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Added Fixed-Base Miller-Rabin

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This commit is contained in:
Mahrud Sayrafi 2018-02-27 00:23:51 -08:00
parent d418b4aa40
commit b518d27ff0
No known key found for this signature in database
GPG Key ID: C24071B956C3245F
2 changed files with 40 additions and 30 deletions
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32
src/crypto/public_key/prime.js
View File

@ -69,6 +69,9 @@ function isProbablePrime(n, e, k) {
if (!fermat(n)) {
return false;
}
if (!millerRabin(n, k, () => new BN(lowprimes[Math.random() * lowprimes.length | 0]))) {
return false;
}
if (!millerRabin(n, k)) {
return false;
}
@ -87,6 +90,17 @@ function fermat(n, b) {
return b.toRed(BN.mont(n)).redPow(n.subn(1)).fromRed().cmpn(1) === 0;
}
const lowprimes = [
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173,
179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409,
419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541,
547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809,
811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941,
947, 953, 967, 971, 977, 983, 991, 997];
// Miller-Rabin - Miller Rabin algorithm for primality test
// Copyright Fedor Indutny, 2014.
@ -120,12 +134,12 @@ function fermat(n, b) {
/**
* Tests whether n is probably prime or not using the Miller-Rabin test.
* See HAC Remark 4.28.
* @param {BN} n Number to test
* @param {Integer} k Optional number of iterations of Miller-Rabin test
* @param {Function} cb Optional callback function to call with random witnesses
* @param {BN} n Number to test
* @param {Integer} k Optional number of iterations of Miller-Rabin test
* @param {Function} w Optional function to generate potential witnesses
* @return {boolean}
*/
function millerRabin(n, k, cb) {
function millerRabin(n, k, rand) {
const len = n.bitLength();
const red = BN.mont(n);
const rone = new BN(1).toRed(red);
@ -133,18 +147,16 @@ function millerRabin(n, k, cb) {
if (!k)
k = Math.max(1, (len / 48) | 0);
// Find d and s, (n - 1) = (2 ^ s) * d;
const n1 = n.subn(1);
const rn1 = n1.toRed(red);
// Find d and s, (n - 1) = (2 ^ s) * d;
let s = 0;
while (!n1.testn(s)) { s++; }
const d = n.shrn(s);
const rn1 = n1.toRed(red);
for (; k > 0; k--) {
let a = random.getRandomBN(new BN(2), n1);
if (cb)
cb(a);
let a = rand ? rand() : random.getRandomBN(new BN(2), n1);
let x = a.toRed(red).redPow(d);
if (x.cmp(rone) === 0 || x.cmp(rn1) === 0)

38
src/crypto/public_key/rsa.js
View File

@ -211,28 +211,26 @@ export default {
return key;
}
while (true) {
// 40 iterations of the Miller-Rabin test
// See https://stackoverflow.com/a/6330138 for justification
let p = prime.randomProbablePrime(B - (B >> 1), E, 40);
let q = prime.randomProbablePrime(B >> 1, E, 40);
// RSA keygen fallback using 40 iterations of the Miller-Rabin test
// See https://stackoverflow.com/a/6330138 for justification
let p = prime.randomProbablePrime(B - (B >> 1), E, 40);
let q = prime.randomProbablePrime(B >> 1, E, 40);
if (p.cmp(q) < 0) {
[p, q] = [q, p];
}
const phi = p.subn(1).mul(q.subn(1));
return {
n: p.mul(q),
e: E,
d: E.invm(phi),
q: q,
p: p,
// dq: d.mod(q.subn(1)),
// dp: d.mod(p.subn(1)),
u: p.invm(q)
};
if (p.cmp(q) < 0) {
[p, q] = [q, p];
}
const phi = p.subn(1).mul(q.subn(1));
return {
n: p.mul(q),
e: E,
d: E.invm(phi),
q: q,
p: p,
// dq: d.mod(q.subn(1)),
// dp: d.mod(p.subn(1)),
u: p.invm(q)
};
},
prime: prime