2023-03-03 17:34:15 +00:00
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import { mod_exp } from "./math.js";
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2023-04-17 12:30:34 +00:00
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export const KEY_SIZE = 512;
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2023-04-13 12:32:29 +00:00
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2023-03-19 15:31:29 +00:00
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export function cryptoRandom(bits) {
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if (bits === undefined) {
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2023-04-13 12:32:29 +00:00
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bits = KEY_SIZE;
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2023-03-19 15:31:29 +00:00
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}
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let length = bits / 64;
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const byteArray = new BigUint64Array(length);
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2023-02-08 15:52:02 +00:00
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window.crypto.getRandomValues(byteArray);
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let intRepr = 0n;
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for (let int of byteArray) {
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intRepr <<= 64n;
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intRepr += int;
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}
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return intRepr;
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}
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2023-04-17 15:32:35 +00:00
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window.cryptoRandom = cryptoRandom;
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2023-02-08 15:52:02 +00:00
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/**
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2023-04-14 15:04:24 +00:00
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* Generate random integer of length N bits.
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2023-02-08 15:52:02 +00:00
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*
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2023-04-14 15:04:24 +00:00
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* We generate between 2^(N - 1) and 2^N - 1 by adding differences.
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2023-02-08 15:52:02 +00:00
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*/
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function generate_bigint() {
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2023-03-19 15:31:29 +00:00
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let intRepr = cryptoRandom();
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2023-02-08 15:52:02 +00:00
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// Drop the MSB to force into range from above
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intRepr >>= 1n;
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2023-02-13 14:36:58 +00:00
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// Add 2^2047 to force into range from below
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2023-04-13 12:32:29 +00:00
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intRepr += 2n ** BigInt(KEY_SIZE - 1);
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2023-02-08 15:52:02 +00:00
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return intRepr;
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}
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function small_prime_test(n) {
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// Assumes that n > 10000
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for (let p of SMALL_PRIMES) {
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if (n % p === 0n) {
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return false;
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}
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}
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return true;
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}
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function miller_rabin(n, k) {
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// Eradicate the trivial case
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if (n % 2n === 0n) {
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return false;
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}
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// Extract factors of 2
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let s = 0n;
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let d = n - 1n;
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while (d % 2n === 0n) {
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d >>= 1n;
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s += 1n;
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}
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for (; k > 0; k--) {
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2023-03-19 15:31:29 +00:00
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let a = cryptoRandom();
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2023-03-03 17:34:15 +00:00
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let x = mod_exp(a, d, n);
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2023-02-08 15:52:02 +00:00
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if (x === 1n || x === n - 1n) {
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continue;
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}
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let composite = true;
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for (let s_ = 0; s_ < s; s_++) {
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x = x ** 2n % n;
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if (x === n - 1n) {
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composite = false;
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break;
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}
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}
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if (composite) {
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return false;
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}
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}
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return true;
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}
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2023-03-03 17:34:15 +00:00
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export function generate_prime() {
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2023-02-08 15:52:02 +00:00
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while (true) {
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let n = generate_bigint();
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if (small_prime_test(n) && miller_rabin(n, 40)) {
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return n;
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}
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}
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}
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2023-04-20 09:13:03 +00:00
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export function generate_safe_prime() {
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while (true) {
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let n = generate_prime();
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if (small_prime_test((n - 1n) / 2n) && miller_rabin((n - 1n) / 2n, 40)) {
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return n;
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}
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}
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}
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2023-02-08 15:52:02 +00:00
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const SMALL_PRIMES = [
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2n,
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3n,
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5n,
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7n,
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11n,
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13n,
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17n,
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19n,
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23n,
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29n,
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31n,
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37n,
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41n,
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43n,
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47n,
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53n,
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59n,
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61n,
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67n,
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71n,
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73n,
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79n,
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83n,
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89n,
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97n,
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101n,
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103n,
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107n,
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109n,
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113n,
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127n,
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131n,
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137n,
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139n,
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149n,
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151n,
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157n,
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163n,
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167n,
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173n,
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179n,
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181n,
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191n,
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193n,
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197n,
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199n,
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211n,
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223n,
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227n,
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229n,
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233n,
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239n,
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241n,
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251n,
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257n,
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263n,
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269n,
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271n,
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277n,
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281n,
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283n,
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293n,
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307n,
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311n,
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313n,
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317n,
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331n,
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337n,
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347n,
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349n,
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353n,
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359n,
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367n,
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373n,
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379n,
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383n,
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389n,
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397n,
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401n,
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409n,
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419n,
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421n,
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431n,
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433n,
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439n,
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443n,
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449n,
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457n,
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461n,
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463n,
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467n,
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479n,
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487n,
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491n,
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499n,
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503n,
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509n,
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521n,
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523n,
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541n,
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547n,
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557n,
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563n,
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569n,
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571n,
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577n,
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587n,
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593n,
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599n,
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601n,
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607n,
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613n,
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617n,
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619n,
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631n,
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641n,
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643n,
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647n,
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653n,
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659n,
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661n,
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673n,
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677n,
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683n,
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691n,
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701n,
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709n,
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719n,
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727n,
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733n,
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739n,
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743n,
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751n,
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757n,
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761n,
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769n,
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773n,
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787n,
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797n,
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809n,
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811n,
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821n,
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823n,
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827n,
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829n,
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839n,
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853n,
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857n,
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859n,
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863n,
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877n,
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881n,
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883n,
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887n,
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907n,
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911n,
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919n,
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929n,
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937n,
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941n,
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947n,
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953n,
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967n,
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971n,
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977n,
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983n,
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991n,
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997n,
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1009n,
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1013n,
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1019n,
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1021n,
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1031n,
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1033n,
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1039n,
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1049n,
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1051n,
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1061n,
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1063n,
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1069n,
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1087n,
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1091n,
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1093n,
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1097n,
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1103n,
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1109n,
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1117n,
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1123n,
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1129n,
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1151n,
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1153n,
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1163n,
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1171n,
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1181n,
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1187n,
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1193n,
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1201n,
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1213n,
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1217n,
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1223n,
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1229n,
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1231n,
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1237n,
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1249n,
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1259n,
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1277n,
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1279n,
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1283n,
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1289n,
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1291n,
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1297n,
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1301n,
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1303n,
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1307n,
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1319n,
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1321n,
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1327n,
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1361n,
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1367n,
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1373n,
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1381n,
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1399n,
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1409n,
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1423n,
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1427n,
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1429n,
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1433n,
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1439n,
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1447n,
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1451n,
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1453n,
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1459n,
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1471n,
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1481n,
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1483n,
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1487n,
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1489n,
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1493n,
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1499n,
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1511n,
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1523n,
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1531n,
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1543n,
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1549n,
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1553n,
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1559n,
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1567n,
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1571n,
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1579n,
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1583n,
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1597n,
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1601n,
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1607n,
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1609n,
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1613n,
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1619n,
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1621n,
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1627n,
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1637n,
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1657n,
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1663n,
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1667n,
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1669n,
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1693n,
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1697n,
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1699n,
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1709n,
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1801n,
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1871n,
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1873n,
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1877n,
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1879n,
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1889n,
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1901n,
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1907n,
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1913n,
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1931n,
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1933n,
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1949n,
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1951n,
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1973n,
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1979n,
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1987n,
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1993n,
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1997n,
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1999n,
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2003n,
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2011n,
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2017n,
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2027n,
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2029n,
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2039n,
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2999n,
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3019n,
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3119n,
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8363n,
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8369n,
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8377n,
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8387n,
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8389n,
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8419n,
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8423n,
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8429n,
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8431n,
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8443n,
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8447n,
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8461n,
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8467n,
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8501n,
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8513n,
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8521n,
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8527n,
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8537n,
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8539n,
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8543n,
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8563n,
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8573n,
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8581n,
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8597n,
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8599n,
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8609n,
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8623n,
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8627n,
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8629n,
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8641n,
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8647n,
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8663n,
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8669n,
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8677n,
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8681n,
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8689n,
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8693n,
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8699n,
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8707n,
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8713n,
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8719n,
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8731n,
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8737n,
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8741n,
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8747n,
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8753n,
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8761n,
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8779n,
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8783n,
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8803n,
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8807n,
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8819n,
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8821n,
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8831n,
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8837n,
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8839n,
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8849n,
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8861n,
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8863n,
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8867n,
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8887n,
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8893n,
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8923n,
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8929n,
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8933n,
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8941n,
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8951n,
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8963n,
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8969n,
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8971n,
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8999n,
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9001n,
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9007n,
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9011n,
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9013n,
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9029n,
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9041n,
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9043n,
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9049n,
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9059n,
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9067n,
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9091n,
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9103n,
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9109n,
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9127n,
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9133n,
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9137n,
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9151n,
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9157n,
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9161n,
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9173n,
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9181n,
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9187n,
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9199n,
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9203n,
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9209n,
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9221n,
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9227n,
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9239n,
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9241n,
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9257n,
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9277n,
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9281n,
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9283n,
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9293n,
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9311n,
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9319n,
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9323n,
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9337n,
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9341n,
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9343n,
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9349n,
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9371n,
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9377n,
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9391n,
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9397n,
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9403n,
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9413n,
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9419n,
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9421n,
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9431n,
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9433n,
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9437n,
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9439n,
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9461n,
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9463n,
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9467n,
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9473n,
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9479n,
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9491n,
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9497n,
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9511n,
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9521n,
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9533n,
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9539n,
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9547n,
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9551n,
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9587n,
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9601n,
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9613n,
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9619n,
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9623n,
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9629n,
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9631n,
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9643n,
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9649n,
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9661n,
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9677n,
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9679n,
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9689n,
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9697n,
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9719n,
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9721n,
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9733n,
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9739n,
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9743n,
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9749n,
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9767n,
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9769n,
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9781n,
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9787n,
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9791n,
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9803n,
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9811n,
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9817n,
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9829n,
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9833n,
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9839n,
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9851n,
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9857n,
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9859n,
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9871n,
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9883n,
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9887n,
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9901n,
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9907n,
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9923n,
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9929n,
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9931n,
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9941n,
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9949n,
|
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9967n,
|
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9973n,
|
|
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|
|
];
|
