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