jwk-rsa-compute-primes/factor.js

Compute p, q, dp, dq, and qi from e, d, and n for private JWKs without these parameters

import * as BN from 'bn.js';
import * as crypto from 'crypto';
const zero = new BN(0);
const one = new BN(1);
const two = new BN(2);
function rand(low, high) {
    let b;
    do {
        b = new BN(crypto.randomBytes(high.byteLength()));
    } while (b.cmp(low) <= 0 || b.cmp(high) >= 0);
    return b;
}
function odd(n) {
    if (n.cmp(zero) === 0) {
        return zero;
    }
    let r = n;
    while (r.isEven()) {
        r = r.div(two);
    }
    return r;
}
function rootOne(x, r, n) {
    let i = x.toRed(BN.red(n)).redPow(r).fromRed();
    let o = zero;
    while (i.cmp(one) !== 0) {
        o = i;
        i = i.mul(i).mod(n);
    }
    if (o.cmp(n.sub(one)) === 0) {
        return zero;
    }
    return o;
}
/**
 * Calculate primes using e, d, and n.
 * @param e
 * @param d
 * @param n
 * @return the two primes used. p will be greater than q.
 */
export function factor(e, d, n) {
    const k = e.mul(d).sub(one);
    const r = odd(k);
    let y;
    do {
        y = rootOne(rand(two, n), r, n);
    } while (y.cmp(zero) === 0);
    const p = y.sub(one).gcd(n);
    const q = n.div(p);
    return {
        p: p.gt(q) ? p : q,
        q: p.gt(q) ? q : p,
    };
}
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