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authorMinteck <contact@minteck.org>2023-01-10 14:54:04 +0100
committerMinteck <contact@minteck.org>2023-01-10 14:54:04 +0100
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+/**
+ * RSA Key Generation Worker.
+ *
+ * @author Dave Longley
+ *
+ * Copyright (c) 2013 Digital Bazaar, Inc.
+ */
+importScripts('jsbn.js');
+
+// prime constants
+var LOW_PRIMES = [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];
+var LP_LIMIT = (1 << 26) / LOW_PRIMES[LOW_PRIMES.length - 1];
+
+var BigInteger = forge.jsbn.BigInteger;
+var BIG_TWO = new BigInteger(null);
+BIG_TWO.fromInt(2);
+
+self.addEventListener('message', function(e) {
+ var result = findPrime(e.data);
+ self.postMessage(result);
+});
+
+// start receiving ranges to check
+self.postMessage({found: false});
+
+// primes are 30k+i for i = 1, 7, 11, 13, 17, 19, 23, 29
+var GCD_30_DELTA = [6, 4, 2, 4, 2, 4, 6, 2];
+
+function findPrime(data) {
+ // TODO: abstract based on data.algorithm (PRIMEINC vs. others)
+
+ // create BigInteger from given random bytes
+ var num = new BigInteger(data.hex, 16);
+
+ /* Note: All primes are of the form 30k+i for i < 30 and gcd(30, i)=1. The
+ number we are given is always aligned at 30k + 1. Each time the number is
+ determined not to be prime we add to get to the next 'i', eg: if the number
+ was at 30k + 1 we add 6. */
+ var deltaIdx = 0;
+
+ // find nearest prime
+ var workLoad = data.workLoad;
+ for(var i = 0; i < workLoad; ++i) {
+ // do primality test
+ if(isProbablePrime(num)) {
+ return {found: true, prime: num.toString(16)};
+ }
+ // get next potential prime
+ num.dAddOffset(GCD_30_DELTA[deltaIdx++ % 8], 0);
+ }
+
+ return {found: false};
+}
+
+function isProbablePrime(n) {
+ // divide by low primes, ignore even checks, etc (n alread aligned properly)
+ var i = 1;
+ while(i < LOW_PRIMES.length) {
+ var m = LOW_PRIMES[i];
+ var j = i + 1;
+ while(j < LOW_PRIMES.length && m < LP_LIMIT) {
+ m *= LOW_PRIMES[j++];
+ }
+ m = n.modInt(m);
+ while(i < j) {
+ if(m % LOW_PRIMES[i++] === 0) {
+ return false;
+ }
+ }
+ }
+ return runMillerRabin(n);
+}
+
+// HAC 4.24, Miller-Rabin
+function runMillerRabin(n) {
+ // n1 = n - 1
+ var n1 = n.subtract(BigInteger.ONE);
+
+ // get s and d such that n1 = 2^s * d
+ var s = n1.getLowestSetBit();
+ if(s <= 0) {
+ return false;
+ }
+ var d = n1.shiftRight(s);
+
+ var k = _getMillerRabinTests(n.bitLength());
+ var prng = getPrng();
+ var a;
+ for(var i = 0; i < k; ++i) {
+ // select witness 'a' at random from between 1 and n - 1
+ do {
+ a = new BigInteger(n.bitLength(), prng);
+ } while(a.compareTo(BigInteger.ONE) <= 0 || a.compareTo(n1) >= 0);
+
+ /* See if 'a' is a composite witness. */
+
+ // x = a^d mod n
+ var x = a.modPow(d, n);
+
+ // probably prime
+ if(x.compareTo(BigInteger.ONE) === 0 || x.compareTo(n1) === 0) {
+ continue;
+ }
+
+ var j = s;
+ while(--j) {
+ // x = x^2 mod a
+ x = x.modPowInt(2, n);
+
+ // 'n' is composite because no previous x == -1 mod n
+ if(x.compareTo(BigInteger.ONE) === 0) {
+ return false;
+ }
+ // x == -1 mod n, so probably prime
+ if(x.compareTo(n1) === 0) {
+ break;
+ }
+ }
+
+ // 'x' is first_x^(n1/2) and is not +/- 1, so 'n' is not prime
+ if(j === 0) {
+ return false;
+ }
+ }
+
+ return true;
+}
+
+// get pseudo random number generator
+function getPrng() {
+ // create prng with api that matches BigInteger secure random
+ return {
+ // x is an array to fill with bytes
+ nextBytes: function(x) {
+ for(var i = 0; i < x.length; ++i) {
+ x[i] = Math.floor(Math.random() * 0xFF);
+ }
+ }
+ };
+}
+
+/**
+ * Returns the required number of Miller-Rabin tests to generate a
+ * prime with an error probability of (1/2)^80.
+ *
+ * See Handbook of Applied Cryptography Chapter 4, Table 4.4.
+ *
+ * @param bits the bit size.
+ *
+ * @return the required number of iterations.
+ */
+function _getMillerRabinTests(bits) {
+ if(bits <= 100) return 27;
+ if(bits <= 150) return 18;
+ if(bits <= 200) return 15;
+ if(bits <= 250) return 12;
+ if(bits <= 300) return 9;
+ if(bits <= 350) return 8;
+ if(bits <= 400) return 7;
+ if(bits <= 500) return 6;
+ if(bits <= 600) return 5;
+ if(bits <= 800) return 4;
+ if(bits <= 1250) return 3;
+ return 2;
+}