diff --git a/.gitignore b/.gitignore index 37727f9..94408df 100644 --- a/.gitignore +++ b/.gitignore @@ -9,3 +9,4 @@ # Generated by Cargo /target/ +Cargo.lock diff --git a/Cargo.lock b/Cargo.lock index 1ee36af..dd4f055 100644 --- a/Cargo.lock +++ b/Cargo.lock @@ -2,7 +2,7 @@ name = "pumpkin" version = "0.1.0" dependencies = [ - "num 0.1.27 (registry+https://github.com/rust-lang/crates.io-index)", + "ramp 0.1.8 (registry+https://github.com/rust-lang/crates.io-index)", "rand 0.3.11 (registry+https://github.com/rust-lang/crates.io-index)", ] @@ -15,18 +15,27 @@ dependencies = [ "winapi-build 0.1.1 (registry+https://github.com/rust-lang/crates.io-index)", ] +[[package]] +name = "gcc" +version = "0.3.17" +source = "registry+https://github.com/rust-lang/crates.io-index" +dependencies = [ + "advapi32-sys 0.1.2 (registry+https://github.com/rust-lang/crates.io-index)", + "winapi 0.2.4 (registry+https://github.com/rust-lang/crates.io-index)", +] + [[package]] name = "libc" version = "0.1.10" source = "registry+https://github.com/rust-lang/crates.io-index" [[package]] -name = "num" -version = "0.1.27" +name = "ramp" +version = "0.1.8" source = "registry+https://github.com/rust-lang/crates.io-index" dependencies = [ + "gcc 0.3.17 (registry+https://github.com/rust-lang/crates.io-index)", "rand 0.3.11 (registry+https://github.com/rust-lang/crates.io-index)", - "rustc-serialize 0.3.16 (registry+https://github.com/rust-lang/crates.io-index)", ] [[package]] @@ -39,11 +48,6 @@ dependencies = [ "winapi 0.2.4 (registry+https://github.com/rust-lang/crates.io-index)", ] -[[package]] -name = "rustc-serialize" -version = "0.3.16" -source = "registry+https://github.com/rust-lang/crates.io-index" - [[package]] name = "winapi" version = "0.2.4" diff --git a/Cargo.toml b/Cargo.toml index b9aebd7..076d4c3 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -4,5 +4,5 @@ version = "0.1.0" authors = ["Zach Dziura "] [dependencies] -num = "0.1.27" +ramp = "0.1.8" rand = "0.3.11" diff --git a/src/lib.rs b/src/lib.rs index 7b8b3a9..fd67033 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -1,4 +1,8 @@ -extern crate num; +#![feature(augmented_assignments)] +#![feature(core)] + +extern crate core; +extern crate ramp; extern crate rand; -pub mod primes; +pub mod prime; diff --git a/src/prime.rs b/src/prime.rs new file mode 100644 index 0000000..867b9fe --- /dev/null +++ b/src/prime.rs @@ -0,0 +1,213 @@ +use core::ops::{Add, BitAnd, Mul, Rem, Shr, Sub}; + +use ramp::{Int, RandomInt}; + +use rand::{OsRng, thread_rng}; + +use std::fmt; + +static SMALL_PRIMES: [u32; 999] = [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, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, +2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, +2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, +2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, +2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, +2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, +2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, +2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, +3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, +3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, +3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, +3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, +3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, +3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, +3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, +3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, +4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, +4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, +4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, +4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, +4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, +4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, +4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, +5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, +5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, +5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, +5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, +5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, +5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, +5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, +6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, +6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, +6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, +6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, +6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, +6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, +6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, +6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, +7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, +7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, +7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, +7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, +7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, +7873, 7877, 7879, 7883, 7901, 7907, 7919]; + +#[derive(Debug)] +pub struct Prime { + bit_length: usize, + num: Int +} + +impl Prime { + pub fn new(bit_length: usize) -> Prime { + let one = Int::one(); + let two = &one + &one; + let mut rngesus = match OsRng::new() { + Ok(rng) => rng, + Err(reason) => panic!("Error initializing RNG: {}", reason) + }; + let mut candidate = rngesus.gen_uint(bit_length); + + // Make sure candidate is odd before continuing... + if &candidate & (&one) == 0 { + candidate += &one; + } + while !is_prime(&candidate) { + candidate += &two; + } + + Prime { + bit_length: bit_length, + num: candidate + } + } + +} + +impl fmt::Display for Prime { + fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { + write!(f, "{}", self.num) + } +} + + +pub fn is_prime(candidate: &Int) -> bool { + // First, iterate through the array of small primes and divide the + // candidate. If the candidate divides any of them, then we know the number + // is a multiple of that prime; that is, the candidate is composite. + let zero = Int::zero(); + + for p in SMALL_PRIMES.into_iter() { + let prime: Int = Int::from(*p); + let (_, r) = candidate.divmod(&prime); + + if r != zero { + continue; + } else { + return false; + } + } + + // Second, do a Fermat test on the candidate + if !fermat(candidate) { + return false; + } + + // Finally, do a Miller-Rabin test + if !miller_rabin(candidate) { + return false; + } + + true +} + +pub fn fermat(candidate: &Int) -> bool { + // Perform Fermat's little theorem on the candidate to determine probable + // primality. + let one = Int::one(); + let random = thread_rng().gen_int_range(&one, candidate); + + let result = mod_exp(&random, &candidate.sub(&one), candidate); + + if result == one { + true + } else { + false + } +} + +pub fn miller_rabin(candidate: &Int) -> bool { + // Perform five iterations of the Miller-Rabin test on the candidate. + let (s, d) = rewrite(candidate); + let one = Int::one(); + let two = (&one).add(&one); + + for _ in (0..5) { + let basis = thread_rng().gen_int_range(&two, candidate); + let mut x = mod_exp(&basis, &d, candidate); + + if x.eq(&one) || x.eq(&(candidate.sub(&one))) { + continue; + } else { + for _ in (one.clone() .. s.sub(&one)) { + x = mod_exp(&x, &two, candidate); + if x == one.clone() { + return false; + } else if x == (candidate.sub(&one)) { + break; + } + } + return false; + } + } + + true +} + +fn mod_exp(base: &Int, exponent: &Int, modulus: &Int) -> Int { + let (zero, one) = (Int::zero(), Int::one()); + let mut result = one.clone(); + let mut base = base.clone(); + let mut exponent = exponent.clone(); + + while &exponent > &zero { + if (&exponent).bitand(&one) == (one.clone()) { + result = ((&result).mul(&base)).rem(modulus); + } + + base = ((&base).mul(&base)).rem(modulus); + exponent = exponent.clone().shr(1); + } + + result +} + +fn rewrite(candidate: &Int) -> (Int, Int) { + let one = Int::one(); + + let mut d = candidate.sub(&one); + let mut s = Int::zero(); + + while (&d).bitand(&one) == one { + d = d.clone().shr(1); + s = (&s).add(&one); + } + + (s, d) +} diff --git a/src/primes.rs b/src/primes.rs deleted file mode 100644 index 63e15cc..0000000 --- a/src/primes.rs +++ /dev/null @@ -1,108 +0,0 @@ -use num::{BigUint, FromPrimitive, One, Zero, pow}; -use num::bigint::RandBigInt; -use num::integer::Integer; - -use rand::{OsRng, thread_rng}; - -pub fn generate_prime() -> BigUint { - /* Generates a large prime number within the range [2^2048, 2^2049); - * that is, generates a large prime number between 2^2048 inclusive and - * 2^2049 exclusive. - */ - - // Generate the RNG, which will be sourced from the OS's secure source - // of entropy. Also, give it a sweet name. - let one: BigUint = One::one(); - let two = one.clone() + one.clone(); - let mut rngesus = match OsRng::new() { - Ok(o) => o, - Err(err) => panic!("Error initializing RNG: {}", err) - }; - - let lower_bound = pow(BigUint::from_u8(2).unwrap(), 2048); - let upper_bound = pow(BigUint::from_u8(2).unwrap(), 2049); - - let mut candidate = rngesus.gen_biguint_range(&lower_bound, - &upper_bound); - if candidate.is_even() { - candidate = candidate + one.clone(); - } - while !test_prime(&candidate, 128) { - candidate = candidate + two.clone(); - } - - candidate -} - -fn test_prime(candidate: &BigUint, limit: u8) -> bool { - let (zero, one): (BigUint, BigUint) = (Zero::zero(), One::one()); - let two = one.clone() + one.clone(); - - if *candidate < two { - false - } else if *candidate == two { - true - } else if candidate.is_even() { - false - } else { - let (s, d) = rewrite(&(candidate - one.clone())); - let mut k = 0; - - while k < limit { - let basis = thread_rng().gen_biguint_range(&two, candidate); - let mut v = modulo(&basis, &d, candidate); - - if v != one.clone() && v != (candidate - one.clone()) { - let mut i = zero.clone(); - loop { - v = modulo(&v, &two, candidate); - if v == (candidate - one.clone()) { - break - } else if v == one.clone() || i == (s.clone() - one.clone()) { - return false; - } - - i = i + one.clone(); - } - } - - k = k + 2; - } - - true - } -} - -fn rewrite(n: &BigUint) -> (BigUint, BigUint) { - let mut d = n.clone(); - let mut s: BigUint = Zero::zero(); - let one: BigUint = One::one(); - let two = one.clone() + one.clone(); - - while d.is_even() { - d = d.clone() / two.clone(); - s = s.clone() + one.clone(); - } - - (s, d) -} - -fn modulo(base: &BigUint, exponent: &BigUint, modulus: &BigUint) -> BigUint { - // Modular exponentiation function, with BigUints! - // Warning!! Ahead, thar be clones! - let (zero, one): (BigUint, BigUint) = (Zero::zero(), One::one()); - let mut result = one.clone(); - let mut b = base.clone(); - let mut e = exponent.clone(); - - while e > zero { - if (exponent & one.clone()) == one { - result = (result * b.clone()) % modulus; - } - - b = (b.clone() * b.clone()) % modulus; - e = e >> 1; - } - - result -}