {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, + -16236442, -32461234, -12290683}, + }, +}; + +/* r = a * A + b * B + * where a = a[0]+256*a[1]+...+256^31 a[31]. + * and b = b[0]+256*b[1]+...+256^31 b[31]. + * B is the Ed25519 base point (x,4/5) with x positive. */ +void GFp_ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, + const ge_p3 *A, const uint8_t *b) { + signed char aslide[256]; + signed char bslide[256]; + ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ + ge_p1p1 t; + ge_p3 u; + ge_p3 A2; + int i; + + slide(aslide, a); + slide(bslide, b); + + x25519_ge_p3_to_cached(&Ai[0], A); + ge_p3_dbl(&t, A); + x25519_ge_p1p1_to_p3(&A2, &t); + x25519_ge_add(&t, &A2, &Ai[0]); + x25519_ge_p1p1_to_p3(&u, &t); + x25519_ge_p3_to_cached(&Ai[1], &u); + x25519_ge_add(&t, &A2, &Ai[1]); + x25519_ge_p1p1_to_p3(&u, &t); + x25519_ge_p3_to_cached(&Ai[2], &u); + x25519_ge_add(&t, &A2, &Ai[2]); + x25519_ge_p1p1_to_p3(&u, &t); + x25519_ge_p3_to_cached(&Ai[3], &u); + x25519_ge_add(&t, &A2, &Ai[3]); + x25519_ge_p1p1_to_p3(&u, &t); + x25519_ge_p3_to_cached(&Ai[4], &u); + x25519_ge_add(&t, &A2, &Ai[4]); + x25519_ge_p1p1_to_p3(&u, &t); + x25519_ge_p3_to_cached(&Ai[5], &u); + x25519_ge_add(&t, &A2, &Ai[5]); + x25519_ge_p1p1_to_p3(&u, &t); + x25519_ge_p3_to_cached(&Ai[6], &u); + x25519_ge_add(&t, &A2, &Ai[6]); + x25519_ge_p1p1_to_p3(&u, &t); + x25519_ge_p3_to_cached(&Ai[7], &u); + + ge_p2_0(r); + + for (i = 255; i >= 0; --i) { + if (aslide[i] || bslide[i]) { + break; + } + } + + for (; i >= 0; --i) { + ge_p2_dbl(&t, r); + + if (aslide[i] > 0) { + x25519_ge_p1p1_to_p3(&u, &t); + x25519_ge_add(&t, &u, &Ai[aslide[i] / 2]); + } else if (aslide[i] < 0) { + x25519_ge_p1p1_to_p3(&u, &t); + x25519_ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); + } + + if (bslide[i] > 0) { + x25519_ge_p1p1_to_p3(&u, &t); + ge_madd(&t, &u, &Bi[bslide[i] / 2]); + } else if (bslide[i] < 0) { + x25519_ge_p1p1_to_p3(&u, &t); + ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); + } + + x25519_ge_p1p1_to_p2(r, &t); + } +} + +/* The set of scalars is \Z/l + * where l = 2^252 + 27742317777372353535851937790883648493. */ + +/* Input: + * s[0]+256*s[1]+...+256^63*s[63] = s + * + * Output: + * s[0]+256*s[1]+...+256^31*s[31] = s mod l + * where l = 2^252 + 27742317777372353535851937790883648493. + * Overwrites s in place. */ +void GFp_x25519_sc_reduce(uint8_t *s) { + int64_t s0 = 2097151 & load_3(s); + int64_t s1 = 2097151 & (load_4(s + 2) >> 5); + int64_t s2 = 2097151 & (load_3(s + 5) >> 2); + int64_t s3 = 2097151 & (load_4(s + 7) >> 7); + int64_t s4 = 2097151 & (load_4(s + 10) >> 4); + int64_t s5 = 2097151 & (load_3(s + 13) >> 1); + int64_t s6 = 2097151 & (load_4(s + 15) >> 6); + int64_t s7 = 2097151 & (load_3(s + 18) >> 3); + int64_t s8 = 2097151 & load_3(s + 21); + int64_t s9 = 2097151 & (load_4(s + 23) >> 5); + int64_t s10 = 2097151 & (load_3(s + 26) >> 2); + int64_t s11 = 2097151 & (load_4(s + 28) >> 7); + int64_t s12 = 2097151 & (load_4(s + 31) >> 4); + int64_t s13 = 2097151 & (load_3(s + 34) >> 1); + int64_t s14 = 2097151 & (load_4(s + 36) >> 6); + int64_t s15 = 2097151 & (load_3(s + 39) >> 3); + int64_t s16 = 2097151 & load_3(s + 42); + int64_t s17 = 2097151 & (load_4(s + 44) >> 5); + int64_t s18 = 2097151 & (load_3(s + 47) >> 2); + int64_t s19 = 2097151 & (load_4(s + 49) >> 7); + int64_t s20 = 2097151 & (load_4(s + 52) >> 4); + int64_t s21 = 2097151 & (load_3(s + 55) >> 1); + int64_t s22 = 2097151 & (load_4(s + 57) >> 6); + int64_t s23 = (load_4(s + 60) >> 3); + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + int64_t carry12; + int64_t carry13; + int64_t carry14; + int64_t carry15; + int64_t carry16; + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + s23 = 0; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + s22 = 0; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + s21 = 0; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + s20 = 0; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + s19 = 0; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + s18 = 0; + + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 << 21; + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 << 21; + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 << 21; + + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 << 21; + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 << 21; + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + s17 = 0; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + s16 = 0; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + s15 = 0; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + s14 = 0; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + s13 = 0; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (1 << 20)) >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry11 = s11 >> 21; + s12 += carry11; + s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 << 21; + + s[0] = (uint8_t)(s0 >> 0); + s[1] = (uint8_t)(s0 >> 8); + s[2] = (uint8_t)((s0 >> 16) | (s1 << 5)); + s[3] = (uint8_t)(s1 >> 3); + s[4] = (uint8_t)(s1 >> 11); + s[5] = (uint8_t)((s1 >> 19) | (s2 << 2)); + s[6] = (uint8_t)(s2 >> 6); + s[7] = (uint8_t)((s2 >> 14) | (s3 << 7)); + s[8] = (uint8_t)(s3 >> 1); + s[9] = (uint8_t)(s3 >> 9); + s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); + s[11] = (uint8_t)(s4 >> 4); + s[12] = (uint8_t)(s4 >> 12); + s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); + s[14] = (uint8_t)(s5 >> 7); + s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); + s[16] = (uint8_t)(s6 >> 2); + s[17] = (uint8_t)(s6 >> 10); + s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); + s[19] = (uint8_t)(s7 >> 5); + s[20] = (uint8_t)(s7 >> 13); + s[21] = (uint8_t)(s8 >> 0); + s[22] = (uint8_t)(s8 >> 8); + s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); + s[24] = (uint8_t)(s9 >> 3); + s[25] = (uint8_t)(s9 >> 11); + s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); + s[27] = (uint8_t)(s10 >> 6); + s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); + s[29] = (uint8_t)(s11 >> 1); + s[30] = (uint8_t)(s11 >> 9); + s[31] = (uint8_t)(s11 >> 17); +} + +/* Input: + * a[0]+256*a[1]+...+256^31*a[31] = a + * b[0]+256*b[1]+...+256^31*b[31] = b + * c[0]+256*c[1]+...+256^31*c[31] = c + * + * Output: + * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l + * where l = 2^252 + 27742317777372353535851937790883648493. */ +void GFp_x25519_sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b, + const uint8_t *c) { + int64_t a0 = 2097151 & load_3(a); + int64_t a1 = 2097151 & (load_4(a + 2) >> 5); + int64_t a2 = 2097151 & (load_3(a + 5) >> 2); + int64_t a3 = 2097151 & (load_4(a + 7) >> 7); + int64_t a4 = 2097151 & (load_4(a + 10) >> 4); + int64_t a5 = 2097151 & (load_3(a + 13) >> 1); + int64_t a6 = 2097151 & (load_4(a + 15) >> 6); + int64_t a7 = 2097151 & (load_3(a + 18) >> 3); + int64_t a8 = 2097151 & load_3(a + 21); + int64_t a9 = 2097151 & (load_4(a + 23) >> 5); + int64_t a10 = 2097151 & (load_3(a + 26) >> 2); + int64_t a11 = (load_4(a + 28) >> 7); + int64_t b0 = 2097151 & load_3(b); + int64_t b1 = 2097151 & (load_4(b + 2) >> 5); + int64_t b2 = 2097151 & (load_3(b + 5) >> 2); + int64_t b3 = 2097151 & (load_4(b + 7) >> 7); + int64_t b4 = 2097151 & (load_4(b + 10) >> 4); + int64_t b5 = 2097151 & (load_3(b + 13) >> 1); + int64_t b6 = 2097151 & (load_4(b + 15) >> 6); + int64_t b7 = 2097151 & (load_3(b + 18) >> 3); + int64_t b8 = 2097151 & load_3(b + 21); + int64_t b9 = 2097151 & (load_4(b + 23) >> 5); + int64_t b10 = 2097151 & (load_3(b + 26) >> 2); + int64_t b11 = (load_4(b + 28) >> 7); + int64_t c0 = 2097151 & load_3(c); + int64_t c1 = 2097151 & (load_4(c + 2) >> 5); + int64_t c2 = 2097151 & (load_3(c + 5) >> 2); + int64_t c3 = 2097151 & (load_4(c + 7) >> 7); + int64_t c4 = 2097151 & (load_4(c + 10) >> 4); + int64_t c5 = 2097151 & (load_3(c + 13) >> 1); + int64_t c6 = 2097151 & (load_4(c + 15) >> 6); + int64_t c7 = 2097151 & (load_3(c + 18) >> 3); + int64_t c8 = 2097151 & load_3(c + 21); + int64_t c9 = 2097151 & (load_4(c + 23) >> 5); + int64_t c10 = 2097151 & (load_3(c + 26) >> 2); + int64_t c11 = (load_4(c + 28) >> 7); + int64_t s0; + int64_t s1; + int64_t s2; + int64_t s3; + int64_t s4; + int64_t s5; + int64_t s6; + int64_t s7; + int64_t s8; + int64_t s9; + int64_t s10; + int64_t s11; + int64_t s12; + int64_t s13; + int64_t s14; + int64_t s15; + int64_t s16; + int64_t s17; + int64_t s18; + int64_t s19; + int64_t s20; + int64_t s21; + int64_t s22; + int64_t s23; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + int64_t carry12; + int64_t carry13; + int64_t carry14; + int64_t carry15; + int64_t carry16; + int64_t carry17; + int64_t carry18; + int64_t carry19; + int64_t carry20; + int64_t carry21; + int64_t carry22; + + s0 = c0 + a0 * b0; + s1 = c1 + a0 * b1 + a1 * b0; + s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; + s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; + s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; + s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; + s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; + s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + + a6 * b1 + a7 * b0; + s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + + a6 * b2 + a7 * b1 + a8 * b0; + s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; + s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; + s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; + s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; + s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + + a9 * b4 + a10 * b3 + a11 * b2; + s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + + a10 * b4 + a11 * b3; + s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + + a11 * b4; + s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; + s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; + s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; + s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; + s20 = a9 * b11 + a10 * b10 + a11 * b9; + s21 = a10 * b11 + a11 * b10; + s22 = a11 * b11; + s23 = 0; + + carry0 = (s0 + (1 << 20)) >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 << 21; + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 << 21; + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 << 21; + carry18 = (s18 + (1 << 20)) >> 21; + s19 += carry18; + s18 -= carry18 << 21; + carry20 = (s20 + (1 << 20)) >> 21; + s21 += carry20; + s20 -= carry20 << 21; + carry22 = (s22 + (1 << 20)) >> 21; + s23 += carry22; + s22 -= carry22 << 21; + + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 << 21; + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 << 21; + carry17 = (s17 + (1 << 20)) >> 21; + s18 += carry17; + s17 -= carry17 << 21; + carry19 = (s19 + (1 << 20)) >> 21; + s20 += carry19; + s19 -= carry19 << 21; + carry21 = (s21 + (1 << 20)) >> 21; + s22 += carry21; + s21 -= carry21 << 21; + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + s23 = 0; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + s22 = 0; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + s21 = 0; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + s20 = 0; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + s19 = 0; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + s18 = 0; + + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 << 21; + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 << 21; + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 << 21; + + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 << 21; + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 << 21; + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + s17 = 0; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + s16 = 0; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + s15 = 0; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + s14 = 0; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + s13 = 0; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (1 << 20)) >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry11 = s11 >> 21; + s12 += carry11; + s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 << 21; + + s[0] = (uint8_t)(s0 >> 0); + s[1] = (uint8_t)(s0 >> 8); + s[2] = (uint8_t)((s0 >> 16) | (s1 << 5)); + s[3] = (uint8_t)(s1 >> 3); + s[4] = (uint8_t)(s1 >> 11); + s[5] = (uint8_t)((s1 >> 19) | (s2 << 2)); + s[6] = (uint8_t)(s2 >> 6); + s[7] = (uint8_t)((s2 >> 14) | (s3 << 7)); + s[8] = (uint8_t)(s3 >> 1); + s[9] = (uint8_t)(s3 >> 9); + s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); + s[11] = (uint8_t)(s4 >> 4); + s[12] = (uint8_t)(s4 >> 12); + s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); + s[14] = (uint8_t)(s5 >> 7); + s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); + s[16] = (uint8_t)(s6 >> 2); + s[17] = (uint8_t)(s6 >> 10); + s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); + s[19] = (uint8_t)(s7 >> 5); + s[20] = (uint8_t)(s7 >> 13); + s[21] = (uint8_t)(s8 >> 0); + s[22] = (uint8_t)(s8 >> 8); + s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); + s[24] = (uint8_t)(s9 >> 3); + s[25] = (uint8_t)(s9 >> 11); + s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); + s[27] = (uint8_t)(s10 >> 6); + s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); + s[29] = (uint8_t)(s11 >> 1); + s[30] = (uint8_t)(s11 >> 9); + s[31] = (uint8_t)(s11 >> 17); +} + +void GFp_curve25519_scalar_mask(uint8_t a[32]) { + a[0] &= 248; + a[31] &= 127; + a[31] |= 64; +} + +#if defined(BORINGSSL_X25519_X86_64) + +void GFp_x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], + const uint8_t point[32]) { + GFp_x25519_x86_64(out, scalar, point); +} + +#else + +/* Replace (f,g) with (g,f) if b == 1; + * replace (f,g) with (f,g) if b == 0. + * + * Preconditions: b in {0,1}. */ +static void fe_cswap(fe f, fe g, unsigned int b) { + b = 0-b; + unsigned i; + for (i = 0; i < 10; i++) { + int32_t x = f[i] ^ g[i]; + x &= b; + f[i] ^= x; + g[i] ^= x; + } +} + +/* h = f * 121666 + * Can overlap h with f. + * + * Preconditions: + * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + * + * Postconditions: + * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ +static void GFp_fe_mul121666(fe h, fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int64_t h0 = f0 * (int64_t) 121666; + int64_t h1 = f1 * (int64_t) 121666; + int64_t h2 = f2 * (int64_t) 121666; + int64_t h3 = f3 * (int64_t) 121666; + int64_t h4 = f4 * (int64_t) 121666; + int64_t h5 = f5 * (int64_t) 121666; + int64_t h6 = f6 * (int64_t) 121666; + int64_t h7 = f7 * (int64_t) 121666; + int64_t h8 = f8 * (int64_t) 121666; + int64_t h9 = f9 * (int64_t) 121666; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + h[0] = (int32_t)h0; + h[1] = (int32_t)h1; + h[2] = (int32_t)h2; + h[3] = (int32_t)h3; + h[4] = (int32_t)h4; + h[5] = (int32_t)h5; + h[6] = (int32_t)h6; + h[7] = (int32_t)h7; + h[8] = (int32_t)h8; + h[9] = (int32_t)h9; +} + +static void x25519_scalar_mult_generic(uint8_t out[32], + const uint8_t scalar[32], + const uint8_t point[32]) { + fe x1, x2, z2, x3, z3, tmp0, tmp1; + + uint8_t e[32]; + memcpy(e, scalar, 32); + GFp_curve25519_scalar_mask(e); + fe_frombytes(x1, point); + fe_1(x2); + fe_0(z2); + fe_copy(x3, x1); + fe_1(z3); + + unsigned swap = 0; + int pos; + for (pos = 254; pos >= 0; --pos) { + unsigned b = 1 & (e[pos / 8] >> (pos & 7)); + swap ^= b; + fe_cswap(x2, x3, swap); + fe_cswap(z2, z3, swap); + swap = b; + fe_sub(tmp0, x3, z3); + fe_sub(tmp1, x2, z2); + fe_add(x2, x2, z2); + fe_add(z2, x3, z3); + GFp_fe_mul(z3, tmp0, x2); + GFp_fe_mul(z2, z2, tmp1); + fe_sq(tmp0, tmp1); + fe_sq(tmp1, x2); + fe_add(x3, z3, z2); + fe_sub(z2, z3, z2); + GFp_fe_mul(x2, tmp1, tmp0); + fe_sub(tmp1, tmp1, tmp0); + fe_sq(z2, z2); + GFp_fe_mul121666(z3, tmp1); + fe_sq(x3, x3); + fe_add(tmp0, tmp0, z3); + GFp_fe_mul(z3, x1, z2); + GFp_fe_mul(z2, tmp1, tmp0); + } + fe_cswap(x2, x3, swap); + fe_cswap(z2, z3, swap); + + GFp_fe_invert(z2, z2); + GFp_fe_mul(x2, x2, z2); + GFp_fe_tobytes(out, x2); +} + +void GFp_x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], + const uint8_t point[32]) { +#if defined(BORINGSSL_X25519_NEON) + if (GFp_is_NEON_capable()) { + GFp_x25519_NEON(out, scalar, point); + return; + } +#endif + + x25519_scalar_mult_generic(out, scalar, point); +} + +#endif /* BORINGSSL_X25519_X86_64 */ + + +/* Prototypes to avoid -Wmissing-prototypes warnings. */ +void GFp_x25519_public_from_private(uint8_t out_public_value[32], + const uint8_t private_key[32]); + +#if defined(BORINGSSL_X25519_X86_64) + +/* When |BORINGSSL_X25519_X86_64| is set, base point multiplication is done with + * the Montgomery ladder because it's faster. Otherwise it's done using the + * Ed25519 tables. */ + +void GFp_x25519_public_from_private(uint8_t out_public_value[32], + const uint8_t private_key[32]) { + static const uint8_t kMongomeryBasePoint[32] = {9}; + GFp_x25519_scalar_mult(out_public_value, private_key, kMongomeryBasePoint); +} + +#else + +void GFp_x25519_public_from_private(uint8_t out_public_value[32], + const uint8_t private_key[32]) { +#if defined(BORINGSSL_X25519_NEON) + if (GFp_is_NEON_capable()) { + static const uint8_t kMongomeryBasePoint[32] = {9}; + GFp_x25519_NEON(out_public_value, private_key, kMongomeryBasePoint); + return; + } +#endif + + uint8_t e[32]; + memcpy(e, private_key, 32); + GFp_curve25519_scalar_mask(e); + + ge_p3 A; + GFp_x25519_ge_scalarmult_base(&A, e); + + /* We only need the u-coordinate of the curve25519 point. The map is + * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */ + fe zplusy, zminusy, zminusy_inv; + fe_add(zplusy, A.Z, A.Y); + fe_sub(zminusy, A.Z, A.Y); + GFp_fe_invert(zminusy_inv, zminusy); + GFp_fe_mul(zplusy, zplusy, zminusy_inv); + GFp_fe_tobytes(out_public_value, zplusy); +} + +#endif /* BORINGSSL_X25519_X86_64 */ diff --git a/test-generator/cbits/internal.h b/test-generator/cbits/internal.h new file mode 100644 index 0000000..b78f649 --- /dev/null +++ b/test-generator/cbits/internal.h @@ -0,0 +1,109 @@ +/* Copyright (c) 2015, Google Inc. + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY + * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION + * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN + * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ + +#ifndef OPENSSL_HEADER_CURVE25519_INTERNAL_H +#define OPENSSL_HEADER_CURVE25519_INTERNAL_H + +#include + +#include + + +#if defined(__cplusplus) +extern "C" { +#endif + + +#if defined(OPENSSL_X86_64) && !defined(OPENSSL_SMALL) && \ + !defined(OPENSSL_WINDOWS) && !defined(OPENSSL_NO_ASM) +/* This isn't compatible with Windows because the asm code makes use of the red + * zone, which Windows doesn't support. */ +#define BORINGSSL_X25519_X86_64 + +void GFp_x25519_x86_64(uint8_t out[32], const uint8_t scalar[32], + const uint8_t point[32]); +#endif + + +#if defined(OPENSSL_ARM) && !defined(OPENSSL_NO_ASM) +#define BORINGSSL_X25519_NEON + +/* x25519_NEON is defined in asm/x25519-arm.S. */ +void GFp_x25519_NEON(uint8_t out[32], const uint8_t scalar[32], + const uint8_t point[32]); +#endif + +/* fe means field element. Here the field is \Z/(2^255-19). An element t, + * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 + * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on + * context. + * + * Keep in sync with `Elem` and `ELEM_LIMBS` in curve25519/ops.rs. */ +typedef int32_t fe[10]; + +/* ge means group element. + + * Here the group is the set of pairs (x,y) of field elements (see fe.h) + * satisfying -x^2 + y^2 = 1 + d x^2y^2 + * where d = -121665/121666. + * + * Representations: + * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z + * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT + * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T + * ge_precomp (Duif): (y+x,y-x,2dxy) + */ + +/* Keep in sync with `Point` in curve25519/ops.rs. */ +typedef struct { + fe X; + fe Y; + fe Z; +} ge_p2; + + +/* Keep in sync with `ExtPoint` in curve25519/ops.rs. */ +typedef struct { + fe X; + fe Y; + fe Z; + fe T; +} ge_p3; + +typedef struct { + fe X; + fe Y; + fe Z; + fe T; +} ge_p1p1; + +typedef struct { + fe yplusx; + fe yminusx; + fe xy2d; +} ge_precomp; + +typedef struct { + fe YplusX; + fe YminusX; + fe Z; + fe T2d; +} ge_cached; + + +#if defined(__cplusplus) +} /* extern C */ +#endif + +#endif /* OPENSSL_HEADER_CURVE25519_INTERNAL_H */ diff --git a/test-generator/cbits/internal2.h b/test-generator/cbits/internal2.h new file mode 100644 index 0000000..75aa5b7 --- /dev/null +++ b/test-generator/cbits/internal2.h @@ -0,0 +1,361 @@ +/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) + * All rights reserved. + * + * This package is an SSL implementation written + * by Eric Young (eay@cryptsoft.com). + * The implementation was written so as to conform with Netscapes SSL. + * + * This library is free for commercial and non-commercial use as long as + * the following conditions are aheared to. The following conditions + * apply to all code found in this distribution, be it the RC4, RSA, + * lhash, DES, etc., code; not just the SSL code. The SSL documentation + * included with this distribution is covered by the same copyright terms + * except that the holder is Tim Hudson (tjh@cryptsoft.com). + * + * Copyright remains Eric Young's, and as such any Copyright notices in + * the code are not to be removed. + * If this package is used in a product, Eric Young should be given attribution + * as the author of the parts of the library used. + * This can be in the form of a textual message at program startup or + * in documentation (online or textual) provided with the package. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * "This product includes cryptographic software written by + * Eric Young (eay@cryptsoft.com)" + * The word 'cryptographic' can be left out if the rouines from the library + * being used are not cryptographic related :-). + * 4. If you include any Windows specific code (or a derivative thereof) from + * the apps directory (application code) you must include an acknowledgement: + * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" + * + * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * The licence and distribution terms for any publically available version or + * derivative of this code cannot be changed. i.e. this code cannot simply be + * copied and put under another distribution licence + * [including the GNU Public Licence.] + */ +/* ==================================================================== + * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * openssl-core@openssl.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.openssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). */ + +#ifndef OPENSSL_HEADER_CRYPTO_INTERNAL_H +#define OPENSSL_HEADER_CRYPTO_INTERNAL_H + +#include + +#if defined(__clang__) || defined(_MSC_VER) +#include +#endif + +#include + +#include +#include + +#if defined(_MSC_VER) +#pragma warning(push, 3) +#include +#pragma warning(pop) +#if !defined(__cplusplus) +#define alignas(x) __declspec(align(x)) +#define alignof __alignof +#endif +#elif !defined(__clang__) && defined(__GNUC__) && __GNUC__ == 4 && \ + __GNUC_MINOR__ <= 6 +#define alignas(x) __attribute__((aligned (x))) +#define alignof __alignof__ +#else +#include +#endif + +#if defined(__cplusplus) +extern "C" { +#endif + + +#if defined(OPENSSL_X86) || defined(OPENSSL_X86_64) || defined(OPENSSL_ARM) || \ + defined(OPENSSL_AARCH64) || defined(OPENSSL_PPC64LE) +/* OPENSSL_cpuid_setup initializes the platform-specific feature cache. */ +void GFp_cpuid_setup(void); +#endif + +#define OPENSSL_LITTLE_ENDIAN 1 +#define OPENSSL_BIG_ENDIAN 2 + +#if defined(OPENSSL_X86_64) || defined(OPENSSL_X86) || \ + (defined(__BYTE_ORDER__) && defined(__ORDER_LITTLE_ENDIAN__) && \ + __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__) +#define OPENSSL_ENDIAN OPENSSL_LITTLE_ENDIAN +#elif defined(__BYTE_ORDER__) && defined(__ORDER_BIG_ENDIAN__) && \ + __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ +#define OPENSSL_ENDIAN OPENSSL_BIG_ENDIAN +#else +#error "Cannot determine endianness" +#endif + + +#if defined(__GNUC__) +#define bswap_u32(x) __builtin_bswap32(x) +#define bswap_u64(x) __builtin_bswap64(x) +#elif defined(_MSC_VER) +#pragma intrinsic(_byteswap_ulong, _byteswap_uint64) +#define bswap_u32(x) _byteswap_ulong(x) +#define bswap_u64(x) _byteswap_uint64(x) +#endif + + +#if !defined(_MSC_VER) && defined(OPENSSL_64_BIT) +typedef __int128_t int128_t; +typedef __uint128_t uint128_t; +#endif + + +/* Constant-time utility functions. + * + * The following methods return a bitmask of all ones (0xff...f) for true and 0 + * for false. This is useful for choosing a value based on the result of a + * conditional in constant time. */ + +/* constant_time_msb returns the given value with the MSB copied to all the + * other bits. */ +static inline unsigned int constant_time_msb_unsigned(unsigned int a) { + return (unsigned int)((int)(a) >> (sizeof(int) * 8 - 1)); +} + +OPENSSL_COMPILE_ASSERT(sizeof(ptrdiff_t) == sizeof(size_t), + ptrdiff_t_and_size_t_are_different_sizes); + +static inline size_t constant_time_msb_size_t(size_t a) { + return (size_t)((ptrdiff_t)(a) >> (sizeof(ptrdiff_t) * 8 - 1)); +} + + +/* constant_time_is_zero returns 0xff..f if a == 0 and 0 otherwise. */ +static inline unsigned int constant_time_is_zero_unsigned(unsigned int a) { + /* Here is an SMT-LIB verification of this formula: + * + * (define-fun is_zero ((a (_ BitVec 32))) (_ BitVec 32) + * (bvand (bvnot a) (bvsub a #x00000001)) + * ) + * + * (declare-fun a () (_ BitVec 32)) + * + * (assert (not (= (= #x00000001 (bvlshr (is_zero a) #x0000001f)) (= a #x00000000)))) + * (check-sat) + * (get-model) + */ + return constant_time_msb_unsigned(~a & (a - 1)); +} + +/* constant_time_is_zero_size_t is like |constant_time_is_zero_unsigned| but + * operates on |size_t|. */ +static inline size_t constant_time_is_zero_size_t(size_t a) { + return constant_time_msb_size_t(~a & (a - 1)); +} + +static inline size_t constant_time_is_nonzero_size_t(size_t a) { + return constant_time_is_zero_size_t(constant_time_is_zero_size_t(a)); +} + +/* constant_time_eq_int returns 0xff..f if a == b and 0 otherwise. */ +static inline unsigned int constant_time_eq_int(int a, int b) { + return constant_time_is_zero_unsigned((unsigned)(a) ^ (unsigned)(b)); +} + +/* constant_time_eq_size_t acts like |constant_time_eq_int| but operates on + * |size_t|. */ +static inline size_t constant_time_eq_size_t(size_t a, size_t b) { + return constant_time_is_zero_size_t(a ^ b); +} + +/* constant_time_select_size_t returns (mask & a) | (~mask & b). When |mask| is + * all 1s or all 0s (as returned by the methods above), the select methods + * return either |a| (if |mask| is nonzero) or |b| (if |mask| is zero). it is + * derived from BoringSSL's |constant_time_select|. */ +static inline size_t constant_time_select_size_t(size_t mask, size_t a, + size_t b) { + return (mask & a) | (~mask & b); +} + +/* from_be_u32_ptr returns the 32-bit big-endian-encoded value at |data|. */ +static inline uint32_t from_be_u32_ptr(const uint8_t *data) { +#if defined(__clang__) || defined(_MSC_VER) + /* XXX: Unlike GCC, Clang doesn't optimize compliant access to unaligned data + * well. See https://llvm.org/bugs/show_bug.cgi?id=20605, + * https://llvm.org/bugs/show_bug.cgi?id=17603, + * http://blog.regehr.org/archives/702, and + * http://blog.regehr.org/archives/1055. MSVC seems to have similar problems. + */ + uint32_t value; + memcpy(&value, data, sizeof(value)); +#if OPENSSL_ENDIAN != OPENSSL_BIG_ENDIAN + value = bswap_u32(value); +#endif + return value; +#else + return ((uint32_t)data[0] << 24) | + ((uint32_t)data[1] << 16) | + ((uint32_t)data[2] << 8) | + ((uint32_t)data[3]); +#endif +} + + +/* from_be_u64_ptr returns the 64-bit big-endian-encoded value at |data|. */ +static inline uint64_t from_be_u64_ptr(const uint8_t *data) { +#if defined(__clang__) || defined(_MSC_VER) + /* XXX: Unlike GCC, Clang doesn't optimize compliant access to unaligned data + * well. See https://llvm.org/bugs/show_bug.cgi?id=20605, + * https://llvm.org/bugs/show_bug.cgi?id=17603, + * http://blog.regehr.org/archives/702, and + * http://blog.regehr.org/archives/1055. MSVC seems to have similar problems. + */ + uint64_t value; + memcpy(&value, data, sizeof(value)); +#if OPENSSL_ENDIAN != OPENSSL_BIG_ENDIAN + value = bswap_u64(value); +#endif + return value; +#else + return ((uint64_t)data[0] << 56) | + ((uint64_t)data[1] << 48) | + ((uint64_t)data[2] << 40) | + ((uint64_t)data[3] << 32) | + ((uint64_t)data[4] << 24) | + ((uint64_t)data[5] << 16) | + ((uint64_t)data[6] << 8) | + ((uint64_t)data[7]); +#endif +} + +/* to_be_u32_ptr writes the value |x| to the location |out| in big-endian + order. */ +static inline void to_be_u32_ptr(uint8_t *out, uint32_t value) { +#if defined(__clang__) || defined(_MSC_VER) + /* XXX: Unlike GCC, Clang doesn't optimize compliant access to unaligned data + * well. See https://llvm.org/bugs/show_bug.cgi?id=20605, + * https://llvm.org/bugs/show_bug.cgi?id=17603, + * http://blog.regehr.org/archives/702, and + * http://blog.regehr.org/archives/1055. MSVC seems to have similar problems. + */ +#if OPENSSL_ENDIAN != OPENSSL_BIG_ENDIAN + value = bswap_u32(value); +#endif + memcpy(out, &value, sizeof(value)); +#else + out[0] = (uint8_t)(value >> 24); + out[1] = (uint8_t)(value >> 16); + out[2] = (uint8_t)(value >> 8); + out[3] = (uint8_t)value; +#endif +} + +/* to_be_u64_ptr writes the value |value| to the location |out| in big-endian + order. */ +static inline void to_be_u64_ptr(uint8_t *out, uint64_t value) { +#if defined(__clang__) || defined(_MSC_VER) + /* XXX: Unlike GCC, Clang doesn't optimize compliant access to unaligned data + * well. See https://llvm.org/bugs/show_bug.cgi?id=20605, + * https://llvm.org/bugs/show_bug.cgi?id=17603, + * http://blog.regehr.org/archives/702, and + * http://blog.regehr.org/archives/1055. MSVC seems to have similar problems. + */ +#if OPENSSL_ENDIAN != OPENSSL_BIG_ENDIAN + value = bswap_u64(value); +#endif + memcpy(out, &value, sizeof(value)); +#else + out[0] = (uint8_t)(value >> 56); + out[1] = (uint8_t)(value >> 48); + out[2] = (uint8_t)(value >> 40); + out[3] = (uint8_t)(value >> 32); + out[4] = (uint8_t)(value >> 24); + out[5] = (uint8_t)(value >> 16); + out[6] = (uint8_t)(value >> 8); + out[7] = (uint8_t)value; +#endif +} + +/* from_be_u64 returns the native representation of the 64-bit + * big-endian-encoded value |x|. */ +static inline uint64_t from_be_u64(uint64_t x) { +#if OPENSSL_ENDIAN != OPENSSL_BIG_ENDIAN + x = bswap_u64(x); +#endif + return x; +} + + +#if defined(__cplusplus) +} /* extern C */ +#endif + +#endif /* OPENSSL_HEADER_CRYPTO_INTERNAL_H */ diff --git a/test-generator/cbits/x25519-asm-x86_64.S b/test-generator/cbits/x25519-asm-x86_64.S new file mode 100644 index 0000000..f43be46 --- /dev/null +++ b/test-generator/cbits/x25519-asm-x86_64.S @@ -0,0 +1,1921 @@ +/* Copyright (c) 2015, Google Inc. + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY + * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION + * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN + * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ + +/* This file is adapted from crypto_scalarmult/curve25519/amd64-51/ in + * SUPERCOP 20141124 (http://bench.cr.yp.to/supercop.html). That code is public + * domain licensed but the standard ISC license is included above to keep + * licensing simple. */ + +#if !defined(OPENSSL_NO_ASM) +#if defined(__x86_64__) + +.data +.p2align 4 + +#if defined(__APPLE__) +/* OS X's C ABI prefixes functions with underscore. */ +#define C_ABI(x) _ ## x +#define HIDDEN .private_extern +#elif defined(__MINGW32__) || defined(__MINGW64__) +#define C_ABI(x) x +#define HIDDEN .globl +#else +#define C_ABI(x) x +#define HIDDEN .hidden +#endif + +x25519_x86_64_REDMASK51: .quad 0x0007FFFFFFFFFFFF +x25519_x86_64_121666_213: .quad 996687872 +x25519_x86_64_2P0: .quad 0xFFFFFFFFFFFDA +x25519_x86_64_2P1234: .quad 0xFFFFFFFFFFFFE +x25519_x86_64_4P0: .quad 0x1FFFFFFFFFFFB4 +x25519_x86_64_4P1234: .quad 0x1FFFFFFFFFFFFC +x25519_x86_64_MU0: .quad 0xED9CE5A30A2C131B +x25519_x86_64_MU1: .quad 0x2106215D086329A7 +x25519_x86_64_MU2: .quad 0xFFFFFFFFFFFFFFEB +x25519_x86_64_MU3: .quad 0xFFFFFFFFFFFFFFFF +x25519_x86_64_MU4: .quad 0x000000000000000F +x25519_x86_64_ORDER0: .quad 0x5812631A5CF5D3ED +x25519_x86_64_ORDER1: .quad 0x14DEF9DEA2F79CD6 +x25519_x86_64_ORDER2: .quad 0x0000000000000000 +x25519_x86_64_ORDER3: .quad 0x1000000000000000 +x25519_x86_64_EC2D0: .quad 1859910466990425 +x25519_x86_64_EC2D1: .quad 932731440258426 +x25519_x86_64_EC2D2: .quad 1072319116312658 +x25519_x86_64_EC2D3: .quad 1815898335770999 +x25519_x86_64_EC2D4: .quad 633789495995903 +x25519_x86_64__38: .quad 38 + +.text +.p2align 5 + +.globl C_ABI(GFp_x25519_x86_64_freeze) +HIDDEN C_ABI(GFp_x25519_x86_64_freeze) +C_ABI(GFp_x25519_x86_64_freeze): +.cfi_startproc +/* This is a leaf function and uses the redzone for saving registers. */ +movq %r12,-8(%rsp) +.cfi_rel_offset r12, -8 +movq 0(%rdi),%rsi +movq 8(%rdi),%rdx +movq 16(%rdi),%rcx +movq 24(%rdi),%r8 +movq 32(%rdi),%r9 +movq x25519_x86_64_REDMASK51(%rip),%rax +mov %rax,%r10 +sub $18,%r10 +mov $3,%r11 +._reduceloop: +mov %rsi,%r12 +shr $51,%r12 +and %rax,%rsi +add %r12,%rdx +mov %rdx,%r12 +shr $51,%r12 +and %rax,%rdx +add %r12,%rcx +mov %rcx,%r12 +shr $51,%r12 +and %rax,%rcx +add %r12,%r8 +mov %r8,%r12 +shr $51,%r12 +and %rax,%r8 +add %r12,%r9 +mov %r9,%r12 +shr $51,%r12 +and %rax,%r9 +imulq $19,%r12,%r12 +add %r12,%rsi +sub $1,%r11 +ja ._reduceloop +mov $1,%r12 +cmp %r10,%rsi +cmovl %r11,%r12 +cmp %rax,%rdx +cmovne %r11,%r12 +cmp %rax,%rcx +cmovne %r11,%r12 +cmp %rax,%r8 +cmovne %r11,%r12 +cmp %rax,%r9 +cmovne %r11,%r12 +neg %r12 +and %r12,%rax +and %r12,%r10 +sub %r10,%rsi +sub %rax,%rdx +sub %rax,%rcx +sub %rax,%r8 +sub %rax,%r9 +movq %rsi,0(%rdi) +movq %rdx,8(%rdi) +movq %rcx,16(%rdi) +movq %r8,24(%rdi) +movq %r9,32(%rdi) +movq -8(%rsp),%r12 +ret +.cfi_endproc + +.p2align 5 +.globl C_ABI(GFp_x25519_x86_64_mul) +HIDDEN C_ABI(GFp_x25519_x86_64_mul) +C_ABI(GFp_x25519_x86_64_mul): +.cfi_startproc +/* This is a leaf function and uses the redzone for saving registers. */ +movq %r12,-8(%rsp) +.cfi_rel_offset r12, -8 +movq %r13,-16(%rsp) +.cfi_rel_offset r13, -16 +movq %r14,-24(%rsp) +.cfi_rel_offset r14, -24 +movq %r15,-32(%rsp) +.cfi_rel_offset r15, -32 +movq %rbx,-40(%rsp) +.cfi_rel_offset rbx, -40 +movq %rbp,-48(%rsp) +.cfi_rel_offset rbp, -48 +mov %rdx,%rcx +movq 24(%rsi),%rdx +imulq $19,%rdx,%rax +movq %rax,-64(%rsp) +mulq 16(%rcx) +mov %rax,%r8 +mov %rdx,%r9 +movq 32(%rsi),%rdx +imulq $19,%rdx,%rax +movq %rax,-72(%rsp) +mulq 8(%rcx) +add %rax,%r8 +adc %rdx,%r9 +movq 0(%rsi),%rax +mulq 0(%rcx) +add %rax,%r8 +adc %rdx,%r9 +movq 0(%rsi),%rax +mulq 8(%rcx) +mov %rax,%r10 +mov %rdx,%r11 +movq 0(%rsi),%rax +mulq 16(%rcx) +mov %rax,%r12 +mov %rdx,%r13 +movq 0(%rsi),%rax +mulq 24(%rcx) +mov %rax,%r14 +mov %rdx,%r15 +movq 0(%rsi),%rax +mulq 32(%rcx) +mov %rax,%rbx +mov %rdx,%rbp +movq 8(%rsi),%rax +mulq 0(%rcx) +add %rax,%r10 +adc %rdx,%r11 +movq 8(%rsi),%rax +mulq 8(%rcx) +add %rax,%r12 +adc %rdx,%r13 +movq 8(%rsi),%rax +mulq 16(%rcx) +add %rax,%r14 +adc %rdx,%r15 +movq 8(%rsi),%rax +mulq 24(%rcx) +add %rax,%rbx +adc %rdx,%rbp +movq 8(%rsi),%rdx +imulq $19,%rdx,%rax +mulq 32(%rcx) +add %rax,%r8 +adc %rdx,%r9 +movq 16(%rsi),%rax +mulq 0(%rcx) +add %rax,%r12 +adc %rdx,%r13 +movq 16(%rsi),%rax +mulq 8(%rcx) +add %rax,%r14 +adc %rdx,%r15 +movq 16(%rsi),%rax +mulq 16(%rcx) +add %rax,%rbx +adc %rdx,%rbp +movq 16(%rsi),%rdx +imulq $19,%rdx,%rax +mulq 24(%rcx) +add %rax,%r8 +adc %rdx,%r9 +movq 16(%rsi),%rdx +imulq $19,%rdx,%rax +mulq 32(%rcx) +add %rax,%r10 +adc %rdx,%r11 +movq 24(%rsi),%rax +mulq 0(%rcx) +add %rax,%r14 +adc %rdx,%r15 +movq 24(%rsi),%rax +mulq 8(%rcx) +add %rax,%rbx +adc %rdx,%rbp +movq -64(%rsp),%rax +mulq 24(%rcx) +add %rax,%r10 +adc %rdx,%r11 +movq -64(%rsp),%rax +mulq 32(%rcx) +add %rax,%r12 +adc %rdx,%r13 +movq 32(%rsi),%rax +mulq 0(%rcx) +add %rax,%rbx +adc %rdx,%rbp +movq -72(%rsp),%rax +mulq 16(%rcx) +add %rax,%r10 +adc %rdx,%r11 +movq -72(%rsp),%rax +mulq 24(%rcx) +add %rax,%r12 +adc %rdx,%r13 +movq -72(%rsp),%rax +mulq 32(%rcx) +add %rax,%r14 +adc %rdx,%r15 +movq x25519_x86_64_REDMASK51(%rip),%rsi +shld $13,%r8,%r9 +and %rsi,%r8 +shld $13,%r10,%r11 +and %rsi,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rsi,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rsi,%r14 +add %r13,%r14 +shld $13,%rbx,%rbp +and %rsi,%rbx +add %r15,%rbx +imulq $19,%rbp,%rdx +add %rdx,%r8 +mov %r8,%rdx +shr $51,%rdx +add %r10,%rdx +mov %rdx,%rcx +shr $51,%rdx +and %rsi,%r8 +add %r12,%rdx +mov %rdx,%r9 +shr $51,%rdx +and %rsi,%rcx +add %r14,%rdx +mov %rdx,%rax +shr $51,%rdx +and %rsi,%r9 +add %rbx,%rdx +mov %rdx,%r10 +shr $51,%rdx +and %rsi,%rax +imulq $19,%rdx,%rdx +add %rdx,%r8 +and %rsi,%r10 +movq %r8,0(%rdi) +movq %rcx,8(%rdi) +movq %r9,16(%rdi) +movq %rax,24(%rdi) +movq %r10,32(%rdi) +movq -8(%rsp),%r12 +movq -16(%rsp),%r13 +movq -24(%rsp),%r14 +movq -32(%rsp),%r15 +movq -40(%rsp),%rbx +movq -48(%rsp),%rbp +ret +.cfi_endproc + +.p2align 5 +.globl C_ABI(GFp_x25519_x86_64_square) +HIDDEN C_ABI(GFp_x25519_x86_64_square) +C_ABI(GFp_x25519_x86_64_square): +.cfi_startproc +/* This is a leaf function and uses the redzone for saving registers. */ +movq %r12,-8(%rsp) +.cfi_rel_offset r12, -8 +movq %r13,-16(%rsp) +.cfi_rel_offset r13, -16 +movq %r14,-24(%rsp) +.cfi_rel_offset r14, -24 +movq %r15,-32(%rsp) +.cfi_rel_offset r15, -32 +movq %rbx,-40(%rsp) +.cfi_rel_offset rbx, -40 +movq 0(%rsi),%rax +mulq 0(%rsi) +mov %rax,%rcx +mov %rdx,%r8 +movq 0(%rsi),%rax +shl $1,%rax +mulq 8(%rsi) +mov %rax,%r9 +mov %rdx,%r10 +movq 0(%rsi),%rax +shl $1,%rax +mulq 16(%rsi) +mov %rax,%r11 +mov %rdx,%r12 +movq 0(%rsi),%rax +shl $1,%rax +mulq 24(%rsi) +mov %rax,%r13 +mov %rdx,%r14 +movq 0(%rsi),%rax +shl $1,%rax +mulq 32(%rsi) +mov %rax,%r15 +mov %rdx,%rbx +movq 8(%rsi),%rax +mulq 8(%rsi) +add %rax,%r11 +adc %rdx,%r12 +movq 8(%rsi),%rax +shl $1,%rax +mulq 16(%rsi) +add %rax,%r13 +adc %rdx,%r14 +movq 8(%rsi),%rax +shl $1,%rax +mulq 24(%rsi) +add %rax,%r15 +adc %rdx,%rbx +movq 8(%rsi),%rdx +imulq $38,%rdx,%rax +mulq 32(%rsi) +add %rax,%rcx +adc %rdx,%r8 +movq 16(%rsi),%rax +mulq 16(%rsi) +add %rax,%r15 +adc %rdx,%rbx +movq 16(%rsi),%rdx +imulq $38,%rdx,%rax +mulq 24(%rsi) +add %rax,%rcx +adc %rdx,%r8 +movq 16(%rsi),%rdx +imulq $38,%rdx,%rax +mulq 32(%rsi) +add %rax,%r9 +adc %rdx,%r10 +movq 24(%rsi),%rdx +imulq $19,%rdx,%rax +mulq 24(%rsi) +add %rax,%r9 +adc %rdx,%r10 +movq 24(%rsi),%rdx +imulq $38,%rdx,%rax +mulq 32(%rsi) +add %rax,%r11 +adc %rdx,%r12 +movq 32(%rsi),%rdx +imulq $19,%rdx,%rax +mulq 32(%rsi) +add %rax,%r13 +adc %rdx,%r14 +movq x25519_x86_64_REDMASK51(%rip),%rsi +shld $13,%rcx,%r8 +and %rsi,%rcx +shld $13,%r9,%r10 +and %rsi,%r9 +add %r8,%r9 +shld $13,%r11,%r12 +and %rsi,%r11 +add %r10,%r11 +shld $13,%r13,%r14 +and %rsi,%r13 +add %r12,%r13 +shld $13,%r15,%rbx +and %rsi,%r15 +add %r14,%r15 +imulq $19,%rbx,%rdx +add %rdx,%rcx +mov %rcx,%rdx +shr $51,%rdx +add %r9,%rdx +and %rsi,%rcx +mov %rdx,%r8 +shr $51,%rdx +add %r11,%rdx +and %rsi,%r8 +mov %rdx,%r9 +shr $51,%rdx +add %r13,%rdx +and %rsi,%r9 +mov %rdx,%rax +shr $51,%rdx +add %r15,%rdx +and %rsi,%rax +mov %rdx,%r10 +shr $51,%rdx +imulq $19,%rdx,%rdx +add %rdx,%rcx +and %rsi,%r10 +movq %rcx,0(%rdi) +movq %r8,8(%rdi) +movq %r9,16(%rdi) +movq %rax,24(%rdi) +movq %r10,32(%rdi) +movq -8(%rsp),%r12 +movq -16(%rsp),%r13 +movq -24(%rsp),%r14 +movq -32(%rsp),%r15 +movq -40(%rsp),%rbx +ret +.cfi_endproc + +.p2align 5 +.globl C_ABI(GFp_x25519_x86_64_ladderstep) +HIDDEN C_ABI(GFp_x25519_x86_64_ladderstep) +C_ABI(GFp_x25519_x86_64_ladderstep): +.cfi_startproc +sub $344,%rsp +.cfi_adjust_cfa_offset 344 +movq %r12,296(%rsp) +.cfi_rel_offset r12, 296 +movq %r13,304(%rsp) +.cfi_rel_offset r13, 304 +movq %r14,312(%rsp) +.cfi_rel_offset r14, 312 +movq %r15,320(%rsp) +.cfi_rel_offset r15, 320 +movq %rbx,328(%rsp) +.cfi_rel_offset rbx, 328 +movq %rbp,336(%rsp) +.cfi_rel_offset rbp, 336 +movq 40(%rdi),%rsi +movq 48(%rdi),%rdx +movq 56(%rdi),%rcx +movq 64(%rdi),%r8 +movq 72(%rdi),%r9 +mov %rsi,%rax +mov %rdx,%r10 +mov %rcx,%r11 +mov %r8,%r12 +mov %r9,%r13 +add x25519_x86_64_2P0(%rip),%rax +add x25519_x86_64_2P1234(%rip),%r10 +add x25519_x86_64_2P1234(%rip),%r11 +add x25519_x86_64_2P1234(%rip),%r12 +add x25519_x86_64_2P1234(%rip),%r13 +addq 80(%rdi),%rsi +addq 88(%rdi),%rdx +addq 96(%rdi),%rcx +addq 104(%rdi),%r8 +addq 112(%rdi),%r9 +subq 80(%rdi),%rax +subq 88(%rdi),%r10 +subq 96(%rdi),%r11 +subq 104(%rdi),%r12 +subq 112(%rdi),%r13 +movq %rsi,0(%rsp) +movq %rdx,8(%rsp) +movq %rcx,16(%rsp) +movq %r8,24(%rsp) +movq %r9,32(%rsp) +movq %rax,40(%rsp) +movq %r10,48(%rsp) +movq %r11,56(%rsp) +movq %r12,64(%rsp) +movq %r13,72(%rsp) +movq 40(%rsp),%rax +mulq 40(%rsp) +mov %rax,%rsi +mov %rdx,%rcx +movq 40(%rsp),%rax +shl $1,%rax +mulq 48(%rsp) +mov %rax,%r8 +mov %rdx,%r9 +movq 40(%rsp),%rax +shl $1,%rax +mulq 56(%rsp) +mov %rax,%r10 +mov %rdx,%r11 +movq 40(%rsp),%rax +shl $1,%rax +mulq 64(%rsp) +mov %rax,%r12 +mov %rdx,%r13 +movq 40(%rsp),%rax +shl $1,%rax +mulq 72(%rsp) +mov %rax,%r14 +mov %rdx,%r15 +movq 48(%rsp),%rax +mulq 48(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 48(%rsp),%rax +shl $1,%rax +mulq 56(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 48(%rsp),%rax +shl $1,%rax +mulq 64(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 48(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 72(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 56(%rsp),%rax +mulq 56(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 56(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 64(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 56(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 72(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 64(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 64(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 64(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 72(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 72(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 72(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +and %rdx,%rsi +mov %rcx,%r8 +shr $51,%rcx +add %r10,%rcx +and %rdx,%r8 +mov %rcx,%r9 +shr $51,%rcx +add %r12,%rcx +and %rdx,%r9 +mov %rcx,%rax +shr $51,%rcx +add %r14,%rcx +and %rdx,%rax +mov %rcx,%r10 +shr $51,%rcx +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,80(%rsp) +movq %r8,88(%rsp) +movq %r9,96(%rsp) +movq %rax,104(%rsp) +movq %r10,112(%rsp) +movq 0(%rsp),%rax +mulq 0(%rsp) +mov %rax,%rsi +mov %rdx,%rcx +movq 0(%rsp),%rax +shl $1,%rax +mulq 8(%rsp) +mov %rax,%r8 +mov %rdx,%r9 +movq 0(%rsp),%rax +shl $1,%rax +mulq 16(%rsp) +mov %rax,%r10 +mov %rdx,%r11 +movq 0(%rsp),%rax +shl $1,%rax +mulq 24(%rsp) +mov %rax,%r12 +mov %rdx,%r13 +movq 0(%rsp),%rax +shl $1,%rax +mulq 32(%rsp) +mov %rax,%r14 +mov %rdx,%r15 +movq 8(%rsp),%rax +mulq 8(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 8(%rsp),%rax +shl $1,%rax +mulq 16(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 8(%rsp),%rax +shl $1,%rax +mulq 24(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 8(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 32(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 16(%rsp),%rax +mulq 16(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 16(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 24(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 16(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 32(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 24(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 24(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 24(%rsp),%rdx +imulq $38,%rdx,%rax +mulq 32(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 32(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 32(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +and %rdx,%rsi +mov %rcx,%r8 +shr $51,%rcx +add %r10,%rcx +and %rdx,%r8 +mov %rcx,%r9 +shr $51,%rcx +add %r12,%rcx +and %rdx,%r9 +mov %rcx,%rax +shr $51,%rcx +add %r14,%rcx +and %rdx,%rax +mov %rcx,%r10 +shr $51,%rcx +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,120(%rsp) +movq %r8,128(%rsp) +movq %r9,136(%rsp) +movq %rax,144(%rsp) +movq %r10,152(%rsp) +mov %rsi,%rsi +mov %r8,%rdx +mov %r9,%rcx +mov %rax,%r8 +mov %r10,%r9 +add x25519_x86_64_2P0(%rip),%rsi +add x25519_x86_64_2P1234(%rip),%rdx +add x25519_x86_64_2P1234(%rip),%rcx +add x25519_x86_64_2P1234(%rip),%r8 +add x25519_x86_64_2P1234(%rip),%r9 +subq 80(%rsp),%rsi +subq 88(%rsp),%rdx +subq 96(%rsp),%rcx +subq 104(%rsp),%r8 +subq 112(%rsp),%r9 +movq %rsi,160(%rsp) +movq %rdx,168(%rsp) +movq %rcx,176(%rsp) +movq %r8,184(%rsp) +movq %r9,192(%rsp) +movq 120(%rdi),%rsi +movq 128(%rdi),%rdx +movq 136(%rdi),%rcx +movq 144(%rdi),%r8 +movq 152(%rdi),%r9 +mov %rsi,%rax +mov %rdx,%r10 +mov %rcx,%r11 +mov %r8,%r12 +mov %r9,%r13 +add x25519_x86_64_2P0(%rip),%rax +add x25519_x86_64_2P1234(%rip),%r10 +add x25519_x86_64_2P1234(%rip),%r11 +add x25519_x86_64_2P1234(%rip),%r12 +add x25519_x86_64_2P1234(%rip),%r13 +addq 160(%rdi),%rsi +addq 168(%rdi),%rdx +addq 176(%rdi),%rcx +addq 184(%rdi),%r8 +addq 192(%rdi),%r9 +subq 160(%rdi),%rax +subq 168(%rdi),%r10 +subq 176(%rdi),%r11 +subq 184(%rdi),%r12 +subq 192(%rdi),%r13 +movq %rsi,200(%rsp) +movq %rdx,208(%rsp) +movq %rcx,216(%rsp) +movq %r8,224(%rsp) +movq %r9,232(%rsp) +movq %rax,240(%rsp) +movq %r10,248(%rsp) +movq %r11,256(%rsp) +movq %r12,264(%rsp) +movq %r13,272(%rsp) +movq 224(%rsp),%rsi +imulq $19,%rsi,%rax +movq %rax,280(%rsp) +mulq 56(%rsp) +mov %rax,%rsi +mov %rdx,%rcx +movq 232(%rsp),%rdx +imulq $19,%rdx,%rax +movq %rax,288(%rsp) +mulq 48(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 200(%rsp),%rax +mulq 40(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 200(%rsp),%rax +mulq 48(%rsp) +mov %rax,%r8 +mov %rdx,%r9 +movq 200(%rsp),%rax +mulq 56(%rsp) +mov %rax,%r10 +mov %rdx,%r11 +movq 200(%rsp),%rax +mulq 64(%rsp) +mov %rax,%r12 +mov %rdx,%r13 +movq 200(%rsp),%rax +mulq 72(%rsp) +mov %rax,%r14 +mov %rdx,%r15 +movq 208(%rsp),%rax +mulq 40(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 208(%rsp),%rax +mulq 48(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 208(%rsp),%rax +mulq 56(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 208(%rsp),%rax +mulq 64(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 208(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 72(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 216(%rsp),%rax +mulq 40(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 216(%rsp),%rax +mulq 48(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 216(%rsp),%rax +mulq 56(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 216(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 64(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 216(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 72(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 224(%rsp),%rax +mulq 40(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 224(%rsp),%rax +mulq 48(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 280(%rsp),%rax +mulq 64(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 280(%rsp),%rax +mulq 72(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 232(%rsp),%rax +mulq 40(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 288(%rsp),%rax +mulq 56(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 288(%rsp),%rax +mulq 64(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 288(%rsp),%rax +mulq 72(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +mov %rcx,%r8 +shr $51,%rcx +and %rdx,%rsi +add %r10,%rcx +mov %rcx,%r9 +shr $51,%rcx +and %rdx,%r8 +add %r12,%rcx +mov %rcx,%rax +shr $51,%rcx +and %rdx,%r9 +add %r14,%rcx +mov %rcx,%r10 +shr $51,%rcx +and %rdx,%rax +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,40(%rsp) +movq %r8,48(%rsp) +movq %r9,56(%rsp) +movq %rax,64(%rsp) +movq %r10,72(%rsp) +movq 264(%rsp),%rsi +imulq $19,%rsi,%rax +movq %rax,200(%rsp) +mulq 16(%rsp) +mov %rax,%rsi +mov %rdx,%rcx +movq 272(%rsp),%rdx +imulq $19,%rdx,%rax +movq %rax,208(%rsp) +mulq 8(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 240(%rsp),%rax +mulq 0(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 240(%rsp),%rax +mulq 8(%rsp) +mov %rax,%r8 +mov %rdx,%r9 +movq 240(%rsp),%rax +mulq 16(%rsp) +mov %rax,%r10 +mov %rdx,%r11 +movq 240(%rsp),%rax +mulq 24(%rsp) +mov %rax,%r12 +mov %rdx,%r13 +movq 240(%rsp),%rax +mulq 32(%rsp) +mov %rax,%r14 +mov %rdx,%r15 +movq 248(%rsp),%rax +mulq 0(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 248(%rsp),%rax +mulq 8(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 248(%rsp),%rax +mulq 16(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 248(%rsp),%rax +mulq 24(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 248(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 32(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 256(%rsp),%rax +mulq 0(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 256(%rsp),%rax +mulq 8(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 256(%rsp),%rax +mulq 16(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 256(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 24(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 256(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 32(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 264(%rsp),%rax +mulq 0(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 264(%rsp),%rax +mulq 8(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 200(%rsp),%rax +mulq 24(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 200(%rsp),%rax +mulq 32(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 272(%rsp),%rax +mulq 0(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 208(%rsp),%rax +mulq 16(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 208(%rsp),%rax +mulq 24(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 208(%rsp),%rax +mulq 32(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +mov %rcx,%r8 +shr $51,%rcx +and %rdx,%rsi +add %r10,%rcx +mov %rcx,%r9 +shr $51,%rcx +and %rdx,%r8 +add %r12,%rcx +mov %rcx,%rax +shr $51,%rcx +and %rdx,%r9 +add %r14,%rcx +mov %rcx,%r10 +shr $51,%rcx +and %rdx,%rax +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +mov %rsi,%rdx +mov %r8,%rcx +mov %r9,%r11 +mov %rax,%r12 +mov %r10,%r13 +add x25519_x86_64_2P0(%rip),%rdx +add x25519_x86_64_2P1234(%rip),%rcx +add x25519_x86_64_2P1234(%rip),%r11 +add x25519_x86_64_2P1234(%rip),%r12 +add x25519_x86_64_2P1234(%rip),%r13 +addq 40(%rsp),%rsi +addq 48(%rsp),%r8 +addq 56(%rsp),%r9 +addq 64(%rsp),%rax +addq 72(%rsp),%r10 +subq 40(%rsp),%rdx +subq 48(%rsp),%rcx +subq 56(%rsp),%r11 +subq 64(%rsp),%r12 +subq 72(%rsp),%r13 +movq %rsi,120(%rdi) +movq %r8,128(%rdi) +movq %r9,136(%rdi) +movq %rax,144(%rdi) +movq %r10,152(%rdi) +movq %rdx,160(%rdi) +movq %rcx,168(%rdi) +movq %r11,176(%rdi) +movq %r12,184(%rdi) +movq %r13,192(%rdi) +movq 120(%rdi),%rax +mulq 120(%rdi) +mov %rax,%rsi +mov %rdx,%rcx +movq 120(%rdi),%rax +shl $1,%rax +mulq 128(%rdi) +mov %rax,%r8 +mov %rdx,%r9 +movq 120(%rdi),%rax +shl $1,%rax +mulq 136(%rdi) +mov %rax,%r10 +mov %rdx,%r11 +movq 120(%rdi),%rax +shl $1,%rax +mulq 144(%rdi) +mov %rax,%r12 +mov %rdx,%r13 +movq 120(%rdi),%rax +shl $1,%rax +mulq 152(%rdi) +mov %rax,%r14 +mov %rdx,%r15 +movq 128(%rdi),%rax +mulq 128(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 128(%rdi),%rax +shl $1,%rax +mulq 136(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq 128(%rdi),%rax +shl $1,%rax +mulq 144(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 128(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 152(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 136(%rdi),%rax +mulq 136(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 136(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 144(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 136(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 152(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 144(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 144(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 144(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 152(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 152(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 152(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +and %rdx,%rsi +mov %rcx,%r8 +shr $51,%rcx +add %r10,%rcx +and %rdx,%r8 +mov %rcx,%r9 +shr $51,%rcx +add %r12,%rcx +and %rdx,%r9 +mov %rcx,%rax +shr $51,%rcx +add %r14,%rcx +and %rdx,%rax +mov %rcx,%r10 +shr $51,%rcx +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,120(%rdi) +movq %r8,128(%rdi) +movq %r9,136(%rdi) +movq %rax,144(%rdi) +movq %r10,152(%rdi) +movq 160(%rdi),%rax +mulq 160(%rdi) +mov %rax,%rsi +mov %rdx,%rcx +movq 160(%rdi),%rax +shl $1,%rax +mulq 168(%rdi) +mov %rax,%r8 +mov %rdx,%r9 +movq 160(%rdi),%rax +shl $1,%rax +mulq 176(%rdi) +mov %rax,%r10 +mov %rdx,%r11 +movq 160(%rdi),%rax +shl $1,%rax +mulq 184(%rdi) +mov %rax,%r12 +mov %rdx,%r13 +movq 160(%rdi),%rax +shl $1,%rax +mulq 192(%rdi) +mov %rax,%r14 +mov %rdx,%r15 +movq 168(%rdi),%rax +mulq 168(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 168(%rdi),%rax +shl $1,%rax +mulq 176(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq 168(%rdi),%rax +shl $1,%rax +mulq 184(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 168(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 192(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 176(%rdi),%rax +mulq 176(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 176(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 184(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 176(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 192(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 184(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 184(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 184(%rdi),%rdx +imulq $38,%rdx,%rax +mulq 192(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 192(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 192(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +and %rdx,%rsi +mov %rcx,%r8 +shr $51,%rcx +add %r10,%rcx +and %rdx,%r8 +mov %rcx,%r9 +shr $51,%rcx +add %r12,%rcx +and %rdx,%r9 +mov %rcx,%rax +shr $51,%rcx +add %r14,%rcx +and %rdx,%rax +mov %rcx,%r10 +shr $51,%rcx +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,160(%rdi) +movq %r8,168(%rdi) +movq %r9,176(%rdi) +movq %rax,184(%rdi) +movq %r10,192(%rdi) +movq 184(%rdi),%rsi +imulq $19,%rsi,%rax +movq %rax,0(%rsp) +mulq 16(%rdi) +mov %rax,%rsi +mov %rdx,%rcx +movq 192(%rdi),%rdx +imulq $19,%rdx,%rax +movq %rax,8(%rsp) +mulq 8(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 160(%rdi),%rax +mulq 0(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 160(%rdi),%rax +mulq 8(%rdi) +mov %rax,%r8 +mov %rdx,%r9 +movq 160(%rdi),%rax +mulq 16(%rdi) +mov %rax,%r10 +mov %rdx,%r11 +movq 160(%rdi),%rax +mulq 24(%rdi) +mov %rax,%r12 +mov %rdx,%r13 +movq 160(%rdi),%rax +mulq 32(%rdi) +mov %rax,%r14 +mov %rdx,%r15 +movq 168(%rdi),%rax +mulq 0(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 168(%rdi),%rax +mulq 8(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 168(%rdi),%rax +mulq 16(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq 168(%rdi),%rax +mulq 24(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 168(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 32(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 176(%rdi),%rax +mulq 0(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 176(%rdi),%rax +mulq 8(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq 176(%rdi),%rax +mulq 16(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 176(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 24(%rdi) +add %rax,%rsi +adc %rdx,%rcx +movq 176(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 32(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 184(%rdi),%rax +mulq 0(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq 184(%rdi),%rax +mulq 8(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 0(%rsp),%rax +mulq 24(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 0(%rsp),%rax +mulq 32(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 192(%rdi),%rax +mulq 0(%rdi) +add %rax,%r14 +adc %rdx,%r15 +movq 8(%rsp),%rax +mulq 16(%rdi) +add %rax,%r8 +adc %rdx,%r9 +movq 8(%rsp),%rax +mulq 24(%rdi) +add %rax,%r10 +adc %rdx,%r11 +movq 8(%rsp),%rax +mulq 32(%rdi) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +mov %rcx,%r8 +shr $51,%rcx +and %rdx,%rsi +add %r10,%rcx +mov %rcx,%r9 +shr $51,%rcx +and %rdx,%r8 +add %r12,%rcx +mov %rcx,%rax +shr $51,%rcx +and %rdx,%r9 +add %r14,%rcx +mov %rcx,%r10 +shr $51,%rcx +and %rdx,%rax +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,160(%rdi) +movq %r8,168(%rdi) +movq %r9,176(%rdi) +movq %rax,184(%rdi) +movq %r10,192(%rdi) +movq 144(%rsp),%rsi +imulq $19,%rsi,%rax +movq %rax,0(%rsp) +mulq 96(%rsp) +mov %rax,%rsi +mov %rdx,%rcx +movq 152(%rsp),%rdx +imulq $19,%rdx,%rax +movq %rax,8(%rsp) +mulq 88(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 120(%rsp),%rax +mulq 80(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 120(%rsp),%rax +mulq 88(%rsp) +mov %rax,%r8 +mov %rdx,%r9 +movq 120(%rsp),%rax +mulq 96(%rsp) +mov %rax,%r10 +mov %rdx,%r11 +movq 120(%rsp),%rax +mulq 104(%rsp) +mov %rax,%r12 +mov %rdx,%r13 +movq 120(%rsp),%rax +mulq 112(%rsp) +mov %rax,%r14 +mov %rdx,%r15 +movq 128(%rsp),%rax +mulq 80(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 128(%rsp),%rax +mulq 88(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 128(%rsp),%rax +mulq 96(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 128(%rsp),%rax +mulq 104(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 128(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 112(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 136(%rsp),%rax +mulq 80(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 136(%rsp),%rax +mulq 88(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 136(%rsp),%rax +mulq 96(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 136(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 104(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 136(%rsp),%rdx +imulq $19,%rdx,%rax +mulq 112(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 144(%rsp),%rax +mulq 80(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 144(%rsp),%rax +mulq 88(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 0(%rsp),%rax +mulq 104(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 0(%rsp),%rax +mulq 112(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 152(%rsp),%rax +mulq 80(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 8(%rsp),%rax +mulq 96(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 8(%rsp),%rax +mulq 104(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 8(%rsp),%rax +mulq 112(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +mov %rcx,%r8 +shr $51,%rcx +and %rdx,%rsi +add %r10,%rcx +mov %rcx,%r9 +shr $51,%rcx +and %rdx,%r8 +add %r12,%rcx +mov %rcx,%rax +shr $51,%rcx +and %rdx,%r9 +add %r14,%rcx +mov %rcx,%r10 +shr $51,%rcx +and %rdx,%rax +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,40(%rdi) +movq %r8,48(%rdi) +movq %r9,56(%rdi) +movq %rax,64(%rdi) +movq %r10,72(%rdi) +movq 160(%rsp),%rax +mulq x25519_x86_64_121666_213(%rip) +shr $13,%rax +mov %rax,%rsi +mov %rdx,%rcx +movq 168(%rsp),%rax +mulq x25519_x86_64_121666_213(%rip) +shr $13,%rax +add %rax,%rcx +mov %rdx,%r8 +movq 176(%rsp),%rax +mulq x25519_x86_64_121666_213(%rip) +shr $13,%rax +add %rax,%r8 +mov %rdx,%r9 +movq 184(%rsp),%rax +mulq x25519_x86_64_121666_213(%rip) +shr $13,%rax +add %rax,%r9 +mov %rdx,%r10 +movq 192(%rsp),%rax +mulq x25519_x86_64_121666_213(%rip) +shr $13,%rax +add %rax,%r10 +imulq $19,%rdx,%rdx +add %rdx,%rsi +addq 80(%rsp),%rsi +addq 88(%rsp),%rcx +addq 96(%rsp),%r8 +addq 104(%rsp),%r9 +addq 112(%rsp),%r10 +movq %rsi,80(%rdi) +movq %rcx,88(%rdi) +movq %r8,96(%rdi) +movq %r9,104(%rdi) +movq %r10,112(%rdi) +movq 104(%rdi),%rsi +imulq $19,%rsi,%rax +movq %rax,0(%rsp) +mulq 176(%rsp) +mov %rax,%rsi +mov %rdx,%rcx +movq 112(%rdi),%rdx +imulq $19,%rdx,%rax +movq %rax,8(%rsp) +mulq 168(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 80(%rdi),%rax +mulq 160(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 80(%rdi),%rax +mulq 168(%rsp) +mov %rax,%r8 +mov %rdx,%r9 +movq 80(%rdi),%rax +mulq 176(%rsp) +mov %rax,%r10 +mov %rdx,%r11 +movq 80(%rdi),%rax +mulq 184(%rsp) +mov %rax,%r12 +mov %rdx,%r13 +movq 80(%rdi),%rax +mulq 192(%rsp) +mov %rax,%r14 +mov %rdx,%r15 +movq 88(%rdi),%rax +mulq 160(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 88(%rdi),%rax +mulq 168(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 88(%rdi),%rax +mulq 176(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 88(%rdi),%rax +mulq 184(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 88(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 192(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 96(%rdi),%rax +mulq 160(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 96(%rdi),%rax +mulq 168(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 96(%rdi),%rax +mulq 176(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 96(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 184(%rsp) +add %rax,%rsi +adc %rdx,%rcx +movq 96(%rdi),%rdx +imulq $19,%rdx,%rax +mulq 192(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 104(%rdi),%rax +mulq 160(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq 104(%rdi),%rax +mulq 168(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 0(%rsp),%rax +mulq 184(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 0(%rsp),%rax +mulq 192(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 112(%rdi),%rax +mulq 160(%rsp) +add %rax,%r14 +adc %rdx,%r15 +movq 8(%rsp),%rax +mulq 176(%rsp) +add %rax,%r8 +adc %rdx,%r9 +movq 8(%rsp),%rax +mulq 184(%rsp) +add %rax,%r10 +adc %rdx,%r11 +movq 8(%rsp),%rax +mulq 192(%rsp) +add %rax,%r12 +adc %rdx,%r13 +movq x25519_x86_64_REDMASK51(%rip),%rdx +shld $13,%rsi,%rcx +and %rdx,%rsi +shld $13,%r8,%r9 +and %rdx,%r8 +add %rcx,%r8 +shld $13,%r10,%r11 +and %rdx,%r10 +add %r9,%r10 +shld $13,%r12,%r13 +and %rdx,%r12 +add %r11,%r12 +shld $13,%r14,%r15 +and %rdx,%r14 +add %r13,%r14 +imulq $19,%r15,%rcx +add %rcx,%rsi +mov %rsi,%rcx +shr $51,%rcx +add %r8,%rcx +mov %rcx,%r8 +shr $51,%rcx +and %rdx,%rsi +add %r10,%rcx +mov %rcx,%r9 +shr $51,%rcx +and %rdx,%r8 +add %r12,%rcx +mov %rcx,%rax +shr $51,%rcx +and %rdx,%r9 +add %r14,%rcx +mov %rcx,%r10 +shr $51,%rcx +and %rdx,%rax +imulq $19,%rcx,%rcx +add %rcx,%rsi +and %rdx,%r10 +movq %rsi,80(%rdi) +movq %r8,88(%rdi) +movq %r9,96(%rdi) +movq %rax,104(%rdi) +movq %r10,112(%rdi) +movq 296(%rsp),%r12 +movq 304(%rsp),%r13 +movq 312(%rsp),%r14 +movq 320(%rsp),%r15 +movq 328(%rsp),%rbx +movq 336(%rsp),%rbp +add $344,%rsp +.cfi_adjust_cfa_offset -344 +ret +.cfi_endproc + +.p2align 5 +.globl C_ABI(GFp_x25519_x86_64_work_cswap) +HIDDEN C_ABI(GFp_x25519_x86_64_work_cswap) +C_ABI(GFp_x25519_x86_64_work_cswap): +.cfi_startproc +cmp $1,%rsi +movq 0(%rdi),%rsi +movq 80(%rdi),%rdx +movq 8(%rdi),%rcx +movq 88(%rdi),%r8 +mov %rsi,%r9 +cmove %rdx,%rsi +cmove %r9,%rdx +mov %rcx,%r9 +cmove %r8,%rcx +cmove %r9,%r8 +movq %rsi,0(%rdi) +movq %rdx,80(%rdi) +movq %rcx,8(%rdi) +movq %r8,88(%rdi) +movq 16(%rdi),%rsi +movq 96(%rdi),%rdx +movq 24(%rdi),%rcx +movq 104(%rdi),%r8 +mov %rsi,%r9 +cmove %rdx,%rsi +cmove %r9,%rdx +mov %rcx,%r9 +cmove %r8,%rcx +cmove %r9,%r8 +movq %rsi,16(%rdi) +movq %rdx,96(%rdi) +movq %rcx,24(%rdi) +movq %r8,104(%rdi) +movq 32(%rdi),%rsi +movq 112(%rdi),%rdx +movq 40(%rdi),%rcx +movq 120(%rdi),%r8 +mov %rsi,%r9 +cmove %rdx,%rsi +cmove %r9,%rdx +mov %rcx,%r9 +cmove %r8,%rcx +cmove %r9,%r8 +movq %rsi,32(%rdi) +movq %rdx,112(%rdi) +movq %rcx,40(%rdi) +movq %r8,120(%rdi) +movq 48(%rdi),%rsi +movq 128(%rdi),%rdx +movq 56(%rdi),%rcx +movq 136(%rdi),%r8 +mov %rsi,%r9 +cmove %rdx,%rsi +cmove %r9,%rdx +mov %rcx,%r9 +cmove %r8,%rcx +cmove %r9,%r8 +movq %rsi,48(%rdi) +movq %rdx,128(%rdi) +movq %rcx,56(%rdi) +movq %r8,136(%rdi) +movq 64(%rdi),%rsi +movq 144(%rdi),%rdx +movq 72(%rdi),%rcx +movq 152(%rdi),%r8 +mov %rsi,%r9 +cmove %rdx,%rsi +cmove %r9,%rdx +mov %rcx,%r9 +cmove %r8,%rcx +cmove %r9,%r8 +movq %rsi,64(%rdi) +movq %rdx,144(%rdi) +movq %rcx,72(%rdi) +movq %r8,152(%rdi) +mov %rdi,%rax +mov %rsi,%rdx +ret +.cfi_endproc + +#endif /* __x86_64__ */ +#endif /* !OPENSSL_NO_ASM */ diff --git a/test-generator/cbits/x25519-x86_64.c b/test-generator/cbits/x25519-x86_64.c new file mode 100644 index 0000000..c2836b9 --- /dev/null +++ b/test-generator/cbits/x25519-x86_64.c @@ -0,0 +1,244 @@ +/* Copyright (c) 2015, Google Inc. + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY + * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION + * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN + * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ + +/* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP + * 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as + * public domain but this file has the ISC license just to keep licencing + * simple. + * + * The field functions are shared by Ed25519 and X25519 where possible. */ + +#include + +#include "internal.h" + + +#if defined(BORINGSSL_X25519_X86_64) + +typedef struct { uint64_t v[5]; } fe25519; + +/* These functions are defined in asm/x25519-x86_64.S */ +void GFp_x25519_x86_64_work_cswap(fe25519 *, uint64_t); +void GFp_x25519_x86_64_mul(fe25519 *out, const fe25519 *a, const fe25519 *b); +void GFp_x25519_x86_64_square(fe25519 *out, const fe25519 *a); +void GFp_x25519_x86_64_freeze(fe25519 *); +void GFp_x25519_x86_64_ladderstep(fe25519 *work); + +static void fe25519_setint(fe25519 *r, unsigned v) { + r->v[0] = v; + r->v[1] = 0; + r->v[2] = 0; + r->v[3] = 0; + r->v[4] = 0; +} + +/* Assumes input x being reduced below 2^255 */ +static void fe25519_pack(unsigned char r[32], const fe25519 *x) { + fe25519 t; + t = *x; + GFp_x25519_x86_64_freeze(&t); + + r[0] = (uint8_t)(t.v[0] & 0xff); + r[1] = (uint8_t)((t.v[0] >> 8) & 0xff); + r[2] = (uint8_t)((t.v[0] >> 16) & 0xff); + r[3] = (uint8_t)((t.v[0] >> 24) & 0xff); + r[4] = (uint8_t)((t.v[0] >> 32) & 0xff); + r[5] = (uint8_t)((t.v[0] >> 40) & 0xff); + r[6] = (uint8_t)((t.v[0] >> 48)); + + r[6] ^= (uint8_t)((t.v[1] << 3) & 0xf8); + r[7] = (uint8_t)((t.v[1] >> 5) & 0xff); + r[8] = (uint8_t)((t.v[1] >> 13) & 0xff); + r[9] = (uint8_t)((t.v[1] >> 21) & 0xff); + r[10] = (uint8_t)((t.v[1] >> 29) & 0xff); + r[11] = (uint8_t)((t.v[1] >> 37) & 0xff); + r[12] = (uint8_t)((t.v[1] >> 45)); + + r[12] ^= (uint8_t)((t.v[2] << 6) & 0xc0); + r[13] = (uint8_t)((t.v[2] >> 2) & 0xff); + r[14] = (uint8_t)((t.v[2] >> 10) & 0xff); + r[15] = (uint8_t)((t.v[2] >> 18) & 0xff); + r[16] = (uint8_t)((t.v[2] >> 26) & 0xff); + r[17] = (uint8_t)((t.v[2] >> 34) & 0xff); + r[18] = (uint8_t)((t.v[2] >> 42) & 0xff); + r[19] = (uint8_t)((t.v[2] >> 50)); + + r[19] ^= (uint8_t)((t.v[3] << 1) & 0xfe); + r[20] = (uint8_t)((t.v[3] >> 7) & 0xff); + r[21] = (uint8_t)((t.v[3] >> 15) & 0xff); + r[22] = (uint8_t)((t.v[3] >> 23) & 0xff); + r[23] = (uint8_t)((t.v[3] >> 31) & 0xff); + r[24] = (uint8_t)((t.v[3] >> 39) & 0xff); + r[25] = (uint8_t)((t.v[3] >> 47)); + + r[25] ^= (uint8_t)((t.v[4] << 4) & 0xf0); + r[26] = (uint8_t)((t.v[4] >> 4) & 0xff); + r[27] = (uint8_t)((t.v[4] >> 12) & 0xff); + r[28] = (uint8_t)((t.v[4] >> 20) & 0xff); + r[29] = (uint8_t)((t.v[4] >> 28) & 0xff); + r[30] = (uint8_t)((t.v[4] >> 36) & 0xff); + r[31] = (uint8_t)((t.v[4] >> 44)); +} + +static void fe25519_unpack(fe25519 *r, const uint8_t x[32]) { + r->v[0] = x[0]; + r->v[0] += (uint64_t)x[1] << 8; + r->v[0] += (uint64_t)x[2] << 16; + r->v[0] += (uint64_t)x[3] << 24; + r->v[0] += (uint64_t)x[4] << 32; + r->v[0] += (uint64_t)x[5] << 40; + r->v[0] += ((uint64_t)x[6] & 7) << 48; + + r->v[1] = x[6] >> 3; + r->v[1] += (uint64_t)x[7] << 5; + r->v[1] += (uint64_t)x[8] << 13; + r->v[1] += (uint64_t)x[9] << 21; + r->v[1] += (uint64_t)x[10] << 29; + r->v[1] += (uint64_t)x[11] << 37; + r->v[1] += ((uint64_t)x[12] & 63) << 45; + + r->v[2] = x[12] >> 6; + r->v[2] += (uint64_t)x[13] << 2; + r->v[2] += (uint64_t)x[14] << 10; + r->v[2] += (uint64_t)x[15] << 18; + r->v[2] += (uint64_t)x[16] << 26; + r->v[2] += (uint64_t)x[17] << 34; + r->v[2] += (uint64_t)x[18] << 42; + r->v[2] += ((uint64_t)x[19] & 1) << 50; + + r->v[3] = x[19] >> 1; + r->v[3] += (uint64_t)x[20] << 7; + r->v[3] += (uint64_t)x[21] << 15; + r->v[3] += (uint64_t)x[22] << 23; + r->v[3] += (uint64_t)x[23] << 31; + r->v[3] += (uint64_t)x[24] << 39; + r->v[3] += ((uint64_t)x[25] & 15) << 47; + + r->v[4] = x[25] >> 4; + r->v[4] += (uint64_t)x[26] << 4; + r->v[4] += (uint64_t)x[27] << 12; + r->v[4] += (uint64_t)x[28] << 20; + r->v[4] += (uint64_t)x[29] << 28; + r->v[4] += (uint64_t)x[30] << 36; + r->v[4] += ((uint64_t)x[31] & 127) << 44; +} + +static void fe25519_invert(fe25519 *r, const fe25519 *x) { + fe25519 z2; + fe25519 z9; + fe25519 z11; + fe25519 z2_5_0; + fe25519 z2_10_0; + fe25519 z2_20_0; + fe25519 z2_50_0; + fe25519 z2_100_0; + fe25519 t; + int i; + + /* 2 */ GFp_x25519_x86_64_square(&z2, x); + /* 4 */ GFp_x25519_x86_64_square(&t, &z2); + /* 8 */ GFp_x25519_x86_64_square(&t, &t); + /* 9 */ GFp_x25519_x86_64_mul(&z9, &t, x); + /* 11 */ GFp_x25519_x86_64_mul(&z11, &z9, &z2); + /* 22 */ GFp_x25519_x86_64_square(&t, &z11); + /* 2^5 - 2^0 = 31 */ GFp_x25519_x86_64_mul(&z2_5_0, &t, &z9); + + /* 2^6 - 2^1 */ GFp_x25519_x86_64_square(&t, &z2_5_0); + /* 2^20 - 2^10 */ for (i = 1; i < 5; i++) { GFp_x25519_x86_64_square(&t, &t); } + /* 2^10 - 2^0 */ GFp_x25519_x86_64_mul(&z2_10_0, &t, &z2_5_0); + + /* 2^11 - 2^1 */ GFp_x25519_x86_64_square(&t, &z2_10_0); + /* 2^20 - 2^10 */ for (i = 1; i < 10; i++) { GFp_x25519_x86_64_square(&t, &t); } + /* 2^20 - 2^0 */ GFp_x25519_x86_64_mul(&z2_20_0, &t, &z2_10_0); + + /* 2^21 - 2^1 */ GFp_x25519_x86_64_square(&t, &z2_20_0); + /* 2^40 - 2^20 */ for (i = 1; i < 20; i++) { GFp_x25519_x86_64_square(&t, &t); } + /* 2^40 - 2^0 */ GFp_x25519_x86_64_mul(&t, &t, &z2_20_0); + + /* 2^41 - 2^1 */ GFp_x25519_x86_64_square(&t, &t); + /* 2^50 - 2^10 */ for (i = 1; i < 10; i++) { GFp_x25519_x86_64_square(&t, &t); } + /* 2^50 - 2^0 */ GFp_x25519_x86_64_mul(&z2_50_0, &t, &z2_10_0); + + /* 2^51 - 2^1 */ GFp_x25519_x86_64_square(&t, &z2_50_0); + /* 2^100 - 2^50 */ for (i = 1; i < 50; i++) { GFp_x25519_x86_64_square(&t, &t); } + /* 2^100 - 2^0 */ GFp_x25519_x86_64_mul(&z2_100_0, &t, &z2_50_0); + + /* 2^101 - 2^1 */ GFp_x25519_x86_64_square(&t, &z2_100_0); + /* 2^200 - 2^100 */ for (i = 1; i < 100; i++) { + GFp_x25519_x86_64_square(&t, &t); + } + /* 2^200 - 2^0 */ GFp_x25519_x86_64_mul(&t, &t, &z2_100_0); + + /* 2^201 - 2^1 */ GFp_x25519_x86_64_square(&t, &t); + /* 2^250 - 2^50 */ for (i = 1; i < 50; i++) { GFp_x25519_x86_64_square(&t, &t); } + /* 2^250 - 2^0 */ GFp_x25519_x86_64_mul(&t, &t, &z2_50_0); + + /* 2^251 - 2^1 */ GFp_x25519_x86_64_square(&t, &t); + /* 2^252 - 2^2 */ GFp_x25519_x86_64_square(&t, &t); + /* 2^253 - 2^3 */ GFp_x25519_x86_64_square(&t, &t); + + /* 2^254 - 2^4 */ GFp_x25519_x86_64_square(&t, &t); + + /* 2^255 - 2^5 */ GFp_x25519_x86_64_square(&t, &t); + /* 2^255 - 21 */ GFp_x25519_x86_64_mul(r, &t, &z11); +} + +static void mladder(fe25519 *xr, fe25519 *zr, const uint8_t s[32]) { + fe25519 work[5]; + + work[0] = *xr; + fe25519_setint(work + 1, 1); + fe25519_setint(work + 2, 0); + work[3] = *xr; + fe25519_setint(work + 4, 1); + + int i, j; + uint8_t prevbit = 0; + + j = 6; + for (i = 31; i >= 0; i--) { + while (j >= 0) { + const uint8_t bit = 1 & (s[i] >> j); + const uint64_t swap = bit ^ prevbit; + prevbit = bit; + GFp_x25519_x86_64_work_cswap(work + 1, swap); + GFp_x25519_x86_64_ladderstep(work); + j -= 1; + } + j = 7; + } + + *xr = work[1]; + *zr = work[2]; +} + +void GFp_x25519_x86_64(uint8_t out[32], const uint8_t scalar[32], + const uint8_t point[32]) { + uint8_t e[32]; + memcpy(e, scalar, sizeof(e)); + + e[0] &= 248; + e[31] &= 127; + e[31] |= 64; + + fe25519 t; + fe25519 z; + fe25519_unpack(&t, point); + mladder(&t, &z, e); + fe25519_invert(&z, &z); + GFp_x25519_x86_64_mul(&t, &t, &z); + fe25519_pack(out, &t); +} + +#endif /* BORINGSSL_X25519_X86_64 */ diff --git a/test-generator/test-generator.cabal b/test-generator/test-generator.cabal index a0092f4..1c7a87a 100644 --- a/test-generator/test-generator.cabal +++ b/test-generator/test-generator.cabal @@ -20,9 +20,13 @@ extra-source-files: CHANGELOG.md executable gen-tests main-is: Main.hs - other-modules: Database, DSA, ECDSATesting, Math, RFC6979, RSA, Task, Utils + other-modules: Database, DSA, ECDSATesting, ED25519, ED25519.PrecompPoints, Math, RFC6979, RSA, Task, Utils -- other-extensions: build-depends: base >=4.11 && < 4.14, ascii-progress, bytestring, containers, crypto-api, cryptonite, directory, DSA, filepath, integer-gmp, memory, random hs-source-dirs: . + c-sources: cbits/curve25519.c cbits/x25519-x86_64.c cbits/x25519-asm-x86_64.S + include-dirs: cbits default-language: Haskell2010 ghc-options: -Wall -O2 -threaded -rtsopts -with-rtsopts=-N + if os(Windows) || !arch(x86_64) + buildable: False \ No newline at end of file diff --git a/testdata/ed25519/addsub.test b/testdata/ed25519/addsub.test new file mode 100644 index 0000000..2069288 --- /dev/null +++ b/testdata/ed25519/addsub.test @@ -0,0 +1,4004 @@ +a: 035c7d011d91dbff5272a4010deef4ff40d42ffe1bb5b70022b8b2fe315cf300c9bc76ffe2b0e2ff +b: 7b17030067ce1aff5a9abe01a2f609ff59d35f00b30279ff037c5d01c367fcff49b01eff80432aff +c: 7e738001845ff6feac0c6303afe4fefe99a78ffeceb7300025341000f4c3ef00126d95fe62f40cff +d: 88447a01b6c2c000f8d7e5ff6bf7ea00e700d0fd68b23e011f3c55fd6ef4f600800c5800626db800 +a: 737653fe1f738affda4af6ff0575440060547200af60e7000bcd970137d5fe003548fbfedd707aff +b: 0b43ecff868dc1001addf3feb3f835fff8e68b00ea9e5eff023492015beb8dffbe4e690026dfffff +c: 7eb93ffea5004c00f427eafeb86d7aff583bfe0099ff45000d012a0392c08c00f39664ff03507aff +d: 683367fe99e5c8fec06d0201527c0e01686de6ffc5c1880109990500dce9700177f991feb7917aff +a: 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