@noble/curves
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Audited & minimal JS implementation of elliptic curve cryptography
693 lines • 30.6 kB
JavaScript
/**
* Twisted Edwards curve. The formula is: ax² + y² = 1 + dx²y².
* For design rationale of types / exports, see weierstrass module documentation.
* Untwisted Edwards curves exist, but they aren't used in real-world protocols.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { abool, abytes, aInRange, asafenumber, bytesToHex, bytesToNumberLE, concatBytes, copyBytes, hexToBytes, isBytes, notImplemented, validateObject, randomBytes as wcRandomBytes, } from "../utils.js";
import { createCurveFields, createKeygen, normalizeZ, wNAF, } from "./curve.js";
import {} from "./modular.js";
// Be friendly to bad ECMAScript parsers by not using bigint literals
// prettier-ignore
const _0n = /* @__PURE__ */ BigInt(0), _1n = /* @__PURE__ */ BigInt(1), _2n = /* @__PURE__ */ BigInt(2), _8n = /* @__PURE__ */ BigInt(8);
// Affine Edwards-equation check only; this does not prove subgroup membership, canonical
// encoding, prime-order base-point requirements, or identity exclusion.
function isEdValidXY(Fp, CURVE, x, y) {
const x2 = Fp.sqr(x);
const y2 = Fp.sqr(y);
const left = Fp.add(Fp.mul(CURVE.a, x2), y2);
const right = Fp.add(Fp.ONE, Fp.mul(CURVE.d, Fp.mul(x2, y2)));
return Fp.eql(left, right);
}
/**
* @param params - Curve parameters. See {@link EdwardsOpts}.
* @param extraOpts - Optional helpers and overrides. See {@link EdwardsExtraOpts}.
* @returns Edwards point constructor. Generator validation here only checks
* that `(Gx, Gy)` satisfies the affine Edwards equation.
* RFC 8032 base-point constraints like `B != (0,1)` and `[L]B = 0`
* are left to the caller's chosen parameters, since eager subgroup
* validation here adds about 10-15ms to heavyweight imports like ed448.
* The returned constructor also eagerly marks `Point.BASE` for W=8
* precompute caching. Some code paths still assume
* `Fp.BYTES === Fn.BYTES`, so mismatched byte lengths are not fully audited here.
* @throws If the curve parameters or Edwards overrides are invalid. {@link Error}
* @example
* ```ts
* import { edwards } from '@noble/curves/abstract/edwards.js';
* import { jubjub } from '@noble/curves/misc.js';
* // Build a point constructor from explicit curve parameters, then use its base point.
* const Point = edwards(jubjub.Point.CURVE());
* Point.BASE.toHex();
* ```
*/
export function edwards(params, extraOpts = {}) {
const opts = extraOpts;
const validated = createCurveFields('edwards', params, opts, opts.FpFnLE);
const { Fp, Fn } = validated;
let CURVE = validated.CURVE;
const { h: cofactor } = CURVE;
validateObject(opts, {}, { uvRatio: 'function' });
// Important:
// There are some places where Fp.BYTES is used instead of nByteLength.
// So far, everything has been tested with curves of Fp.BYTES == nByteLength.
// TODO: test and find curves which behave otherwise.
const MASK = _2n << (BigInt(Fn.BYTES * 8) - _1n);
const modP = (n) => Fp.create(n); // Function overrides
// sqrt(u/v)
const uvRatio = opts.uvRatio === undefined
? (u, v) => {
try {
return { isValid: true, value: Fp.sqrt(Fp.div(u, v)) };
}
catch (e) {
return { isValid: false, value: _0n };
}
}
: opts.uvRatio;
// Validate whether the passed curve params are valid.
// equation ax² + y² = 1 + dx²y² should work for generator point.
if (!isEdValidXY(Fp, CURVE, CURVE.Gx, CURVE.Gy))
throw new Error('bad curve params: generator point');
/**
* Asserts coordinate is valid: 0 <= n < MASK.
* Coordinates >= Fp.ORDER are allowed for zip215.
*/
function acoord(title, n, banZero = false) {
const min = banZero ? _1n : _0n;
aInRange('coordinate ' + title, n, min, MASK);
return n;
}
function aedpoint(other) {
if (!(other instanceof Point))
throw new Error('EdwardsPoint 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 {
// base / generator point
static BASE = new Point(CURVE.Gx, CURVE.Gy, _1n, modP(CURVE.Gx * CURVE.Gy));
// zero / infinity / identity point
static ZERO = new Point(_0n, _1n, _1n, _0n); // 0, 1, 1, 0
// math field
static Fp = Fp;
// scalar field
static Fn = Fn;
X;
Y;
Z;
T;
constructor(X, Y, Z, T) {
this.X = acoord('x', X);
this.Y = acoord('y', Y);
this.Z = acoord('z', Z, true);
this.T = acoord('t', T);
Object.freeze(this);
}
static CURVE() {
return CURVE;
}
/**
* Create one extended Edwards point from affine coordinates.
* Does NOT validate that the point is on-curve or torsion-free.
* Use `.assertValidity()` on adversarial inputs.
*/
static fromAffine(p) {
if (p instanceof Point)
throw new Error('extended point not allowed');
const { x, y } = p || {};
acoord('x', x);
acoord('y', y);
return new Point(x, y, _1n, modP(x * y));
}
// Uses algo from RFC8032 5.1.3.
static fromBytes(bytes, zip215 = false) {
const len = Fp.BYTES;
const { a, d } = CURVE;
bytes = copyBytes(abytes(bytes, len, 'point'));
abool(zip215, 'zip215');
const normed = copyBytes(bytes); // copy again, we'll manipulate it
const lastByte = bytes[len - 1]; // select last byte
normed[len - 1] = lastByte & ~0x80; // clear last bit
const y = bytesToNumberLE(normed);
// zip215=true is good for consensus-critical apps. =false follows RFC8032 / NIST186-5.
// RFC8032 prohibits >= p, but ZIP215 doesn't
// zip215=true: 0 <= y < MASK (2^256 for ed25519)
// zip215=false: 0 <= y < P (2^255-19 for ed25519)
const max = zip215 ? MASK : Fp.ORDER;
aInRange('point.y', y, _0n, max);
// 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('bad point: 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('bad point: 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 fromHex(hex, zip215 = false) {
return Point.fromBytes(hexToBytes(hex), zip215);
}
get x() {
return this.toAffine().x;
}
get y() {
return this.toAffine().y;
}
precompute(windowSize = 8, isLazy = true) {
wnaf.createCache(this, windowSize);
if (!isLazy)
this.multiply(_2n); // random number
return this;
}
// Useful in fromAffine() - not for fromBytes(), which always created valid points.
assertValidity() {
const p = this;
const { a, d } = CURVE;
// Keep generic Edwards validation fail-closed on the neutral point.
// Even though ZERO is algebraically valid and can roundtrip through encodings, higher-level
// callers often reach it only through broken hash/scalar plumbing; rejecting it here avoids
// silently treating that degenerate state as an ordinary public point.
if (p.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 { X, Y, Z, T } = p;
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) {
aedpoint(other);
const { X: X1, Y: Y1, Z: Z1 } = this;
const { X: X2, Y: Y2, Z: 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.X), this.Y, this.Z, modP(-this.T));
}
// 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 { X: X1, Y: Y1, Z: 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) {
aedpoint(other);
const { a, d } = CURVE;
const { X: X1, Y: Y1, Z: Z1, T: T1 } = this;
const { X: X2, Y: Y2, Z: Z2, T: T2 } = other;
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) {
// Validate before calling `negate()` so wrong inputs fail with the point guard
// instead of leaking a foreign `negate()` error.
aedpoint(other);
return this.add(other.negate());
}
// Constant-time multiplication.
multiply(scalar) {
// 1 <= scalar < L
// Keep the subgroup-scalar contract strict instead of reducing 0 / n to ZERO.
// In keygen/signing-style callers, those values usually mean broken hash/scalar plumbing,
// and failing closed is safer than silently producing the identity point.
if (!Fn.isValidNot0(scalar))
throw new RangeError('invalid scalar: expected 1 <= sc < curve.n');
const { p, f } = wnaf.cached(this, scalar, (p) => normalizeZ(Point, p));
return normalizeZ(Point, [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.
// Keeps the same subgroup-scalar contract: 0 is allowed for public-scalar callers, but
// n and larger values are rejected instead of being reduced mod n to the identity point.
multiplyUnsafe(scalar) {
// 0 <= scalar < L
if (!Fn.isValid(scalar))
throw new RangeError('invalid scalar: expected 0 <= sc < curve.n');
if (scalar === _0n)
return Point.ZERO;
if (this.is0() || scalar === _1n)
return this;
return wnaf.unsafe(this, scalar, (p) => normalizeZ(Point, p));
}
// Checks if point is of small order.
// If you add something to small order point, you will have "dirty"
// point with torsion component.
// Clears cofactor and checks if the result is 0.
isSmallOrder() {
return this.clearCofactor().is0();
}
// Multiplies point by curve order and checks if the result is 0.
// Returns `false` is the point is dirty.
isTorsionFree() {
return wnaf.unsafe(this, CURVE.n).is0();
}
// Converts Extended point to default (x, y) coordinates.
// Can accept precomputed Z^-1 - for example, from invertBatch.
toAffine(invertedZ) {
const p = this;
let iz = invertedZ;
const { X, Y, Z } = p;
const is0 = p.is0();
if (iz == null)
iz = is0 ? _8n : Fp.inv(Z); // 8 was chosen arbitrarily
const x = modP(X * iz);
const y = modP(Y * iz);
const zz = Fp.mul(Z, iz);
if (is0)
return { x: _0n, y: _1n };
if (zz !== _1n)
throw new Error('invZ was invalid');
return { x, y };
}
clearCofactor() {
if (cofactor === _1n)
return this;
return this.multiplyUnsafe(cofactor);
}
toBytes() {
const { x, y } = this.toAffine();
// Fp.toBytes() allows non-canonical encoding of y (>= p).
const bytes = Fp.toBytes(y);
// Each y has 2 valid points: (x, y), (x,-y).
// When compressing, it's enough to store y and use the last byte to encode sign of x
bytes[bytes.length - 1] |= x & _1n ? 0x80 : 0;
return bytes;
}
toHex() {
return bytesToHex(this.toBytes());
}
toString() {
return `<Point ${this.is0() ? 'ZERO' : this.toHex()}>`;
}
}
const wnaf = new wNAF(Point, Fn.BITS);
// Keep constructor work cheap: subgroup/generator validation belongs to the caller's curve
// parameters, and doing the extra checks here adds about 10-15ms to heavy module imports.
// Callers that construct custom curves are responsible for supplying the correct base point.
// try {
// Point.BASE.assertValidity();
// if (!Point.BASE.isTorsionFree()) throw new Error('bad point: not in prime-order subgroup');
// } catch {
// throw new Error('bad curve params: generator point');
// }
// Tiny toy curves can have scalar fields narrower than 8 bits. Skip the
// eager W=8 cache there instead of rejecting an otherwise valid constructor.
if (Fn.BITS >= 8)
Point.BASE.precompute(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
Object.freeze(Point.prototype);
Object.freeze(Point);
return Point;
}
/**
* Base class for prime-order points like Ristretto255 and Decaf448.
* These points eliminate cofactor issues by representing equivalence classes
* of Edwards curve points. Multiple Edwards representatives can describe the
* same abstract wrapper element, so wrapper validity is not the same thing as
* the hidden representative being torsion-free.
* @param ep - Backing Edwards point.
* @example
* Base class for prime-order points like Ristretto255 and Decaf448.
*
* ```ts
* import { ristretto255 } from '@noble/curves/ed25519.js';
* const point = ristretto255.Point.BASE.multiply(2n);
* ```
*/
export class PrimeEdwardsPoint {
static BASE;
static ZERO;
static Fp;
static Fn;
ep;
/**
* Wrap one internal Edwards representative directly.
* This is not a canonical encoding boundary: alternate Edwards
* representatives may still describe the same abstract wrapper element.
*/
constructor(ep) {
this.ep = ep;
}
// Static methods that must be implemented by subclasses
static fromBytes(_bytes) {
notImplemented();
}
static fromHex(_hex) {
notImplemented();
}
get x() {
return this.toAffine().x;
}
get y() {
return this.toAffine().y;
}
// Common implementations
clearCofactor() {
// no-op for the abstract prime-order wrapper group; this is about the
// wrapper element, not the hidden Edwards representative.
return this;
}
assertValidity() {
// Keep wrapper validity at the abstract-group boundary. Canonical decode
// may choose Edwards representatives that differ by small torsion, so
// checking `this.ep.isTorsionFree()` here would reject valid wrapper points.
this.ep.assertValidity();
}
/**
* Return affine coordinates of the current internal Edwards representative.
* This is a convenience helper, not a canonical Ristretto/Decaf encoding.
* Equal abstract elements may expose different `x` / `y`; use
* `toBytes()` / `fromBytes()` for canonical roundtrips.
*/
toAffine(invertedZ) {
return this.ep.toAffine(invertedZ);
}
toHex() {
return bytesToHex(this.toBytes());
}
toString() {
return this.toHex();
}
isTorsionFree() {
// Abstract Ristretto/Decaf elements are already prime-order even when the
// hidden Edwards representative is not torsion-free.
return true;
}
isSmallOrder() {
return false;
}
add(other) {
this.assertSame(other);
return this.init(this.ep.add(other.ep));
}
subtract(other) {
this.assertSame(other);
return this.init(this.ep.subtract(other.ep));
}
multiply(scalar) {
return this.init(this.ep.multiply(scalar));
}
multiplyUnsafe(scalar) {
return this.init(this.ep.multiplyUnsafe(scalar));
}
double() {
return this.init(this.ep.double());
}
negate() {
return this.init(this.ep.negate());
}
precompute(windowSize, isLazy) {
this.ep.precompute(windowSize, isLazy);
// Keep the wrapper identity stable like the backing Edwards API instead of
// allocating a fresh wrapper around the same cached point.
return this;
}
}
/**
* Initializes EdDSA signatures over given Edwards curve.
* @param Point - Edwards point constructor.
* @param cHash - Hash function.
* @param eddsaOpts - Optional signature helpers. See {@link EdDSAOpts}.
* @returns EdDSA helper namespace.
* @throws If the hash function, options, or derived point operations are invalid. {@link Error}
* @example
* Initializes EdDSA signatures over given Edwards curve.
*
* ```ts
* import { eddsa } from '@noble/curves/abstract/edwards.js';
* import { jubjub } from '@noble/curves/misc.js';
* import { sha512 } from '@noble/hashes/sha2.js';
* const sigs = eddsa(jubjub.Point, sha512);
* const { secretKey, publicKey } = sigs.keygen();
* const msg = new TextEncoder().encode('hello noble');
* const sig = sigs.sign(msg, secretKey);
* const isValid = sigs.verify(sig, msg, publicKey);
* ```
*/
export function eddsa(Point, cHash, eddsaOpts = {}) {
if (typeof cHash !== 'function')
throw new Error('"hash" function param is required');
const hash = cHash;
const opts = eddsaOpts;
validateObject(opts, {}, {
adjustScalarBytes: 'function',
randomBytes: 'function',
domain: 'function',
prehash: 'function',
zip215: 'boolean',
mapToCurve: 'function',
});
const { prehash } = opts;
const { BASE, Fp, Fn } = Point;
const outputLen = hash.outputLen;
const expectedLen = 2 * Fp.BYTES;
// When hash metadata is available, reject incompatible EdDSA wrappers at construction time
// instead of deferring the mismatch until the first keygen/sign call.
if (outputLen !== undefined) {
asafenumber(outputLen, 'hash.outputLen');
if (outputLen !== expectedLen)
throw new Error(`hash.outputLen must be ${expectedLen}, got ${outputLen}`);
}
const randomBytes = opts.randomBytes === undefined ? wcRandomBytes : opts.randomBytes;
const adjustScalarBytes = opts.adjustScalarBytes === undefined
? (bytes) => bytes
: opts.adjustScalarBytes;
const domain = opts.domain === undefined
? (data, ctx, phflag) => {
abool(phflag, 'phflag');
if (ctx.length || phflag)
throw new Error('Contexts/pre-hash are not supported');
return data;
}
: opts.domain; // NOOP
// Parse an EdDSA digest as a little-endian integer and reduce it modulo the scalar field order.
function modN_LE(hash) {
return Fn.create(bytesToNumberLE(hash)); // Not Fn.fromBytes: it has length limit
}
// Get the hashed private scalar per RFC8032 5.1.5
function getPrivateScalar(key) {
const len = lengths.secretKey;
abytes(key, lengths.secretKey, 'secretKey');
// Hash private key with curve's hash function to produce uniformingly random input
// Check byte lengths: ensure(64, h(ensure(32, key)))
const hashed = abytes(hash(key), 2 * len, 'hashedSecretKey');
// Slice before clamping so in-place adjustors don't corrupt the prefix half.
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
return { head, prefix, scalar };
}
/** Convenience method that creates public key from scalar. RFC8032 5.1.5
* Also exposes the derived scalar/prefix tuple and point form reused by sign().
*/
function getExtendedPublicKey(secretKey) {
const { head, prefix, scalar } = getPrivateScalar(secretKey);
const point = BASE.multiply(scalar); // Point on Edwards curve aka public key
const pointBytes = point.toBytes();
return { head, prefix, scalar, point, pointBytes };
}
/** Calculates EdDSA pub key. RFC8032 5.1.5. */
function getPublicKey(secretKey) {
return getExtendedPublicKey(secretKey).pointBytes;
}
// Hash domain-separated chunks into a little-endian scalar modulo the group order.
function hashDomainToScalar(context = Uint8Array.of(), ...msgs) {
const msg = concatBytes(...msgs);
return modN_LE(hash(domain(msg, abytes(context, undefined, 'context'), !!prehash)));
}
/** Signs message with secret key. RFC8032 5.1.6 */
function sign(msg, secretKey, options = {}) {
msg = abytes(msg, undefined, 'message');
if (prehash)
msg = prehash(msg); // for ed25519ph etc.
const { prefix, scalar, pointBytes } = getExtendedPublicKey(secretKey);
const r = hashDomainToScalar(options.context, prefix, msg); // r = dom2(F, C) || prefix || PH(M)
// RFC 8032 5.1.6 allows r mod L = 0, and SUPERCOP ref10 accepts the resulting identity-point
// signature.
// We intentionally keep the safe multiply() rejection here so a miswired all-zero hash provider
// fails loudly instead of silently producing a degenerate signature.
const R = BASE.multiply(r).toBytes(); // R = rG
const k = hashDomainToScalar(options.context, R, pointBytes, msg); // R || A || PH(M)
const s = Fn.create(r + k * scalar); // S = (r + k * s) mod L
if (!Fn.isValid(s))
throw new Error('sign failed: invalid s'); // 0 <= s < L
const rs = concatBytes(R, Fn.toBytes(s));
return abytes(rs, lengths.signature, 'result');
}
// Keep the shared helper strict by default: RFC 8032 / NIST-style wrappers should reject
// non-canonical encodings unless they explicitly opt into ZIP-215's more permissive decode rules.
const verifyOpts = {
zip215: opts.zip215,
};
/**
* Verifies EdDSA signature against message and public key. RFC 8032 §§5.1.7 and 5.2.7.
* A cofactored verification equation is checked.
*/
function verify(sig, msg, publicKey, options = verifyOpts) {
// Preserve the wrapper-selected default for `{}` / `{ zip215: undefined }`, not just omitted opts.
const { context } = options;
const zip215 = options.zip215 === undefined ? !!verifyOpts.zip215 : options.zip215;
const len = lengths.signature;
sig = abytes(sig, len, 'signature');
msg = abytes(msg, undefined, 'message');
publicKey = abytes(publicKey, lengths.publicKey, 'publicKey');
if (zip215 !== undefined)
abool(zip215, 'zip215');
if (prehash)
msg = prehash(msg); // for ed25519ph, etc
const mid = len / 2;
const r = sig.subarray(0, mid);
const s = bytesToNumberLE(sig.subarray(mid, len));
let A, R, SB;
try {
// ZIP-215 is more permissive than RFC 8032 / NIST186-5. Use it only for wrappers that
// explicitly want consensus-style unreduced encoding acceptance.
// zip215=true: 0 <= y < MASK (2^256 for ed25519)
// zip215=false: 0 <= y < P (2^255-19 for ed25519)
A = Point.fromBytes(publicKey, zip215);
R = Point.fromBytes(r, zip215);
SB = BASE.multiplyUnsafe(s); // 0 <= s < l is done inside
}
catch (error) {
return false;
}
// RFC 8032 §§5.1.7/5.2.7 and FIPS 186-5 §§7.7.2/7.8.2 only decode A' and check the cofactored
// verification equation; they do not add a separate low-order-public-key rejection here.
// Strict mode still rejects small-order A' intentionally for SBS-style non-repudiation and to
// avoid ambiguous verification outcomes where unusual low-order keys can make distinct
// key/signature/message combinations verify.
if (!zip215 && A.isSmallOrder())
return false;
// ZIP-215 accepts noncanonical / unreduced point encodings, so the challenge hash must use the
// exact signature/public-key bytes rather than canonicalized re-encodings of the decoded points.
const k = hashDomainToScalar(context, r, publicKey, msg);
const RkA = R.add(A.multiplyUnsafe(k));
// Check the cofactored verification equation via the curve cofactor h.
// [h][S]B = [h]R + [h][k]A'
return RkA.subtract(SB).clearCofactor().is0();
}
const _size = Fp.BYTES; // 32 for ed25519, 57 for ed448
const lengths = {
secretKey: _size,
publicKey: _size,
signature: 2 * _size,
seed: _size,
};
function randomSecretKey(seed) {
seed = seed === undefined ? randomBytes(lengths.seed) : seed;
return abytes(seed, lengths.seed, 'seed');
}
function isValidSecretKey(key) {
return isBytes(key) && key.length === lengths.secretKey;
}
function isValidPublicKey(key, zip215) {
try {
// Preserve the wrapper-selected default for omitted / `undefined` ZIP-215 flags here too.
return !!Point.fromBytes(key, zip215 === undefined ? verifyOpts.zip215 : zip215);
}
catch (error) {
return false;
}
}
const utils = {
getExtendedPublicKey,
randomSecretKey,
isValidSecretKey,
isValidPublicKey,
/**
* Converts ed public key to x public key. Uses formula:
* - ed25519:
* - `(u, v) = ((1+y)/(1-y), sqrt(-486664)*u/x)`
* - `(x, y) = (sqrt(-486664)*u/v, (u-1)/(u+1))`
* - ed448:
* - `(u, v) = ((y-1)/(y+1), sqrt(156324)*u/x)`
* - `(x, y) = (sqrt(156324)*u/v, (1+u)/(1-u))`
*/
toMontgomery(publicKey) {
const { y } = Point.fromBytes(publicKey);
const size = lengths.publicKey;
const is25519 = size === 32;
if (!is25519 && size !== 57)
throw new Error('only defined for 25519 and 448');
const u = is25519 ? Fp.div(_1n + y, _1n - y) : Fp.div(y - _1n, y + _1n);
return Fp.toBytes(u);
},
toMontgomerySecret(secretKey) {
const size = lengths.secretKey;
abytes(secretKey, size);
const hashed = hash(secretKey.subarray(0, size));
return adjustScalarBytes(hashed).subarray(0, size);
},
};
Object.freeze(lengths);
Object.freeze(utils);
return Object.freeze({
keygen: createKeygen(randomSecretKey, getPublicKey),
getPublicKey,
sign,
verify,
utils,
Point,
lengths,
});
}
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