arithmetic-operations-for/integers-modulo-n-big-endian

import assert from 'assert';

import {_mul as n_mul} from '@arithmetic-operations-for/naturals-big-endian';

import _redc from './_redc.js';

// TODO
// mul by non montgomery ?
// abR mod N = (aR mod N)(b mod N) MODULO????

/**
 *
 * abR mod N = REDC((aR mod N)(bR mod N))
 *
 *
 * |N| >= |a| >= |b|
 * |c| = 2*|N| + 1
 * c = 0000.0000 is zero initialized
 *
 */

export default function _mul(r, N, M, a, b, c) {
    const k = N.length;
    const _2kp1 = 2 * k + 1;

    assert(a.length <= k, '|a| > |N|');
    assert(b.length <= a.length, '|b| > |a|');
    assert(c.length === _2kp1, '|c| !== 2*k+1');

    // C = (aR mod N)(bR mod N)
    n_mul(
        r,
        a,
        0,
        a.length,
        b,
        0,
        b.length,
        c,
        _2kp1 - a.length - b.length,
        _2kp1,
    );

    // C = REDC((aR mod N)(bR mod N))
    return _redc(r, k, N, 0, k, M, 0, k, c, 0, _2kp1);
}