diff --git a/src/cryptonum/gold_tests.rs b/src/cryptonum/gold_tests.rs index 4cb8d81..03ab206 100644 --- a/src/cryptonum/gold_tests.rs +++ b/src/cryptonum/gold_tests.rs @@ -3,7 +3,7 @@ use std::fs::File; use std::io::Read; use std::str::Lines; -use cryptonum::unsigned::UCN; +use cryptonum::unsigned::{UCN,BarrettUCN}; use cryptonum::signed::SCN; fn next_value_set(line: &str) -> (String, SCN) @@ -184,6 +184,23 @@ fn modular_exponentiation_test() }); } +#[test] +fn fast_modular_exponentiation_test() +{ + run_test("tests/math/fastmodexp.tests", 6, |scase| { + let case = make_unsigned(scase); + let a = case.get("a").unwrap(); + let b = case.get("b").unwrap(); + let kbig = case.get("k").unwrap(); + let k = usize::from(kbig); + let m = case.get("m").unwrap(); + let u = case.get("u").unwrap(); + let z = case.get("z").unwrap(); + let mu = BarrettUCN{ k: k, u: u.clone(), m: m.clone() }; + assert_eq!(a.fastmodexp(&b, &mu), *z); + }); +} + #[test] fn barrett_reduction_test() { diff --git a/src/cryptonum/unsigned.rs b/src/cryptonum/unsigned.rs index a02e548..c68b738 100644 --- a/src/cryptonum/unsigned.rs +++ b/src/cryptonum/unsigned.rs @@ -237,6 +237,25 @@ impl UCN { eprime >>= 1; } } + + pub fn fastmodexp(&self, e: &UCN, mu: &BarrettUCN) -> UCN { + let mut b = self.reduce(&mu); + let mut eprime = e.clone(); + let mut result = UCN::from(1 as u8); + + loop { + if eprime.is_zero() { + return result; + } + + if eprime.is_odd() { + result = (result * &b).reduce(&mu); + } + + b = (&b * &b).reduce(&mu); + eprime >>= 1; + } + } } fn miller_rabin(g: &mut G, n: &UCN, iters: usize) -> bool { @@ -1256,5 +1275,21 @@ mod test { let barrett = b.barrett_u(); (&a % &b) == a.reduce(&barrett) } + fn fastmodexp(ina: UCN, b: UCN, c: UCN) -> bool { + let mut a = ina.clone(); + + if c.contents.len() == 0 { + return true; + } + + if a.contents.len() > c.contents.len() { + a.contents.resize(c.contents.len(), 0); + } + + let cu = c.barrett_u(); + let slow = a.modexp(&b, &c); + let fast = a.fastmodexp(&b, &cu); + slow == fast + } } } diff --git a/tests/math/GenerateMathTests.hs b/tests/math/GenerateMathTests.hs index 61d5f58..83fff46 100644 --- a/tests/math/GenerateMathTests.hs +++ b/tests/math/GenerateMathTests.hs @@ -151,7 +151,19 @@ main = in if me /= standard then error "Barrett broken" else (Just res, (), g'') - + _ <- runGenerator g9 "fastmodexp" () $ \ g () -> + let (a, g') = randomVal (>= 0) g + (b, g'') = randomVal (>= 0) g' + (m, g''') = randomVal (>= 0) g' + z = powModInteger a b m + barrett = barrett_u m + ak = computeK a + in if ak > bk barrett + then (Nothing, (), g''') + else let res = [("a", a), ("b", b), ("z", z), + ("m", m), ("u", bu barrett), + ("k", fromIntegral (bk barrett))] + in (Just res, (), g''') return () -- Implement Barrett reduction using incredibly simplistic implementations, to @@ -198,47 +210,3 @@ minimize :: Integer -> Integer -> Integer minimize r m | r < 0 = error "BLECH" | r >= m = minimize (r - m) m | otherwise = r - --- runOperation :: Handle -> IO () --- runOperation hndl = --- do m <- randomVal =<< randomRIO (1,size) --- v <- randomVal =<< randomRIO (1,size) --- let barrett = barrett_u m --- let vk = computeK v --- if vk > (2 * (bk barrett)) --- then runOperation hndl --- else do hPutStrLn hndl ("m: " ++ showHex m "") --- hPutStrLn hndl ("k: " ++ show (bk barrett)) --- hPutStrLn hndl ("u: " ++ show (bu barrett)) --- let me = reduce v barrett --- standard = v `mod` m --- unless (me == standard) $ --- fail "Barrett messed up." --- hPutStrLn hndl ("v: " ++ showHex v "") --- hPutStrLn hndl ("r: " ++ showHex me "") --- hFlush hndl --- --- generateFile :: String -> --- IO () --- generateFile file = --- withFile (file ++ "_tests.txt") WriteMode $ \ hndl -> --- forM_ [0..2000] $ \ _ -> --- runOperation hndl --- --- main :: IO () --- main = --- do generateFile "add" $ \ x y -> --- (x, y, x + y) --- generateFile "sub" $ \ x y -> --- let x' = max x y --- y' = min x y --- in (x', y', x' - y') --- generateFile "mul" $ \ x y -> --- (x, y, x * y) --- generateFile "div" $ \ x y -> --- let y' = if y == 0 then 1 else y --- in (x, y', x / y') --- generateFile "mod" $ \ x y -> --- let y' = if y == 0 then 1 else y --- in (x, y', x / y') --- generateFile "barrett" diff --git a/tests/math/fastmodexp.tests b/tests/math/fastmodexp.tests new file mode 100644 index 0000000..9052119 --- /dev/null +++ b/tests/math/fastmodexp.tests @@ -0,0 +1,30000 @@ +a: f3fab85a0b6ab5e2d678f5bcc83d298b4ca82023f60f97f0ac5f92b68175a13 +b: 72c103c498b7ba77f7e7af5eb7bddaf649866c18354118115e7d412b3aaaa387 +k: 4 +m: 72c103c498b7ba77f7e7af5eb7bddaf649866c18354118115e7d412b3aaaa387 +u: 23b19a00e7d814dbb8ec05f3d193639385128224679d3fa37bb08a34b9b2e85b9 +z: 16bfd70d891e120d8892089d28307ccea671fddbb214ecbc244a1fc5f6bc059f +a: 241608e577447f1421f770bd0cbbb175a71b13a8ad348393222f94ee69fb1a39 +b: 7fcc8a7fd54933f32a1120ee42c3a369855dfa9700c865713ec3ef7ab9d82ab02aefda7a34d42570dd03660e65ded827 +k: 6 +m: 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