From b6134a6cfdd8bf4ff541833a4c0ee0d17e7fa49c Mon Sep 17 00:00:00 2001 From: Zach Dziura Date: Wed, 1 Jun 2016 00:35:51 -0400 Subject: [PATCH] Refactored source code into separate modules Now each of the various modules (prime and safe_prime) exist within their own modules. The prime generation logic is now found within the common module. --- Cargo.toml | 2 +- README.md | 2 +- examples/multiply.rs | 6 +- src/common.rs | 246 ++++++++++++++++++++++++++++ src/lib.rs | 65 +++++--- src/prime.rs | 376 ++----------------------------------------- src/safe_prime.rs | 47 ++++++ 7 files changed, 357 insertions(+), 387 deletions(-) create mode 100644 src/common.rs create mode 100644 src/safe_prime.rs diff --git a/Cargo.toml b/Cargo.toml index b2f1fb8..56076da 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -1,6 +1,6 @@ [package] name = "pumpkin" -version = "1.0.1" +version = "2.0.0" authors = ["Zach Dziura "] description = "A cryptographically secure prime number generator" repository = "https://github.com/zcdziura/pumpkin" diff --git a/README.md b/README.md index 0679eb8..5bf549a 100644 --- a/README.md +++ b/README.md @@ -22,7 +22,7 @@ of course your mileage may vary. Add the following to your `Cargo.toml` file: ``` -pumpkin = "1.0.*" +pumpkin = "2.0.*" ``` Note that `pumpkin` requires the `nightly` Rust compiler. diff --git a/examples/multiply.rs b/examples/multiply.rs index 74623d6..806814c 100644 --- a/examples/multiply.rs +++ b/examples/multiply.rs @@ -1,12 +1,12 @@ extern crate pumpkin; -use pumpkin::Prime; +use pumpkin::prime; fn main() { - let p = Prime::new(2048); + let p = prime::new(2048); println!("{:x}", p); - let q = Prime::new(2048); + let q = prime::new(2048); println!("\n{:x}", q); println!("\n{:X}", p * q); diff --git a/src/common.rs b/src/common.rs new file mode 100644 index 0000000..07756d8 --- /dev/null +++ b/src/common.rs @@ -0,0 +1,246 @@ +use ramp::{Int, RandomInt}; +use rand::{OsRng, thread_rng}; + +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]; + +/// Constructs a new prime number with the size of `bit_length` bits, sourced +/// from an already-initialized `OsRng`. +pub fn gen_prime(bit_length: usize, rngesus: &mut OsRng) -> Int { + debug_assert!(bit_length >= 512); + let mut candidate: Int; + + // In order to remove as much bias from the system as possible, test + // 500 potential candidates at a time before re-seeding the candidate + // with a new random number. + loop { + let mut counter = 0; + let mut found_prime = true; + candidate = rngesus.gen_uint(bit_length); + + // We first want to make sure that the candidate is in the appropriate + // size range before continuing. This can easily be done by setting the + // two most significant bits of the candidate number to 1. + candidate.set_bit(bit_length as u32, true); + candidate.set_bit((bit_length-1) as u32, true); + + // Next, flip the least significant bit to 1, to make sure the candidate + // is odd (no sense in testing primality on an even number, after all). + candidate.set_bit(1, true); + + // Now run through the actual primality check! + while !is_prime(&candidate) { + candidate += 2_usize; + counter += 1; + + if counter > 499 { + found_prime = false; + break; + } + } + + if found_prime { + break; + } + } + + candidate +} + +/// Runs the following three tests on a given `candidate` to determine +/// primality: +/// +/// 1. Divide the candidate by the first 999 small prime numbers. +/// 2. Run Fermat's Little Theorem against the candidate. +/// 3. Run five rounds of the Miller-Rabin test on the candidate. +/// +/// Should the candidate number pass all three tests, then you can be +/// reasonably sure that the candiate is prime. +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. + + for p in SMALL_PRIMES.into_iter() { + let prime: Int = Int::from(*p); + let (_, r) = candidate.divmod(&prime); + + if r != 0_usize { + 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, 5) { + return false; + } + + true +} + +fn fermat(candidate: &Int) -> bool { + // Perform Fermat's little theorem on the candidate to determine probable + // primality. + let random = thread_rng().gen_int_range(&Int::one(), candidate); + + let result = mod_exp(&random, &(candidate - 1_usize), candidate); + + result == 1_usize +} + +fn mod_exp(base: &Int, exponent: &Int, modulus: &Int) -> Int { + let mut result = Int::one(); + let mut base = base.clone(); + let mut exponent = exponent.clone(); + + while exponent > 0_usize { + if &exponent & 1_usize == 1_usize { + result = (&base * result) % modulus; + } + + base = (&base.pow(2)) % modulus; + exponent = &exponent >> 1; + } + + result +} + +fn miller_rabin(candidate: &Int, limit: usize) -> bool { + // Perform the Miller-Rabin test on the candidate, 'limit' times. + let (s, d) = rewrite(candidate); + + for _ in 0..limit { + let basis = thread_rng().gen_int_range(&Int::from(2), candidate); + let mut x = mod_exp(&basis, &d, candidate); + + if x == 1_usize || x == (candidate - 1_usize) { + continue; + } else { + for _ in Int::one()..s - 1_usize { + x = mod_exp(&x, &Int::from(2), candidate); + if x == 1_usize { + return false; + } else if x == candidate - 1_usize { + break; + } + } + return false; + } + } + + true +} + +fn rewrite(candidate: &Int) -> (Int, Int) { + let mut d = candidate - 1_usize; + let mut s = Int::zero(); + + while &d & 1 == 1_usize { + d = &d >> 1_usize; + s = &s + 1_usize; + } + + (s, d) +} diff --git a/src/lib.rs b/src/lib.rs index 84d9a85..fea036e 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -6,23 +6,39 @@ #![cfg_attr(feature = "dev", plugin(clippy))] //! A crate for generating large, cryptographically secure prime numbers. -//! `Primes` are seeded from the operating system's main source of entropy, -//! ensuring proper randomness. +//! These numbers are seeded from the operating system's main source of +//! entropy, ensuring proper randomness. //! -//! `Primes` must be AT LEAST 512-bits long. Attempting to generate a `Prime` -//! less than 512-bits long will cause a panic. +//! Numbers are verified to be prime by running the following three tests +//! during initialization: +//! +//! 1. Dividing the initial prime number candidate by the first 1,000 prime +//! numbers, checking the remainder. Should the remainder ever be zero, then +//! add two to the candidate and try again. +//! +//! 2. Run a Fermat Primality Test on the candidate. If it doesn't pass, add +//! two to the candidate and goto Step 1. +//! +//! 3. Finally, complete five rounds of the Miller-Rabin Primality Test. +//! Should any of the tests pass, add two to the candidate and goto Step 1. +//! +//! The preceding steps mirror those used by GnuPG, a leading PGP implementation +//! used by thousands of users all across the world. +//! +//! The prime numbers must be AT LEAST 512-bits long. Attempting to generate a +//! number less than 512-bits long will cause a panic. //! //! ## Example //! //! ``` //! extern crate pumpkin; //! -//! use pumpkin::Prime; +//! use pumpkin::prime; //! //! fn main() { -//! // Generate 2048-bit primes -//! let p = Prime::new(2048); -//! let q = Prime::new(2048); +//! // Generate 2, 2048-bit primes +//! let p = prime::new(2048); +//! let q = prime::new(2048); //! //! let n = p * q; //! println!("{}", n); // Some 4096-bit composite number @@ -37,47 +53,50 @@ extern crate ramp; extern crate rand; extern crate test; -mod prime; -pub use prime::Prime; -pub use prime::SafePrime; +mod common; +pub mod prime; +pub mod safe_prime; #[cfg(test)] mod tests { use rand::OsRng; - use super::*; + use super::{prime, safe_prime}; use test::Bencher; #[test] #[should_panic] fn test_new_small_prime() { - Prime::new(511); + prime::new(511); } #[test] #[should_panic] fn test_new_small_prime_from_rng() { let mut rngesus = OsRng::new().unwrap(); - - Prime::from_rng(511, &mut rngesus); - } - - #[test] - fn test_should_destructure() { - let Prime(n) = Prime::new(512); + prime::from_rng(511, &mut rngesus); } #[bench] fn bench_generate_512_bit_prime(b: &mut Bencher) { - b.iter(|| Prime::new(512)); + let mut rngesus = OsRng::new().unwrap(); + b.iter(|| prime::from_rng(512, &mut rngesus)); } #[bench] fn bench_generate_1024_bit_prime(b: &mut Bencher) { - b.iter(|| Prime::new(1024)); + let mut rngesus = OsRng::new().unwrap(); + b.iter(|| prime::from_rng(1024, &mut rngesus)); } #[bench] fn bench_generate_2048_bit_prime(b: &mut Bencher) { - b.iter(|| Prime::new(2048)); + let mut rngesus = OsRng::new().unwrap(); + b.iter(|| prime::from_rng(2048, &mut rngesus)); + } + + #[bench] + fn bench_generate_1024_bit_safe_prime(b: &mut Bencher) { + let mut rngesus = OsRng::new().unwrap(); + b.iter(|| safe_prime::from_rng(1024, &mut rngesus)); } } diff --git a/src/prime.rs b/src/prime.rs index c4a27f1..9e009e1 100644 --- a/src/prime.rs +++ b/src/prime.rs @@ -1,366 +1,24 @@ -use ramp::{Int, RandomInt}; +//! Generates cryptographically secure prime numbers. -use rand::{OsRng, thread_rng}; +use ramp::Int; +use rand::OsRng; -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]; +pub use common::gen_prime as from_rng; -/// An arbitrarily-length prime number, suitable for cryptographic purposes. +/// Constructs a new prime number with a size of `bit_length` bits. /// -/// All `Prime`s are initially seeded from the `rand::OsRng` random number -/// generator, which itself uses the operating system's main source of entropy. +/// This will initialize an `OsRng` instance and call the +/// `from_rng()` function. /// -/// Primes are verified to be prime by running the following three checks -/// during initialization: -/// -/// 1) Dividing the initial "prime number candidate" by the first 1,000 -/// prime numbers, and checking the remainder. Should the remainder ever be -/// zero, then add two to the candidate and try again. -/// -/// 2) Run a Fermat Primality Test on the candidate. If it doesn't pass, -/// add two to the candidate and goto Step 1. -/// -/// 3) Finally, complete five rounds of the Miller-Rabin Primality Test. -/// Should any of the tests pass, add two to the candidate and goto Step 1. -/// -/// The preceding steps mirror those used by GnuPG, a leading PGP implementation -/// used by thousands of users all across the world. Because the intial prime -/// number candidate is generated from the operating system's source of -/// entropy, we can be reasonably sure that the generated `Prime` is, in fact, -/// prime. -/// -/// `Prime`s are built upon the `Int` type as defined in the `ramp` crate. In -/// fact, all operations that you can do with `Int`s, you can do with `Prime`s -/// as well. `Prime`s simply claim that the number you're dealing with is a -/// prime number. -custom_derive! { - /// A cryptographically secure prime number. - #[derive(NewtypeDebug, NewtypeDisplay, NewtypeBinary, NewtypeOctal, - NewtypeLowerHex, NewtypeUpperHex, NewtypeAdd, NewtypeAdd(Int), - NewtypeSub, NewtypeSub(Int), NewtypeMul, NewtypeMul(Int), NewtypeDiv, - NewtypeDiv(Int), NewtypeRem, NewtypeRem(Int), NewtypeBitAnd, - NewtypeBitAnd(Int), NewtypeBitOr, NewtypeBitOr(Int), NewtypeBitXor, - NewtypeBitXor(Int) - )] - pub struct Prime(pub Int); -} +/// Note: the `bit_length` MUST be at least 512-bits. +pub fn new(bit_length: usize) -> Int { + assert!(bit_length >= 512); + let mut rngesus = match OsRng::new() { + Ok(rng) => rng, + Err(reason) => panic!("Error initializing RNG: {}", reason), + }; -impl Prime { - /// Constructs a new `Prime` with a size of `bit_length` bits. - /// - /// This will initialize an `OsRng` instance and call the - /// `Prime::from_rng()` method. - /// - /// Note: the `bit_length` MUST be at least 512-bits. - pub fn new(bit_length: usize) -> Prime { - debug_assert!(bit_length >= 512); - let mut rngesus = match OsRng::new() { - Ok(rng) => rng, - Err(reason) => panic!("Error initializing RNG: {}", reason), - }; - - Prime::from_rng(bit_length, &mut rngesus) - } - - /// Constructs a new `Prime` with the size of `bit_length` bits, sourced - /// from an already-created `OsRng`. Not that you can **ONLY** use an - /// `OsRng`, as it uses the operating system's secure source of entropy. - pub fn from_rng(bit_length: usize, rngesus: &mut OsRng) -> Prime { - debug_assert!(bit_length >= 512); - let mut candidate: Int; - - // In order to remove as much bias from the system as possible, test - // 500 potential candidates at a time before re-seeding the candidate - // with a new random number. - loop { - let mut counter = 0; - let mut found_prime = true; - candidate = rngesus.gen_uint(bit_length); - - // We first want to make sure that the candidate is in the appropriate - // size range before continuing. This can easily be done by setting the - // two most significant bits of the candidate number to 1. - // Note that Ints are stored in most-significant-bit format, so we - // will right-shift in order to set the two most significant bits. - candidate = &candidate | (Int::from(3) >> (bit_length - 2)); - - // Next, flip the least significant bit to 1, to make sure the candidate - // is odd (no sense in testing primality on an even number, after all). - candidate = &candidate | 1_usize; - - // Now run through the actual primality check! - while !is_prime(&candidate) { - candidate += 2_usize; - counter += 1; - - if counter > 499 { - found_prime = false; - break; - } - } - - if found_prime { - break; - } - } - - Prime(candidate) - } -} - -/// An arbitrarily-length safe prime number, suitable for cryptographic purposes. -/// -/// A safe prime is a prime of the form `p = 2q + 1`, where `q` is also prime. -/// -/// `SafePrime`s are constructed using similar methods as those in `Prime`. An -/// extra iterative check is constructed on each generated `Prime` to ensure it -/// satisfies the safe prime condition. As a result, generation of `SafePrime`s -/// can be quite slow, and should only be used if absolutely necessary. -custom_derive! { - /// A cryptographically secure prime number. - #[derive(NewtypeDebug, NewtypeDisplay, NewtypeBinary, NewtypeOctal, - NewtypeLowerHex, NewtypeUpperHex, NewtypeAdd, NewtypeAdd(Int), - NewtypeSub, NewtypeSub(Int), NewtypeMul, NewtypeMul(Int), NewtypeDiv, - NewtypeDiv(Int), NewtypeRem, NewtypeRem(Int), NewtypeBitAnd, - NewtypeBitAnd(Int), NewtypeBitOr, NewtypeBitOr(Int), NewtypeBitXor, - NewtypeBitXor(Int) - )] - pub struct SafePrime(pub Int); -} - -impl SafePrime { - /// Constructs a new `SafePrime` with a size of `bit_length` bits. - /// - /// This will initialize an `OsRng` instance and call the - /// `SafePrime::from_rng()` method. - /// - /// Note: the `bit_length` MUST be at least 512-bits. - pub fn new(bit_length: usize) -> SafePrime { - debug_assert!(bit_length >= 512); - let mut rngesus = match OsRng::new() { - Ok(rng) => rng, - Err(reason) => panic!("Error initializing RNG: {}", reason), - }; - - SafePrime::from_rng(bit_length, &mut rngesus) - } - - /// Constructs a new `SafePrime` with the size of `bit_length` bits, sourced - /// from an already-created `OsRng`. Not that you can **ONLY** use an - /// `OsRng`, as it uses the operating system's secure source of entropy. - pub fn from_rng(bit_length: usize, mut rngesus: &mut OsRng) -> SafePrime { - debug_assert!(bit_length >= 512); - let mut candidate: Int; - - // Circumvent uninitialized warning (technically valid but compiler - // cannot determine that `clone_from` will fill the value. - let mut candidate_p: Int = Int::zero(); - - loop { - candidate = match Prime::from_rng(bit_length, &mut rngesus) { - Prime(inner) => inner - }; - - candidate_p.clone_from(&candidate); - candidate_p -= &Int::one(); - candidate_p /= &Int::from(2); - - if is_prime(&candidate_p) { - break; - } - } - - SafePrime(candidate) - } -} - -fn mod_exp(base: &Int, exponent: &Int, modulus: &Int) -> Int { - let mut result = Int::one(); - let mut base = base.clone(); - let mut exponent = exponent.clone(); - - while exponent > 0_usize { - if &exponent & 1_usize == 1_usize { - result = (&base * result) % modulus; - } - - base = (&base.pow(2)) % modulus; - exponent = &exponent >> 1; - } - - result -} - -fn rewrite(candidate: &Int) -> (Int, Int) { - let mut d = candidate - 1_usize; - let mut s = Int::zero(); - - while &d & 1 == 1_usize { - d = &d >> 1_usize; - s = &s + 1_usize; - } - - (s, d) -} - -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. - - for p in SMALL_PRIMES.into_iter() { - let prime: Int = Int::from(*p); - let (_, r) = candidate.divmod(&prime); - - if r != 0_usize { - 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 -} - -fn fermat(candidate: &Int) -> bool { - // Perform Fermat's little theorem on the candidate to determine probable - // primality. - let random = thread_rng().gen_int_range(&Int::one(), candidate); - - let result = mod_exp(&random, &(candidate - 1_usize), candidate); - - result == 1_usize -} - -fn miller_rabin(candidate: &Int) -> bool { - // Perform five iterations of the Miller-Rabin test on the candidate. - let (s, d) = rewrite(candidate); - - for _ in 0..5 { - let basis = thread_rng().gen_int_range(&Int::from(2), candidate); - let mut x = mod_exp(&basis, &d, candidate); - - if x == 1_usize || x == (candidate - 1_usize) { - continue; - } else { - for _ in Int::one()..s - 1_usize { - x = mod_exp(&x, &Int::from(2), candidate); - if x == 1_usize { - return false; - } else if x == candidate - 1_usize { - break; - } - } - return false; - } - } - - true + from_rng(bit_length, &mut rngesus) } #[cfg(test)] @@ -381,12 +39,12 @@ mod tests { #[test] fn test_miller_rabin_pass() { - assert!(miller_rabin(&Int::from(7919))); + assert!(miller_rabin(&Int::from(7919), 5)); } #[test] #[should_panic] fn test_miller_rabin_fail() { - assert!(miller_rabin(&Int::from(7920))); + assert!(miller_rabin(&Int::from(7920), 5)); } } diff --git a/src/safe_prime.rs b/src/safe_prime.rs new file mode 100644 index 0000000..10a6d34 --- /dev/null +++ b/src/safe_prime.rs @@ -0,0 +1,47 @@ +//! Generates [safe prime numbers](https://www.wikiwand.com/en/Sophie_Germain_prime). + +use ramp::Int; +use rand::OsRng; + +pub use common::{gen_prime, is_prime}; + +/// Constructs a new `SafePrime` with a size of `bit_length` bits. +/// +/// This will initialize an `OsRng` instance and call the +/// `SafePrime::from_rng()` method. +/// +/// Note: the `bit_length` MUST be at least 512-bits. +pub fn new(bit_length: usize) -> Int { + debug_assert!(bit_length >= 512); + let mut rngesus = match OsRng::new() { + Ok(rng) => rng, + Err(reason) => panic!("Error initializing RNG: {}", reason), + }; + + from_rng(bit_length, &mut rngesus) +} + +/// Constructs a new `SafePrime` with the size of `bit_length` bits, sourced +/// from an already-initialized `OsRng`. +pub fn from_rng(bit_length: usize, mut rngesus: &mut OsRng) -> Int { + debug_assert!(bit_length >= 512); + let mut candidate: Int; + + // Circumvent uninitialized warning (technically valid but compiler + // cannot determine that `clone_from` will fill the value. + let mut candidate_p: Int = Int::zero(); + + loop { + candidate = gen_prime(bit_length, &mut rngesus); + + candidate_p.clone_from(&candidate); + candidate_p -= 1_usize; + candidate_p /= 2_usize; + + if is_prime(&candidate_p) { + break; + } + } + + candidate +}