160 lines
6.4 KiB
JavaScript
160 lines
6.4 KiB
JavaScript
"use strict";
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Object.defineProperty(exports, "__esModule", { value: true });
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exports.montgomery = montgomery;
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/**
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* Montgomery curve methods. It's not really whole montgomery curve,
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* just bunch of very specific methods for X25519 / X448 from
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* [RFC 7748](https://www.rfc-editor.org/rfc/rfc7748)
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* @module
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*/
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/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
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const utils_ts_1 = require("../utils.js");
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const modular_ts_1 = require("./modular.js");
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const _0n = BigInt(0);
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const _1n = BigInt(1);
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const _2n = BigInt(2);
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function validateOpts(curve) {
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(0, utils_ts_1._validateObject)(curve, {
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adjustScalarBytes: 'function',
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powPminus2: 'function',
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});
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return Object.freeze({ ...curve });
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}
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function montgomery(curveDef) {
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const CURVE = validateOpts(curveDef);
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const { P, type, adjustScalarBytes, powPminus2, randomBytes: rand } = CURVE;
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const is25519 = type === 'x25519';
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if (!is25519 && type !== 'x448')
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throw new Error('invalid type');
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const randomBytes_ = rand || utils_ts_1.randomBytes;
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const montgomeryBits = is25519 ? 255 : 448;
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const fieldLen = is25519 ? 32 : 56;
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const Gu = is25519 ? BigInt(9) : BigInt(5);
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// RFC 7748 #5:
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// The constant a24 is (486662 - 2) / 4 = 121665 for curve25519/X25519 and
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// (156326 - 2) / 4 = 39081 for curve448/X448
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// const a = is25519 ? 156326n : 486662n;
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const a24 = is25519 ? BigInt(121665) : BigInt(39081);
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// RFC: x25519 "the resulting integer is of the form 2^254 plus
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// eight times a value between 0 and 2^251 - 1 (inclusive)"
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// x448: "2^447 plus four times a value between 0 and 2^445 - 1 (inclusive)"
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const minScalar = is25519 ? _2n ** BigInt(254) : _2n ** BigInt(447);
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const maxAdded = is25519
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? BigInt(8) * _2n ** BigInt(251) - _1n
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: BigInt(4) * _2n ** BigInt(445) - _1n;
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const maxScalar = minScalar + maxAdded + _1n; // (inclusive)
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const modP = (n) => (0, modular_ts_1.mod)(n, P);
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const GuBytes = encodeU(Gu);
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function encodeU(u) {
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return (0, utils_ts_1.numberToBytesLE)(modP(u), fieldLen);
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}
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function decodeU(u) {
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const _u = (0, utils_ts_1.ensureBytes)('u coordinate', u, fieldLen);
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// RFC: When receiving such an array, implementations of X25519
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// (but not X448) MUST mask the most significant bit in the final byte.
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if (is25519)
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_u[31] &= 127; // 0b0111_1111
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// RFC: Implementations MUST accept non-canonical values and process them as
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// if they had been reduced modulo the field prime. The non-canonical
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// values are 2^255 - 19 through 2^255 - 1 for X25519 and 2^448 - 2^224
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// - 1 through 2^448 - 1 for X448.
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return modP((0, utils_ts_1.bytesToNumberLE)(_u));
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}
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function decodeScalar(scalar) {
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return (0, utils_ts_1.bytesToNumberLE)(adjustScalarBytes((0, utils_ts_1.ensureBytes)('scalar', scalar, fieldLen)));
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}
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function scalarMult(scalar, u) {
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const pu = montgomeryLadder(decodeU(u), decodeScalar(scalar));
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// Some public keys are useless, of low-order. Curve author doesn't think
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// it needs to be validated, but we do it nonetheless.
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// https://cr.yp.to/ecdh.html#validate
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if (pu === _0n)
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throw new Error('invalid private or public key received');
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return encodeU(pu);
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}
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// Computes public key from private. By doing scalar multiplication of base point.
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function scalarMultBase(scalar) {
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return scalarMult(scalar, GuBytes);
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}
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// cswap from RFC7748 "example code"
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function cswap(swap, x_2, x_3) {
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// dummy = mask(swap) AND (x_2 XOR x_3)
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// Where mask(swap) is the all-1 or all-0 word of the same length as x_2
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// and x_3, computed, e.g., as mask(swap) = 0 - swap.
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const dummy = modP(swap * (x_2 - x_3));
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x_2 = modP(x_2 - dummy); // x_2 = x_2 XOR dummy
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x_3 = modP(x_3 + dummy); // x_3 = x_3 XOR dummy
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return { x_2, x_3 };
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}
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/**
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* Montgomery x-only multiplication ladder.
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* @param pointU u coordinate (x) on Montgomery Curve 25519
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* @param scalar by which the point would be multiplied
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* @returns new Point on Montgomery curve
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*/
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function montgomeryLadder(u, scalar) {
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(0, utils_ts_1.aInRange)('u', u, _0n, P);
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(0, utils_ts_1.aInRange)('scalar', scalar, minScalar, maxScalar);
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const k = scalar;
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const x_1 = u;
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let x_2 = _1n;
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let z_2 = _0n;
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let x_3 = u;
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let z_3 = _1n;
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let swap = _0n;
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for (let t = BigInt(montgomeryBits - 1); t >= _0n; t--) {
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const k_t = (k >> t) & _1n;
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swap ^= k_t;
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({ x_2, x_3 } = cswap(swap, x_2, x_3));
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({ x_2: z_2, x_3: z_3 } = cswap(swap, z_2, z_3));
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swap = k_t;
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const A = x_2 + z_2;
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const AA = modP(A * A);
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const B = x_2 - z_2;
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const BB = modP(B * B);
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const E = AA - BB;
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const C = x_3 + z_3;
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const D = x_3 - z_3;
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const DA = modP(D * A);
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const CB = modP(C * B);
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const dacb = DA + CB;
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const da_cb = DA - CB;
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x_3 = modP(dacb * dacb);
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z_3 = modP(x_1 * modP(da_cb * da_cb));
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x_2 = modP(AA * BB);
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z_2 = modP(E * (AA + modP(a24 * E)));
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}
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({ x_2, x_3 } = cswap(swap, x_2, x_3));
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({ x_2: z_2, x_3: z_3 } = cswap(swap, z_2, z_3));
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const z2 = powPminus2(z_2); // `Fp.pow(x, P - _2n)` is much slower equivalent
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return modP(x_2 * z2); // Return x_2 * (z_2^(p - 2))
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}
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const lengths = {
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secretKey: fieldLen,
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publicKey: fieldLen,
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seed: fieldLen,
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};
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const randomSecretKey = (seed = randomBytes_(fieldLen)) => {
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(0, utils_ts_1.abytes)(seed, lengths.seed);
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return seed;
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};
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function keygen(seed) {
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const secretKey = randomSecretKey(seed);
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return { secretKey, publicKey: scalarMultBase(secretKey) };
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}
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const utils = {
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randomSecretKey,
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randomPrivateKey: randomSecretKey,
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};
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return {
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keygen,
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getSharedSecret: (secretKey, publicKey) => scalarMult(secretKey, publicKey),
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getPublicKey: (secretKey) => scalarMultBase(secretKey),
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scalarMult,
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scalarMultBase,
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utils,
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GuBytes: GuBytes.slice(),
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lengths,
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};
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}
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//# sourceMappingURL=montgomery.js.map
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