@bsv/sdk/dist/esm/src/primitives/MontgomoryMethod.js

BSV Blockchain Software Development Kit

import ReductionContext from './ReductionContext.js';
import BigNumber from './BigNumber.js';
/**
 * Represents a Montgomery reduction context, which is a mathematical method
 * for performing modular multiplication without division.
 *
 * Montgomery reduction is an algorithm used mainly in cryptography which can
 * help to speed up calculations in contexts where there are many repeated
 * computations.
 *
 * This class extends the `ReductionContext` class.
 *
 * @class MontgomoryMethod
 * @extends {ReductionContext}
 *
 * @property shift - The number of bits in the modulus.
 * @property r - The 2^shift, shifted left by the bit length of modulus `m`.
 * @property r2 - The square of `r` modulo `m`.
 * @property rinv - The modular multiplicative inverse of `r` mod `m`.
 * @property minv - The modular multiplicative inverse of `m` mod `r`.
 */
export default class MontgomoryMethod extends ReductionContext {
    shift;
    r;
    r2;
    rinv;
    minv;
    /**
     * @constructor
     * @param m - The modulus to be used for the Montgomery method reductions.
     */
    constructor(m) {
        super(m);
        this.shift = this.m.bitLength();
        if (this.shift % 26 !== 0) {
            this.shift += 26 - (this.shift % 26);
        }
        this.r = new BigNumber(1).iushln(this.shift);
        this.r2 = this.imod(this.r.sqr());
        this.rinv = this.r._invmp(this.m);
        this.minv = this.rinv.mul(this.r).isubn(1).div(this.m);
        this.minv = this.minv.umod(this.r);
        this.minv = this.r.sub(this.minv);
    }
    /**
     * Converts a number into the Montgomery domain.
     *
     * @method convertTo
     * @param num - The number to be converted into the Montgomery domain.
     * @returns The result of the conversion into the Montgomery domain.
     *
     * @example
     * const montMethod = new MontgomoryMethod(m);
     * const convertedNum = montMethod.convertTo(num);
     */
    convertTo(num) {
        return this.imod(num.ushln(this.shift));
    }
    /**
     * Converts a number from the Montgomery domain back to the original domain.
     *
     * @method convertFrom
     * @param num - The number to be converted from the Montgomery domain.
     * @returns The result of the conversion from the Montgomery domain.
     *
     * @example
     * const montMethod = new MontgomoryMethod(m);
     * const convertedNum = montMethod.convertFrom(num);
     */
    convertFrom(num) {
        const r = this.imod(num.mul(this.rinv));
        r.red = null;
        return r;
    }
    /**
     * Performs an in-place multiplication of two numbers in the Montgomery domain.
     *
     * @method imul
     * @param a - The first number to multiply.
     * @param b - The second number to multiply.
     * @returns The result of the in-place multiplication.
     *
     * @example
     * const montMethod = new MontgomoryMethod(m);
     * const product = montMethod.imul(a, b);
     */
    imul(a, b) {
        if (a.isZero() || b.isZero()) {
            a.words[0] = 0;
            a.length = 1;
            return a;
        }
        const t = a.imul(b);
        const c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m);
        const u = t.isub(c).iushrn(this.shift);
        let res = u;
        if (u.cmp(this.m) >= 0) {
            res = u.isub(this.m);
        }
        else if (u.cmpn(0) < 0) {
            res = u.iadd(this.m);
        }
        return res.forceRed(this);
    }
    /**
     * Performs the multiplication of two numbers in the Montgomery domain.
     *
     * @method mul
     * @param a - The first number to multiply.
     * @param b - The second number to multiply.
     * @returns The result of the multiplication.
     *
     * @example
     * const montMethod = new MontgomoryMethod(m);
     * const product = montMethod.mul(a, b);
     */
    mul(a, b) {
        if (a.isZero() || b.isZero())
            return new BigNumber(0).forceRed(this);
        const t = a.mul(b);
        const c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m);
        const u = t.isub(c).iushrn(this.shift);
        let res = u;
        if (u.cmp(this.m) >= 0) {
            res = u.isub(this.m);
        }
        else if (u.cmpn(0) < 0) {
            res = u.iadd(this.m);
        }
        return res.forceRed(this);
    }
    /**
     * Calculates the modular multiplicative inverse of a number in the Montgomery domain.
     *
     * @method invm
     * @param a - The number to compute the modular multiplicative inverse of.
     * @returns The modular multiplicative inverse of 'a'.
     *
     * @example
     * const montMethod = new MontgomoryMethod(m);
     * const inverse = montMethod.invm(a);
     */
    invm(a) {
        // (AR)^-1 * R^2 = (A^-1 * R^-1) * R^2 = A^-1 * R
        const res = this.imod(a._invmp(this.m).mul(this.r2));
        return res.forceRed(this);
    }
}
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