From 6418c323ade00e917af654fbe89a280e0cc2c3de Mon Sep 17 00:00:00 2001 From: Adam Wick Date: Thu, 22 Mar 2018 21:03:16 -0700 Subject: [PATCH] Start porting over some of the random generation stuff. --- src/cryptonum/mod.rs | 1 + src/cryptonum/primes.rs | 112 +++++++++++++++++++++++++++++++++++++- src/cryptonum/traits.rs | 2 +- src/cryptonum/unsigned.rs | 2 +- 4 files changed, 112 insertions(+), 5 deletions(-) diff --git a/src/cryptonum/mod.rs b/src/cryptonum/mod.rs index dabdc77..c476320 100644 --- a/src/cryptonum/mod.rs +++ b/src/cryptonum/mod.rs @@ -41,6 +41,7 @@ use std::cmp::Ordering; use std::fmt::{Debug,Error,Formatter}; use std::ops::*; pub use self::traits::*; +use self::primes::SMALL_PRIMES; construct_unsigned!(U512, BarretMu512, u512, 8); construct_unsigned!(U1024, BarretMu1024, u1024, 16); diff --git a/src/cryptonum/primes.rs b/src/cryptonum/primes.rs index 7a49bad..d8c5144 100644 --- a/src/cryptonum/primes.rs +++ b/src/cryptonum/primes.rs @@ -1,9 +1,115 @@ +pub 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]; + macro_rules! derive_prime_operations { - ($type: ident) => { + ($type: ident, $count: expr) => { + impl $type { + fn miller_rabin(&self, g: &mut G, iters: usize) + -> bool + { + let nm1 = self - $type::from(1 as u8); + // Quoth Wikipedia: + // write n - 1 as 2^r*d with d odd by factoring powers of 2 from n - 1 + let mut d = nm1.clone(); + let mut r = 0; + while d.is_even() { + d >>= 1; + r += 1; + assert!(r < ($count * 64)); + } + // WitnessLoop: repeat k times + 'WitnessLoop: for _k in 0..iters { + // pick a random integer a in the range [2, n - 2] + let a = $type::random_in_range(g, &$type::from(2 as u8), &nm1); + // x <- a^d mod n + let mut x = a.modexp(&d, &self); + // if x = 1 or x = n - 1 then + if (&x == &$type::from(1 as u8)) || (&x == &nm1) { + // continue WitnessLoop + continue 'WitnessLoop; + } + // repeat r - 1 times: + for _i in 0..r { + // x <- x^2 mod n + x = x.modexp(&$type::from(2 as u8), &self); + // if x = 1 then + if &x == &$type::from(1 as u8) { + // return composite + return false; + } + // if x = n - 1 then + if &x == &nm1 { + // continue WitnessLoop + continue 'WitnessLoop; + } + } + // return composite + return false; + } + // return probably prime + true + } + + fn random_in_range(rng: &mut G, min: &$type, max: &$type) + -> $type + { + loop { + let candidate = $type::random_number(rng); + if (&candidate >= min) && (&candidate < max) { + return candidate; + } + } + } + + fn random_number(rng: &mut G) -> $type { + let mut components = [0; $count]; + for i in 0..$count { + components[i] = rng.gen(); + } + $type{ contents: components } + } + } + impl CryptoNumPrimes for $type { - fn probably_prime(_g: &mut G, _iters: usize) -> bool { - panic!("probably_prime"); + fn probably_prime(&self, g: &mut G, iters: usize) -> bool { + for tester in SMALL_PRIMES.iter() { + let testvalue = $type::from(*tester); + if (self % testvalue).is_zero() { + return false; + } + } + self.miller_rabin(g, iters) } fn generate_prime(_g: &mut G, _iters: usize, _e: &Self, _min: &Self) -> Self { panic!("generate_prime"); diff --git a/src/cryptonum/traits.rs b/src/cryptonum/traits.rs index 1929df8..1474743 100644 --- a/src/cryptonum/traits.rs +++ b/src/cryptonum/traits.rs @@ -69,7 +69,7 @@ pub trait CryptoNumPrimes /// Determine if the given number is probably prime using a quick spot /// check and Miller-Rabin, using the given random number generator /// and number of iterations. - fn probably_prime(g: &mut G, iters: usize) -> bool; + fn probably_prime(&self, g: &mut G, iters: usize) -> bool; /// Generate a prime using the given random number generator, using /// the given number of rounds to determine if the number is probably /// prime. The other two numbers are a number for which the generator diff --git a/src/cryptonum/unsigned.rs b/src/cryptonum/unsigned.rs index fabe4a0..d97deeb 100644 --- a/src/cryptonum/unsigned.rs +++ b/src/cryptonum/unsigned.rs @@ -194,7 +194,7 @@ macro_rules! construct_unsigned { derive_barrett!($type, $barrett, $count); derive_modulo_operations!($type); - derive_prime_operations!($type); + derive_prime_operations!($type, $count); impl Into for $type { fn into(self) -> BigInt {