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Refactored source code into separate modules

Browse source 
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.
This commit is contained in:
Zach Dziura 2016-06-01 00:35:51 -04:00
parent 7c6a418f3e
commit b6134a6cfd
7 changed files with 357 additions and 387 deletions
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2
Cargo.toml
View file

@ -1,6 +1,6 @@
[package]
name = "pumpkin"
version = "1.0.1"
version = "2.0.0"
authors = ["Zach Dziura <zcdziura@gmail.com>"]
description = "A cryptographically secure prime number generator"
repository = "https://github.com/zcdziura/pumpkin"

2
README.md
View file

@ -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.

6
examples/multiply.rs
View file

@ -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);

246
src/common.rs Normal file
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@ -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)
}

65
src/lib.rs
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@ -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));
}
}

376
src/prime.rs
View file

@ -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));
}
}

47
src/safe_prime.rs Normal file
View file

@ -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
}