bot-28/node/node_modules/@noble/curves/esm/abstract/edwards.js

/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// Twisted Edwards curve. The formula is: ax² + y² = 1 + dx²y²
import { validateBasic, wNAF } from './curve.js';
import { mod } from './modular.js';
import * as ut from './utils.js';
import { ensureBytes } from './utils.js';
// Be friendly to bad ECMAScript parsers by not using bigint literals
// prettier-ignore
const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _8n = BigInt(8);
// verification rule is either zip215 or rfc8032 / nist186-5. Consult fromHex:
const VERIFY_DEFAULT = { zip215: true };
function validateOpts(curve) {
    const opts = validateBasic(curve);
    ut.validateObject(curve, {
        hash: 'function',
        a: 'bigint',
        d: 'bigint',
        randomBytes: 'function',
    }, {
        adjustScalarBytes: 'function',
        domain: 'function',
        uvRatio: 'function',
        mapToCurve: 'function',
    });
    // Set defaults
    return Object.freeze({ ...opts });
}
// It is not generic twisted curve for now, but ed25519/ed448 generic implementation
export function twistedEdwards(curveDef) {
    const CURVE = validateOpts(curveDef);
    const { Fp, n: CURVE_ORDER, prehash: prehash, hash: cHash, randomBytes, nByteLength, h: cofactor, } = CURVE;
    const MASK = _2n << (BigInt(nByteLength * 8) - _1n);
    const modP = Fp.create; // Function overrides
    // sqrt(u/v)
    const uvRatio = CURVE.uvRatio ||
        ((u, v) => {
            try {
                return { isValid: true, value: Fp.sqrt(u * Fp.inv(v)) };
            }
            catch (e) {
                return { isValid: false, value: _0n };
            }
        });
    const adjustScalarBytes = CURVE.adjustScalarBytes || ((bytes) => bytes); // NOOP
    const domain = CURVE.domain ||
        ((data, ctx, phflag) => {
            if (ctx.length || phflag)
                throw new Error('Contexts/pre-hash are not supported');
            return data;
        }); // NOOP
    const inBig = (n) => typeof n === 'bigint' && _0n < n; // n in [1..]
    const inRange = (n, max) => inBig(n) && inBig(max) && n < max; // n in [1..max-1]
    const in0MaskRange = (n) => n === _0n || inRange(n, MASK); // n in [0..MASK-1]
    function assertInRange(n, max) {
        // n in [1..max-1]
        if (inRange(n, max))
            return n;
        throw new Error(`Expected valid scalar < ${max}, got ${typeof n} ${n}`);
    }
    function assertGE0(n) {
        // n in [0..CURVE_ORDER-1]
        return n === _0n ? n : assertInRange(n, CURVE_ORDER); // GE = prime subgroup, not full group
    }
    const pointPrecomputes = new Map();
    function isPoint(other) {
        if (!(other instanceof Point))
            throw new Error('ExtendedPoint expected');
    }
    // Extended Point works in extended coordinates: (x, y, z, t) ∋ (x=x/z, y=y/z, t=xy).
    // https://en.wikipedia.org/wiki/Twisted_Edwards_curve#Extended_coordinates
    class Point {
        constructor(ex, ey, ez, et) {
            this.ex = ex;
            this.ey = ey;
            this.ez = ez;
            this.et = et;
            if (!in0MaskRange(ex))
                throw new Error('x required');
            if (!in0MaskRange(ey))
                throw new Error('y required');
            if (!in0MaskRange(ez))
                throw new Error('z required');
            if (!in0MaskRange(et))
                throw new Error('t required');
        }
        get x() {
            return this.toAffine().x;
        }
        get y() {
            return this.toAffine().y;
        }
        static fromAffine(p) {
            if (p instanceof Point)
                throw new Error('extended point not allowed');
            const { x, y } = p || {};
            if (!in0MaskRange(x) || !in0MaskRange(y))
                throw new Error('invalid affine point');
            return new Point(x, y, _1n, modP(x * y));
        }
        static normalizeZ(points) {
            const toInv = Fp.invertBatch(points.map((p) => p.ez));
            return points.map((p, i) => p.toAffine(toInv[i])).map(Point.fromAffine);
        }
        // "Private method", don't use it directly
        _setWindowSize(windowSize) {
            this._WINDOW_SIZE = windowSize;
            pointPrecomputes.delete(this);
        }
        // Not required for fromHex(), which always creates valid points.
        // Could be useful for fromAffine().
        assertValidity() {
            const { a, d } = CURVE;
            if (this.is0())
                throw new Error('bad point: ZERO'); // TODO: optimize, with vars below?
            // Equation in affine coordinates: ax² + y² = 1 + dx²y²
            // Equation in projective coordinates (X/Z, Y/Z, Z):  (aX² + Y²)Z² = Z⁴ + dX²Y²
            const { ex: X, ey: Y, ez: Z, et: T } = this;
            const X2 = modP(X * X); // X²
            const Y2 = modP(Y * Y); // Y²
            const Z2 = modP(Z * Z); // Z²
            const Z4 = modP(Z2 * Z2); // Z⁴
            const aX2 = modP(X2 * a); // aX²
            const left = modP(Z2 * modP(aX2 + Y2)); // (aX² + Y²)Z²
            const right = modP(Z4 + modP(d * modP(X2 * Y2))); // Z⁴ + dX²Y²
            if (left !== right)
                throw new Error('bad point: equation left != right (1)');
            // In Extended coordinates we also have T, which is x*y=T/Z: check X*Y == Z*T
            const XY = modP(X * Y);
            const ZT = modP(Z * T);
            if (XY !== ZT)
                throw new Error('bad point: equation left != right (2)');
        }
        // Compare one point to another.
        equals(other) {
            isPoint(other);
            const { ex: X1, ey: Y1, ez: Z1 } = this;
            const { ex: X2, ey: Y2, ez: Z2 } = other;
            const X1Z2 = modP(X1 * Z2);
            const X2Z1 = modP(X2 * Z1);
            const Y1Z2 = modP(Y1 * Z2);
            const Y2Z1 = modP(Y2 * Z1);
            return X1Z2 === X2Z1 && Y1Z2 === Y2Z1;
        }
        is0() {
            return this.equals(Point.ZERO);
        }
        negate() {
            // Flips point sign to a negative one (-x, y in affine coords)
            return new Point(modP(-this.ex), this.ey, this.ez, modP(-this.et));
        }
        // Fast algo for doubling Extended Point.
        // https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#doubling-dbl-2008-hwcd
        // Cost: 4M + 4S + 1*a + 6add + 1*2.
        double() {
            const { a } = CURVE;
            const { ex: X1, ey: Y1, ez: Z1 } = this;
            const A = modP(X1 * X1); // A = X12
            const B = modP(Y1 * Y1); // B = Y12
            const C = modP(_2n * modP(Z1 * Z1)); // C = 2*Z12
            const D = modP(a * A); // D = a*A
            const x1y1 = X1 + Y1;
            const E = modP(modP(x1y1 * x1y1) - A - B); // E = (X1+Y1)2-A-B
            const G = D + B; // G = D+B
            const F = G - C; // F = G-C
            const H = D - B; // H = D-B
            const X3 = modP(E * F); // X3 = E*F
            const Y3 = modP(G * H); // Y3 = G*H
            const T3 = modP(E * H); // T3 = E*H
            const Z3 = modP(F * G); // Z3 = F*G
            return new Point(X3, Y3, Z3, T3);
        }
        // Fast algo for adding 2 Extended Points.
        // https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#addition-add-2008-hwcd
        // Cost: 9M + 1*a + 1*d + 7add.
        add(other) {
            isPoint(other);
            const { a, d } = CURVE;
            const { ex: X1, ey: Y1, ez: Z1, et: T1 } = this;
            const { ex: X2, ey: Y2, ez: Z2, et: T2 } = other;
            // Faster algo for adding 2 Extended Points when curve's a=-1.
            // http://hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#addition-add-2008-hwcd-4
            // Cost: 8M + 8add + 2*2.
            // Note: It does not check whether the `other` point is valid.
            if (a === BigInt(-1)) {
                const A = modP((Y1 - X1) * (Y2 + X2));
                const B = modP((Y1 + X1) * (Y2 - X2));
                const F = modP(B - A);
                if (F === _0n)
                    return this.double(); // Same point. Tests say it doesn't affect timing
                const C = modP(Z1 * _2n * T2);
                const D = modP(T1 * _2n * Z2);
                const E = D + C;
                const G = B + A;
                const H = D - C;
                const X3 = modP(E * F);
                const Y3 = modP(G * H);
                const T3 = modP(E * H);
                const Z3 = modP(F * G);
                return new Point(X3, Y3, Z3, T3);
            }
            const A = modP(X1 * X2); // A = X1*X2
            const B = modP(Y1 * Y2); // B = Y1*Y2
            const C = modP(T1 * d * T2); // C = T1*d*T2
            const D = modP(Z1 * Z2); // D = Z1*Z2
            const E = modP((X1 + Y1) * (X2 + Y2) - A - B); // E = (X1+Y1)*(X2+Y2)-A-B
            const F = D - C; // F = D-C
            const G = D + C; // G = D+C
            const H = modP(B - a * A); // H = B-a*A
            const X3 = modP(E * F); // X3 = E*F
            const Y3 = modP(G * H); // Y3 = G*H
            const T3 = modP(E * H); // T3 = E*H
            const Z3 = modP(F * G); // Z3 = F*G
            return new Point(X3, Y3, Z3, T3);
        }
        subtract(other) {
            return this.add(other.negate());
        }
        wNAF(n) {
            return wnaf.wNAFCached(this, pointPrecomputes, n, Point.normalizeZ);
        }
        // Constant-time multiplication.
        multiply(scalar) {
            const { p, f } = this.wNAF(assertInRange(scalar, CURVE_ORDER));
            return Point.normalizeZ([p, f])[0];
        }
        // Non-constant-time multiplication. Uses double-and-add algorithm.
        // It's faster, but should only be used when you don't care about
        // an exposed private key e.g. sig verification.
        // Does NOT allow scalars higher than CURVE.n.
        multiplyUnsafe(scalar) {
            let n = assertGE0(scalar); // 0 <= scalar < CURVE.n
            if (n === _0n)
                return I;
            if (this.equals(I) || n === _1n)
                return this;
            if (this.equals(G))
                return this.wNAF(n).p;
            return wnaf.unsafeLadder(this, n);
        }
        // Checks if point is of small order.
        // If you add something to small order point, you will have "dirty"
        // point with torsion component.
        // Multiplies point by cofactor and checks if the result is 0.
        isSmallOrder() {
            return this.multiplyUnsafe(cofactor).is0();
        }
        // Multiplies point by curve order and checks if the result is 0.
        // Returns `false` is the point is dirty.
        isTorsionFree() {
            return wnaf.unsafeLadder(this, CURVE_ORDER).is0();
        }
        // Converts Extended point to default (x, y) coordinates.
        // Can accept precomputed Z^-1 - for example, from invertBatch.
        toAffine(iz) {
            const { ex: x, ey: y, ez: z } = this;
            const is0 = this.is0();
            if (iz == null)
                iz = is0 ? _8n : Fp.inv(z); // 8 was chosen arbitrarily
            const ax = modP(x * iz);
            const ay = modP(y * iz);
            const zz = modP(z * iz);
            if (is0)
                return { x: _0n, y: _1n };
            if (zz !== _1n)
                throw new Error('invZ was invalid');
            return { x: ax, y: ay };
        }
        clearCofactor() {
            const { h: cofactor } = CURVE;
            if (cofactor === _1n)
                return this;
            return this.multiplyUnsafe(cofactor);
        }
        // Converts hash string or Uint8Array to Point.
        // Uses algo from RFC8032 5.1.3.
        static fromHex(hex, zip215 = false) {
            const { d, a } = CURVE;
            const len = Fp.BYTES;
            hex = ensureBytes('pointHex', hex, len); // copy hex to a new array
            const normed = hex.slice(); // copy again, we'll manipulate it
            const lastByte = hex[len - 1]; // select last byte
            normed[len - 1] = lastByte & ~0x80; // clear last bit
            const y = ut.bytesToNumberLE(normed);
            if (y === _0n) {
                // y=0 is allowed
            }
            else {
                // RFC8032 prohibits >= p, but ZIP215 doesn't
                if (zip215)
                    assertInRange(y, MASK); // zip215=true [1..P-1] (2^255-19-1 for ed25519)
                else
                    assertInRange(y, Fp.ORDER); // zip215=false [1..MASK-1] (2^256-1 for ed25519)
            }
            // Ed25519: x² = (y²-1)/(dy²+1) mod p. Ed448: x² = (y²-1)/(dy²-1) mod p. Generic case:
            // ax²+y²=1+dx²y² => y²-1=dx²y²-ax² => y²-1=x²(dy²-a) => x²=(y²-1)/(dy²-a)
            const y2 = modP(y * y); // denominator is always non-0 mod p.
            const u = modP(y2 - _1n); // u = y² - 1
            const v = modP(d * y2 - a); // v = d y² + 1.
            let { isValid, value: x } = uvRatio(u, v); // √(u/v)
            if (!isValid)
                throw new Error('Point.fromHex: invalid y coordinate');
            const isXOdd = (x & _1n) === _1n; // There are 2 square roots. Use x_0 bit to select proper
            const isLastByteOdd = (lastByte & 0x80) !== 0; // x_0, last bit
            if (!zip215 && x === _0n && isLastByteOdd)
                // if x=0 and x_0 = 1, fail
                throw new Error('Point.fromHex: x=0 and x_0=1');
            if (isLastByteOdd !== isXOdd)
                x = modP(-x); // if x_0 != x mod 2, set x = p-x
            return Point.fromAffine({ x, y });
        }
        static fromPrivateKey(privKey) {
            return getExtendedPublicKey(privKey).point;
        }
        toRawBytes() {
            const { x, y } = this.toAffine();
            const bytes = ut.numberToBytesLE(y, Fp.BYTES); // each y has 2 x values (x, -y)
            bytes[bytes.length - 1] |= x & _1n ? 0x80 : 0; // when compressing, it's enough to store y
            return bytes; // and use the last byte to encode sign of x
        }
        toHex() {
            return ut.bytesToHex(this.toRawBytes()); // Same as toRawBytes, but returns string.
        }
    }
    Point.BASE = new Point(CURVE.Gx, CURVE.Gy, _1n, modP(CURVE.Gx * CURVE.Gy));
    Point.ZERO = new Point(_0n, _1n, _1n, _0n); // 0, 1, 1, 0
    const { BASE: G, ZERO: I } = Point;
    const wnaf = wNAF(Point, nByteLength * 8);
    function modN(a) {
        return mod(a, CURVE_ORDER);
    }
    // Little-endian SHA512 with modulo n
    function modN_LE(hash) {
        return modN(ut.bytesToNumberLE(hash));
    }
    /** Convenience method that creates public key and other stuff. RFC8032 5.1.5 */
    function getExtendedPublicKey(key) {
        const len = nByteLength;
        key = ensureBytes('private key', key, len);
        // Hash private key with curve's hash function to produce uniformingly random input
        // Check byte lengths: ensure(64, h(ensure(32, key)))
        const hashed = ensureBytes('hashed private key', cHash(key), 2 * len);
        const head = adjustScalarBytes(hashed.slice(0, len)); // clear first half bits, produce FE
        const prefix = hashed.slice(len, 2 * len); // second half is called key prefix (5.1.6)
        const scalar = modN_LE(head); // The actual private scalar
        const point = G.multiply(scalar); // Point on Edwards curve aka public key
        const pointBytes = point.toRawBytes(); // Uint8Array representation
        return { head, prefix, scalar, point, pointBytes };
    }
    // Calculates EdDSA pub key. RFC8032 5.1.5. Privkey is hashed. Use first half with 3 bits cleared
    function getPublicKey(privKey) {
        return getExtendedPublicKey(privKey).pointBytes;
    }
    // int('LE', SHA512(dom2(F, C) || msgs)) mod N
    function hashDomainToScalar(context = new Uint8Array(), ...msgs) {
        const msg = ut.concatBytes(...msgs);
        return modN_LE(cHash(domain(msg, ensureBytes('context', context), !!prehash)));
    }
    /** Signs message with privateKey. RFC8032 5.1.6 */
    function sign(msg, privKey, options = {}) {
        msg = ensureBytes('message', msg);
        if (prehash)
            msg = prehash(msg); // for ed25519ph etc.
        const { prefix, scalar, pointBytes } = getExtendedPublicKey(privKey);
        const r = hashDomainToScalar(options.context, prefix, msg); // r = dom2(F, C) || prefix || PH(M)
        const R = G.multiply(r).toRawBytes(); // R = rG
        const k = hashDomainToScalar(options.context, R, pointBytes, msg); // R || A || PH(M)
        const s = modN(r + k * scalar); // S = (r + k * s) mod L
        assertGE0(s); // 0 <= s < l
        const res = ut.concatBytes(R, ut.numberToBytesLE(s, Fp.BYTES));
        return ensureBytes('result', res, nByteLength * 2); // 64-byte signature
    }
    const verifyOpts = VERIFY_DEFAULT;
    function verify(sig, msg, publicKey, options = verifyOpts) {
        const { context, zip215 } = options;
        const len = Fp.BYTES; // Verifies EdDSA signature against message and public key. RFC8032 5.1.7.
        sig = ensureBytes('signature', sig, 2 * len); // An extended group equation is checked.
        msg = ensureBytes('message', msg);
        if (prehash)
            msg = prehash(msg); // for ed25519ph, etc
        const s = ut.bytesToNumberLE(sig.slice(len, 2 * len));
        // zip215: true is good for consensus-critical apps and allows points < 2^256
        // zip215: false follows RFC8032 / NIST186-5 and restricts points to CURVE.p
        let A, R, SB;
        try {
            A = Point.fromHex(publicKey, zip215);
            R = Point.fromHex(sig.slice(0, len), zip215);
            SB = G.multiplyUnsafe(s); // 0 <= s < l is done inside
        }
        catch (error) {
            return false;
        }
        if (!zip215 && A.isSmallOrder())
            return false;
        const k = hashDomainToScalar(context, R.toRawBytes(), A.toRawBytes(), msg);
        const RkA = R.add(A.multiplyUnsafe(k));
        // [8][S]B = [8]R + [8][k]A'
        return RkA.subtract(SB).clearCofactor().equals(Point.ZERO);
    }
    G._setWindowSize(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
    const utils = {
        getExtendedPublicKey,
        // ed25519 private keys are uniform 32b. No need to check for modulo bias, like in secp256k1.
        randomPrivateKey: () => randomBytes(Fp.BYTES),
        /**
         * We're doing scalar multiplication (used in getPublicKey etc) with precomputed BASE_POINT
         * values. This slows down first getPublicKey() by milliseconds (see Speed section),
         * but allows to speed-up subsequent getPublicKey() calls up to 20x.
         * @param windowSize 2, 4, 8, 16
         */
        precompute(windowSize = 8, point = Point.BASE) {
            point._setWindowSize(windowSize);
            point.multiply(BigInt(3));
            return point;
        },
    };
    return {
        CURVE,
        getPublicKey,
        sign,
        verify,
        ExtendedPoint: Point,
        utils,
    };
}
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