diff --git a/src/cryptonum/mod.rs b/src/cryptonum/mod.rs index 8ffbc04..06b4bc9 100644 --- a/src/cryptonum/mod.rs +++ b/src/cryptonum/mod.rs @@ -2,6 +2,7 @@ mod conversions; #[macro_use] mod complete_arith; +mod primes; mod signed; mod unsigned; #[cfg(test)] @@ -9,5 +10,4 @@ mod gold_tests; pub use self::signed::SCN; pub use self::unsigned::UCN; - - +pub use self::primes::*; diff --git a/src/cryptonum/primes.rs b/src/cryptonum/primes.rs new file mode 100644 index 0000000..826fbc8 --- /dev/null +++ b/src/cryptonum/primes.rs @@ -0,0 +1,136 @@ +use cryptonum::unsigned::UCN; +use rand::Rng; + +static SMALL_PRIMES: [u32; 310] = [ + 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, + 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, + 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, + 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, + 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, + 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, + 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, + 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, + 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, + 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, + 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, + 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, + 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, + 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, + 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, + 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, + 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, + 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, + 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, + 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, + 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, + 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, + 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, + 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, + 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, + 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, + 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, + 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, + 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, + 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, + 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053]; + + +impl UCN { + pub fn generate_prime(rng: &mut G, + bitlen: usize, + iterations: usize, + check_value: F) + -> UCN + where + G: Rng, + F: Fn(UCN) -> Option + { + let one = UCN::from(1 as u8); + + assert!((bitlen % 64) == 0); + loop { + let base = random_number(rng, bitlen); + let candidate = base | &one; + + if let Some(proposed) = check_value(candidate) { + if proposed.probably_prime(rng, iterations) { + return proposed; + } + } + } + } + + pub fn probably_prime(&self, g: &mut G, iters: usize) -> bool { + for tester in SMALL_PRIMES.iter() { + if (self % UCN::from(*tester)).is_zero() { + return false; + } + } + miller_rabin(g, &self, iters) + } +} + +fn miller_rabin(g: &mut G, n: &UCN, iters: usize) -> bool { + let one = UCN::from(1 as u8); + let two = UCN::from(2 as u8); + let nm1 = n - &one; + // Quoth Wikipedia: + // write n - 1 as 2^r*d with d odd by factoring powers of 2 from n - 1 + let mut d = nm1.clone(); + let mut r = 0; + while d.is_even() { + d >>= 1; + r += 1; + assert!(r < n.bits()); + } + // WitnessLoop: repeat k times + 'WitnessLoop: for _k in 0..iters { + // pick a random integer a in the range [2, n - 2] + let a = random_in_range(g, &two, &nm1); + // x <- a^d mod n + let mut x = a.modexp(&d, &n); + // if x = 1 or x = n - 1 then + if (&x == &one) || (&x == &nm1) { + // continue WitnessLoop + continue 'WitnessLoop; + } + // repeat r - 1 times: + for _i in 0..r { + // x <- x^2 mod n + x = x.modexp(&two, &n); + // if x = 1 then + if &x == &one { + // return composite + return false; + } + // if x = n - 1 then + if &x == &nm1 { + // continue WitnessLoop + continue 'WitnessLoop; + } + } + // return composite + return false; + } + // return probably prime + true +} + +fn random_in_range(rng: &mut G, min: &UCN, max: &UCN) -> UCN { + let bitlen = ((max.bits() + 63) / 64) * 64; + loop { + let candidate = random_number(rng, bitlen); + + if (&candidate >= min) && (&candidate < max) { + return candidate; + } + } +} + +fn random_number(rng: &mut G, bitlen: usize) -> UCN { + assert!(bitlen % 64 == 0); + let wordlen = bitlen / 64; + let components = rng.gen_iter().take(wordlen).collect(); + UCN{ contents: components } +} + diff --git a/src/cryptonum/unsigned.rs b/src/cryptonum/unsigned.rs index d64e000..b6985af 100644 --- a/src/cryptonum/unsigned.rs +++ b/src/cryptonum/unsigned.rs @@ -1,6 +1,5 @@ use cryptonum::signed::SCN; use num::{BigUint,ToPrimitive,Zero}; -use rand::Rng; use std::fmt; use std::fmt::Write; use std::cmp::Ordering; @@ -18,41 +17,6 @@ pub struct BarrettUCN { pub(crate) m: UCN } -static SMALL_PRIMES: [u32; 310] = [ - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, - 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, - 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, - 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, - 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, - 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, - 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, - 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, - 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, - 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, - 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, - 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, - 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, - 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, - 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, - 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, - 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, - 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, - 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, - 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, - 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, - 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, - 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, - 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, - 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, - 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, - 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, - 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, - 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, - 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, - 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053]; - - - impl UCN { pub fn zero() -> UCN { UCN{ contents: vec![] } @@ -145,41 +109,6 @@ impl UCN { } } - pub fn generate_prime(rng: &mut G, - bitlen: usize, - iterations: usize, - ok_value: F) - -> UCN - where - G: Rng, - F: Fn(&UCN) -> bool - { - let one = UCN::from(1 as u8); - let topbit = &one << (bitlen - 1); - - loop { - let base = random_number(rng, bitlen); - let candidate = base | &topbit | &one; - - if !ok_value(&candidate) { - continue; - } - - if candidate.probably_prime(rng, iterations) { - return candidate - } - } - } - - pub fn probably_prime(&self, g: &mut G, iters: usize) -> bool { - for tester in SMALL_PRIMES.iter() { - if (self % UCN::from(*tester)).is_zero() { - return false; - } - } - miller_rabin(g, &self, iters) - } - pub fn barrett_u(&self) -> BarrettUCN { let k = self.contents.len(); let b = UCN::from(1 as u8) << (64 * 2 * k); @@ -253,70 +182,6 @@ impl UCN { } } -fn miller_rabin(g: &mut G, n: &UCN, iters: usize) -> bool { - let one = UCN::from(1 as u8); - let two = UCN::from(2 as u8); - let nm1 = n - &one; - // Quoth Wikipedia: - // write n - 1 as 2^r*d with d odd by factoring powers of 2 from n - 1 - let mut d = nm1.clone(); - let mut r = 0; - while d.is_even() { - d >>= 1; - r += 1; - assert!(r < n.bits()); - } - // WitnessLoop: repeat k times - 'WitnessLoop: for _k in 0..iters { - // pick a random integer a in the range [2, n - 2] - let a = random_in_range(g, &two, &nm1); - // x <- a^d mod n - let mut x = a.modexp(&d, &n); - // if x = 1 or x = n - 1 then - if (&x == &one) || (&x == &nm1) { - // continue WitnessLoop - continue 'WitnessLoop; - } - // repeat r - 1 times: - for _i in 0..r { - // x <- x^2 mod n - x = x.modexp(&two, &n); - // if x = 1 then - if &x == &one { - // return composite - return false; - } - // if x = n - 1 then - if &x == &nm1 { - // continue WitnessLoop - continue 'WitnessLoop; - } - } - // return composite - return false; - } - // return probably prime - true -} - -fn random_in_range(rng: &mut G, min: &UCN, max: &UCN) -> UCN { - let bitlen = ((max.bits() + 31) / 32) * 32; - loop { - let candidate = random_number(rng, bitlen); - - if (&candidate >= min) && (&candidate < max) { - return candidate; - } - } -} - -fn random_number(rng: &mut G, bitlen: usize) -> UCN { - assert!(bitlen % 32 == 0); - let wordlen = bitlen / 32; - let components = rng.gen_iter().take(wordlen).collect(); - UCN{ contents: components } -} - impl fmt::UpperHex for UCN { fn fmt(&self, fmt: &mut fmt::Formatter) -> Result<(),fmt::Error> { for x in self.contents.iter().rev() {