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@noble/curves - npm Package Compare versions

Comparing version 0.5.1 to 0.5.2

8

lib/_shortw_utils.d.ts

@@ -50,6 +50,4 @@ import { randomBytes } from '@noble/hashes/utils';

getSharedSecret: (privateA: import("./abstract/utils.js").PrivKey, publicB: import("./abstract/weierstrass.js").PubKey, isCompressed?: boolean | undefined) => Uint8Array;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: {
lowS?: boolean | undefined;
extraEntropy?: (true | import("./abstract/utils.js").Hex) | undefined;
} | undefined) => import("./abstract/weierstrass.js").SignatureType;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
signUnhashed: (msg: Uint8Array, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
verify: (signature: import("./abstract/utils.js").Hex | import("./abstract/weierstrass.js").SignatureType, msgHash: import("./abstract/utils.js").Hex, publicKey: import("./abstract/weierstrass.js").PubKey, opts?: {

@@ -62,4 +60,2 @@ lowS?: boolean | undefined;

utils: {
mod: (a: bigint, b?: bigint | undefined) => bigint;
invert: (number: bigint, modulo?: bigint | undefined) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -66,0 +62,0 @@ _bigintToString: (num: bigint) => string;

25

lib/abstract/bls.d.ts
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
/**
* BLS (Barreto-Lynn-Scott) family of pairing-friendly curves.
* Implements BLS (Boneh-Lynn-Shacham) signatures.
* Consists of two curves: G1 and G2:
* - G1 is a subgroup of (x, y) E(Fq) over y² = x³ + 4.
* - G2 is a subgroup of ((x₁, x₂+i), (y₁, y₂+i)) E(Fq²) over y² = x³ + 4(1 + i) where i is √-1
* - Gt, created by bilinear (ate) pairing e(G1, G2), consists of p-th roots of unity in
* Fq^k where k is embedding degree. Only degree 12 is currently supported, 24 is not.
* Pairing is used to aggregate and verify signatures.
* We are using Fp for private keys (shorter) and Fp₂ for signatures (longer).
* Some projects may prefer to swap this relation, it is not supported for now.
*/
import * as mod from './modular.js';
import * as utils from './utils.js';
import * as ut from './utils.js';
import { Hex, PrivKey } from './utils.js';
import { htfOpts, stringToBytes, hash_to_field, expand_message_xmd } from './hash-to-curve.js';
import { htfOpts, stringToBytes, hash_to_field as hashToField, expand_message_xmd as expandMessageXMD } from './hash-to-curve.js';
import { CurvePointsType, PointType, CurvePointsRes } from './weierstrass.js';

@@ -37,3 +49,3 @@ declare type Fp = bigint;

htfDefaults: htfOpts;
hash: utils.CHash;
hash: ut.CHash;
randomBytes: (bytesLength?: number) => Uint8Array;

@@ -70,8 +82,5 @@ };

utils: {
bytesToHex: typeof utils.bytesToHex;
hexToBytes: typeof utils.hexToBytes;
stringToBytes: typeof stringToBytes;
hashToField: typeof hash_to_field;
expandMessageXMD: typeof expand_message_xmd;
mod: typeof mod.mod;
hashToField: typeof hashToField;
expandMessageXMD: typeof expandMessageXMD;
getDSTLabel: () => string;

@@ -78,0 +87,0 @@ setDSTLabel(newLabel: string): void;

93

lib/abstract/bls.js
"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
exports.bls = void 0;
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// Barreto-Lynn-Scott Curves. A family of pairing friendly curves, with embedding degree = 12 or 24
// NOTE: only 12 supported for now
// Constructed from pair of weierstrass curves, based pairing logic
const mod = require("./modular.js");
const utils_js_1 = require("./utils.js");
// Types
const utils_js_2 = require("./utils.js");
const ut = require("./utils.js");
const hash_to_curve_js_1 = require("./hash-to-curve.js");

@@ -16,8 +9,5 @@ const weierstrass_js_1 = require("./weierstrass.js");

// Fields looks pretty specific for curve, so for now we need to pass them with options
const Fp = CURVE.Fp;
const Fr = CURVE.Fr;
const Fp2 = CURVE.Fp2;
const Fp6 = CURVE.Fp6;
const Fp12 = CURVE.Fp12;
const BLS_X_LEN = (0, utils_js_1.bitLen)(CURVE.x);
const { Fp, Fr, Fp2, Fp6, Fp12 } = CURVE;
const BLS_X_LEN = ut.bitLen(CURVE.x);
const groupLen = 32; // TODO: calculate; hardcoded for now
// Pre-compute coefficients for sparse multiplication

@@ -46,3 +36,3 @@ // Point addition and point double calculations is reused for coefficients

Rz = Fp2.mul(t0, t4); // T0 * T4
if ((0, utils_js_1.bitGet)(CURVE.x, i)) {
if (ut.bitGet(CURVE.x, i)) {
// Addition

@@ -68,2 +58,3 @@ let t0 = Fp2.sub(Ry, Fp2.mul(Qy, Rz)); // Ry - Qy * Rz

function millerLoop(ell, g1) {
const { x } = CURVE;
const Px = g1[0];

@@ -75,3 +66,3 @@ const Py = g1[1];

f12 = Fp12.multiplyBy014(f12, E[0], Fp2.mul(E[1], Px), Fp2.mul(E[2], Py));
if ((0, utils_js_1.bitGet)(CURVE.x, i)) {
if (ut.bitGet(x, i)) {
j += 1;

@@ -86,21 +77,5 @@ const F = ell[j];

}
// bls12-381 is a construction of two curves:
// 1. Fp: (x, y)
// 2. Fp₂: ((x₁, x₂+i), (y₁, y₂+i)) - (complex numbers)
//
// Bilinear Pairing (ate pairing) is used to combine both elements into a paired one:
// Fp₁₂ = e(Fp, Fp2)
// where Fp₁₂ = 12-degree polynomial
// Pairing is used to verify signatures.
//
// We are using Fp for private keys (shorter) and Fp2 for signatures (longer).
// Some projects may prefer to swap this relation, it is not supported for now.
const htfDefaults = { ...CURVE.htfDefaults };
function isWithinCurveOrder(num) {
return 0 < num && num < CURVE.r;
}
const utils = {
hexToBytes: utils_js_2.hexToBytes,
bytesToHex: utils_js_2.bytesToHex,
mod: mod.mod,
hexToBytes: ut.hexToBytes,
bytesToHex: ut.bytesToHex,
stringToBytes: hash_to_curve_js_1.stringToBytes,

@@ -110,27 +85,6 @@ // TODO: do we need to export it here?

expandMessageXMD: (msg, DST, lenInBytes, H = CURVE.hash) => (0, hash_to_curve_js_1.expand_message_xmd)(msg, DST, lenInBytes, H),
/**
* Can take 40 or more bytes of uniform input e.g. from CSPRNG or KDF
* and convert them into private key, with the modulo bias being negligible.
* As per FIPS 186 B.1.1.
* https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
* @param hash hash output from sha512, or a similar function
* @returns valid private key
*/
hashToPrivateKey: (hash) => {
hash = (0, utils_js_1.ensureBytes)(hash);
if (hash.length < 40 || hash.length > 1024)
throw new Error('Expected 40-1024 bytes of private key as per FIPS 186');
// hashToPrivateScalar(hash, CURVE.r)
// NOTE: doesn't add +/-1
const num = mod.mod((0, utils_js_1.bytesToNumberBE)(hash), CURVE.r);
// This should never happen
if (num === 0n || num === 1n)
throw new Error('Invalid private key');
return (0, utils_js_1.numberToBytesBE)(num, 32);
},
randomBytes: (bytesLength = 32) => CURVE.randomBytes(bytesLength),
// NIST SP 800-56A rev 3, section 5.6.1.2.2
// https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
randomPrivateKey: () => utils.hashToPrivateKey(utils.randomBytes(40)),
getDSTLabel: () => htfDefaults.DST,
hashToPrivateKey: (hash) => Fr.toBytes(ut.hashToPrivateScalar(hash, CURVE.r)),
randomBytes: (bytesLength = groupLen) => CURVE.randomBytes(bytesLength),
randomPrivateKey: () => utils.hashToPrivateKey(utils.randomBytes(groupLen + 8)),
getDSTLabel: () => CURVE.htfDefaults.DST,
setDSTLabel(newLabel) {

@@ -141,22 +95,5 @@ // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-3.1

}
htfDefaults.DST = newLabel;
CURVE.htfDefaults.DST = newLabel;
},
};
function normalizePrivKey(key) {
let int;
if (key instanceof Uint8Array && key.length === 32)
int = (0, utils_js_1.bytesToNumberBE)(key);
else if (typeof key === 'string' && key.length === 64)
int = BigInt(`0x${key}`);
else if (typeof key === 'number' && key > 0 && Number.isSafeInteger(key))
int = BigInt(key);
else if (typeof key === 'bigint' && key > 0n)
int = key;
else
throw new TypeError('Expected valid private key');
int = mod.mod(int, CURVE.r);
if (!isWithinCurveOrder(int))
throw new Error('Private key must be 0 < key < CURVE.r');
return int;
}
// Point on G1 curve: (x, y)

@@ -215,3 +152,3 @@ const G1 = (0, weierstrass_js_1.weierstrassPoints)({

msgPoint.assertValidity();
const sigPoint = msgPoint.multiply(normalizePrivKey(privateKey));
const sigPoint = msgPoint.multiply(G1.normalizePrivateKey(privateKey));
if (message instanceof G2.Point)

@@ -218,0 +155,0 @@ return sigPoint;

23

lib/abstract/edwards.d.ts
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import * as mod from './modular.js';
import { BasicCurve, Hex, PrivKey } from './utils.js';
import * as ut from './utils.js';
import { Hex, PrivKey } from './utils.js';
import { Group, GroupConstructor } from './group.js';
import { htfOpts } from './hash-to-curve.js';
export declare type CHash = {
(message: Uint8Array | string): Uint8Array;
blockLen: number;
outputLen: number;
create(): any;
};
export declare type CurveType = BasicCurve<bigint> & {
export declare type CurveType = ut.BasicCurve<bigint> & {
a: bigint;
d: bigint;
hash: CHash;
hash: ut.CHash;
randomBytes: (bytesLength?: number) => Uint8Array;

@@ -23,4 +18,3 @@ adjustScalarBytes?: (bytes: Uint8Array) => Uint8Array;

};
preHash?: CHash;
clearCofactor?: (c: ExtendedPointConstructor, point: ExtendedPointType) => ExtendedPointType;
preHash?: ut.CHash;
htfDefaults?: htfOpts;

@@ -45,3 +39,3 @@ mapToCurve?: (scalar: bigint[]) => {

readonly d: bigint;
readonly hash: CHash;
readonly hash: ut.CHash;
readonly randomBytes: (bytesLength?: number | undefined) => Uint8Array;

@@ -54,4 +48,3 @@ readonly adjustScalarBytes?: ((bytes: Uint8Array) => Uint8Array) | undefined;

}) | undefined;
readonly preHash?: CHash | undefined;
readonly clearCofactor?: ((c: ExtendedPointConstructor, point: ExtendedPointType) => ExtendedPointType) | undefined;
readonly preHash?: ut.CHash | undefined;
readonly htfDefaults?: htfOpts | undefined;

@@ -119,4 +112,2 @@ readonly mapToCurve?: ((scalar: bigint[]) => {

utils: {
mod: (a: bigint) => bigint;
invert: (number: bigint) => bigint;
randomPrivateKey: () => Uint8Array;

@@ -123,0 +114,0 @@ getExtendedPublicKey: (key: PrivKey) => {

195

lib/abstract/edwards.js

@@ -7,10 +7,11 @@ "use strict";

// Differences from @noble/ed25519 1.7:
// 1. Different field element lengths in ed448:
// 1. Variable field element lengths between EDDSA/ECDH:
// EDDSA (RFC8032) is 456 bits / 57 bytes, ECDH (RFC7748) is 448 bits / 56 bytes
// 2. Different addition formula (doubling is same)
// 3. uvRatio differs between curves (half-expected, not only pow fn changes)
// 4. Point decompression code is different too (unexpected), now using generalized formula
// 4. Point decompression code is different (unexpected), now using generalized formula
// 5. Domain function was no-op for ed25519, but adds some data even with empty context for ed448
const mod = require("./modular.js");
const utils_js_1 = require("./utils.js"); // TODO: import * as u from './utils.js'?
const ut = require("./utils.js");
const utils_js_1 = require("./utils.js");
const group_js_1 = require("./group.js");

@@ -23,10 +24,10 @@ const hash_to_curve_js_1 = require("./hash-to-curve.js");

const _8n = BigInt(8);
// Should be separate from overrides, since overrides can use information about curve (for example nBits)
function validateOpts(curve) {
const opts = (0, utils_js_1.validateOpts)(curve);
if (typeof opts.hash !== 'function' || !Number.isSafeInteger(opts.hash.outputLen))
const opts = ut.validateOpts(curve);
if (typeof opts.hash !== 'function' || !ut.isPositiveInt(opts.hash.outputLen))
throw new Error('Invalid hash function');
for (const i of ['a', 'd']) {
if (typeof opts[i] !== 'bigint')
throw new Error(`Invalid curve param ${i}=${opts[i]} (${typeof opts[i]})`);
const val = opts[i];
if (typeof val !== 'bigint')
throw new Error(`Invalid curve param ${i}=${val} (${typeof val})`);
}

@@ -37,9 +38,3 @@ for (const fn of ['randomBytes']) {

}
for (const fn of [
'adjustScalarBytes',
'domain',
'uvRatio',
'mapToCurve',
'clearCofactor',
]) {
for (const fn of ['adjustScalarBytes', 'domain', 'uvRatio', 'mapToCurve']) {
if (opts[fn] === undefined)

@@ -60,8 +55,3 @@ continue; // Optional

const CURVE_ORDER = CURVE.n;
const fieldLen = Fp.BYTES; // 32 (length of one field element)
if (fieldLen > 2048)
throw new Error('Field lengths over 2048 are not supported');
const groupLen = CURVE.nByteLength;
// (2n ** 256n).toString(16);
const maxGroupElement = _2n ** BigInt(groupLen * 8); // previous POW_2_256
const maxGroupElement = _2n ** BigInt(CURVE.nByteLength * 8);
// Function overrides

@@ -71,20 +61,18 @@ const { randomBytes } = CURVE;

// sqrt(u/v)
function _uvRatio(u, v) {
try {
const value = Fp.sqrt(u * Fp.invert(v));
return { isValid: true, value };
}
catch (e) {
return { isValid: false, value: _0n };
}
}
const uvRatio = CURVE.uvRatio || _uvRatio;
const _adjustScalarBytes = (bytes) => bytes; // NOOP
const adjustScalarBytes = CURVE.adjustScalarBytes || _adjustScalarBytes;
function _domain(data, ctx, phflag) {
if (ctx.length || phflag)
throw new Error('Contexts/pre-hash are not supported');
return data;
}
const domain = CURVE.domain || _domain; // NOOP
const uvRatio = CURVE.uvRatio ||
((u, v) => {
try {
return { isValid: true, value: Fp.sqrt(u * Fp.invert(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
/**

@@ -226,6 +214,4 @@ * Extended Point works in extended coordinates: (x, y, z, t) ∋ (x=x/z, y=y/z, t=xy).

// an exposed private key e.g. sig verification.
// Allows scalar bigger than curve order, but less than 2^256
multiplyUnsafe(scalar) {
let n = normalizeScalar(scalar, CURVE_ORDER, false);
const G = ExtendedPoint.BASE;
const P0 = ExtendedPoint.ZERO;

@@ -236,6 +222,9 @@ if (n === _0n)

return this;
if (this.equals(G))
if (this.equals(ExtendedPoint.BASE))
return this.wNAF(n);
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.

@@ -245,5 +234,6 @@ isSmallOrder() {

}
// Multiplies point by a very big scalar n and checks if the result is 0.
// Multiplies point by curve order (very big scalar CURVE.n) and checks if the result is 0.
// Returns `false` is the point is dirty.
isTorsionFree() {
return this.multiplyUnsafe(CURVE_ORDER).equals(ExtendedPoint.ZERO);
return wnaf.unsafeLadder(this, CURVE_ORDER).equals(ExtendedPoint.ZERO);
}

@@ -267,9 +257,6 @@ // Converts Extended point to default (x, y) coordinates.

clearCofactor() {
if (CURVE.h === _1n)
return this; // Fast-path
// clear_cofactor(P) := h_eff * P
// hEff = h for ed25519/ed448. Maybe worth moving to params?
if (CURVE.clearCofactor)
return CURVE.clearCofactor(ExtendedPoint, this);
return this.multiplyUnsafe(CURVE.h);
const { h: cofactor } = CURVE;
if (cofactor === _1n)
return this;
return this.multiplyUnsafe(cofactor);
}

@@ -279,3 +266,3 @@ }

ExtendedPoint.ZERO = new ExtendedPoint(_0n, _1n, _1n, _0n);
const wnaf = (0, group_js_1.wNAF)(ExtendedPoint, groupLen * 8);
const wnaf = (0, group_js_1.wNAF)(ExtendedPoint, CURVE.nByteLength * 8);
function assertExtPoint(other) {

@@ -304,3 +291,4 @@ if (!(other instanceof ExtendedPoint))

const { d, a } = CURVE;
hex = (0, utils_js_1.ensureBytes)(hex, fieldLen);
const len = Fp.BYTES;
hex = (0, utils_js_1.ensureBytes)(hex, len);
// 1. First, interpret the string as an integer in little-endian

@@ -312,9 +300,9 @@ // representation. Bit 255 of this number is the least significant

const normed = hex.slice();
const lastByte = hex[fieldLen - 1];
normed[fieldLen - 1] = lastByte & ~0x80;
const y = (0, utils_js_1.bytesToNumberLE)(normed);
const lastByte = hex[len - 1];
normed[len - 1] = lastByte & ~0x80;
const y = ut.bytesToNumberLE(normed);
if (strict && y >= Fp.ORDER)
throw new Error('Expected 0 < hex < P');
if (!strict && y >= maxGroupElement)
throw new Error('Expected 0 < hex < 2**256');
throw new Error('Expected 0 < hex < CURVE.n');
// 2. To recover the x-coordinate, the curve equation implies

@@ -351,4 +339,4 @@ // Ed25519: x² = (y² - 1) / (d y² + 1) (mod p).

toRawBytes() {
const bytes = (0, utils_js_1.numberToBytesLE)(this.y, fieldLen);
bytes[fieldLen - 1] |= this.x & _1n ? 0x80 : 0;
const bytes = ut.numberToBytesLE(this.y, Fp.BYTES);
bytes[Fp.BYTES - 1] |= this.x & _1n ? 0x80 : 0;
return bytes;

@@ -358,4 +346,6 @@ }

toHex() {
return (0, utils_js_1.bytesToHex)(this.toRawBytes());
return ut.bytesToHex(this.toRawBytes());
}
// Determines if point is in prime-order subgroup.
// Returns `false` is the point is dirty.
isTorsionFree() {

@@ -395,8 +385,8 @@ return ExtendedPoint.fromAffine(this).isTorsionFree();

static hashToCurve(msg, options) {
if (!CURVE.mapToCurve)
const { mapToCurve, htfDefaults } = CURVE;
if (!mapToCurve)
throw new Error('No mapToCurve defined for curve');
msg = (0, utils_js_1.ensureBytes)(msg);
const u = (0, hash_to_curve_js_1.hash_to_field)(msg, 2, { ...CURVE.htfDefaults, ...options });
const { x: x0, y: y0 } = CURVE.mapToCurve(u[0]);
const { x: x1, y: y1 } = CURVE.mapToCurve(u[1]);
const u = (0, hash_to_curve_js_1.hash_to_field)((0, utils_js_1.ensureBytes)(msg), 2, { ...htfDefaults, ...options });
const { x: x0, y: y0 } = mapToCurve(u[0]);
const { x: x1, y: y1 } = mapToCurve(u[1]);
const p = new Point(x0, y0).add(new Point(x1, y1)).clearCofactor();

@@ -407,7 +397,7 @@ return p;

static encodeToCurve(msg, options) {
if (!CURVE.mapToCurve)
const { mapToCurve, htfDefaults } = CURVE;
if (!mapToCurve)
throw new Error('No mapToCurve defined for curve');
msg = (0, utils_js_1.ensureBytes)(msg);
const u = (0, hash_to_curve_js_1.hash_to_field)(msg, 1, { ...CURVE.htfDefaults, ...options });
const { x, y } = CURVE.mapToCurve(u[0]);
const u = (0, hash_to_curve_js_1.hash_to_field)((0, utils_js_1.ensureBytes)(msg), 1, { ...htfDefaults, ...options });
const { x, y } = mapToCurve(u[0]);
return new Point(x, y).clearCofactor();

@@ -432,5 +422,6 @@ }

static fromHex(hex) {
const bytes = (0, utils_js_1.ensureBytes)(hex, 2 * fieldLen);
const r = Point.fromHex(bytes.slice(0, fieldLen), false);
const s = (0, utils_js_1.bytesToNumberLE)(bytes.slice(fieldLen, 2 * fieldLen));
const len = Fp.BYTES;
const bytes = (0, utils_js_1.ensureBytes)(hex, 2 * len);
const r = Point.fromHex(bytes.slice(0, len), false);
const s = ut.bytesToNumberLE(bytes.slice(len, 2 * len));
return new Signature(r, s);

@@ -447,11 +438,11 @@ }

toRawBytes() {
return (0, utils_js_1.concatBytes)(this.r.toRawBytes(), (0, utils_js_1.numberToBytesLE)(this.s, fieldLen));
return ut.concatBytes(this.r.toRawBytes(), ut.numberToBytesLE(this.s, Fp.BYTES));
}
toHex() {
return (0, utils_js_1.bytesToHex)(this.toRawBytes());
return ut.bytesToHex(this.toRawBytes());
}
}
// Little-endian SHA512 with modulo n
function modlLE(hash) {
return mod.mod((0, utils_js_1.bytesToNumberLE)(hash), CURVE_ORDER);
function modnLE(hash) {
return mod.mod(ut.bytesToNumberLE(hash), CURVE_ORDER);
}

@@ -467,3 +458,3 @@ /**

throw new TypeError('Specify max value');
if (typeof num === 'number' && Number.isSafeInteger(num))
if (ut.isPositiveInt(num))
num = BigInt(num);

@@ -480,32 +471,26 @@ if (typeof num === 'bigint' && num < max) {

}
throw new TypeError('Expected valid scalar: 0 < scalar < max');
throw new TypeError(`Expected valid scalar: 0 < scalar < ${max}`);
}
function checkPrivateKey(key) {
/** Convenience method that creates public key and other stuff. RFC8032 5.1.5 */
function getExtendedPublicKey(key) {
const groupLen = CURVE.nByteLength;
// Normalize bigint / number / string to Uint8Array
key =
typeof key === 'bigint' || typeof key === 'number'
? (0, utils_js_1.numberToBytesLE)(normalizeScalar(key, maxGroupElement), groupLen)
: (0, utils_js_1.ensureBytes)(key);
if (key.length !== groupLen)
throw new Error(`Expected ${groupLen} bytes, got ${key.length}`);
return key;
}
// Takes 64 bytes
function getKeyFromHash(hashed) {
// First 32 bytes of 64b uniformingly random input are taken,
// clears 3 bits of it to produce a random field element.
const keyb = typeof key === 'bigint' || typeof key === 'number'
? ut.numberToBytesLE(normalizeScalar(key, maxGroupElement), groupLen)
: key;
// Hash private key with curve's hash function to produce uniformingly random input
// We check byte lengths e.g.: ensureBytes(64, hash(ensureBytes(32, key)))
const hashed = (0, utils_js_1.ensureBytes)(CURVE.hash((0, utils_js_1.ensureBytes)(keyb, groupLen)), 2 * groupLen);
// First half's bits are cleared to produce a random field element.
const head = adjustScalarBytes(hashed.slice(0, groupLen));
// Second 32 bytes is called key prefix (5.1.6)
// Second half is called key prefix (5.1.6)
const prefix = hashed.slice(groupLen, 2 * groupLen);
// The actual private scalar
const scalar = modlLE(head);
const scalar = modnLE(head);
// Point on Edwards curve aka public key
const point = Point.BASE.multiply(scalar);
// Uint8Array representation
const pointBytes = point.toRawBytes();
return { head, prefix, scalar, point, pointBytes };
}
/** Convenience method that creates public key and other stuff. RFC8032 5.1.5 */
function getExtendedPublicKey(key) {
return getKeyFromHash(CURVE.hash(checkPrivateKey(key)));
}
/**

@@ -522,3 +507,3 @@ * Calculates ed25519 public key. RFC8032 5.1.5

context = (0, utils_js_1.ensureBytes)(context);
return modlLE(CURVE.hash(domain(message, context, !!CURVE.preHash)));
return modnLE(CURVE.hash(domain(message, context, !!CURVE.preHash)));
}

@@ -531,5 +516,5 @@ /** Signs message with privateKey. RFC8032 5.1.6 */

const { prefix, scalar, pointBytes } = getExtendedPublicKey(privateKey);
const r = hashDomainToScalar((0, utils_js_1.concatBytes)(prefix, message), context);
const r = hashDomainToScalar(ut.concatBytes(prefix, message), context);
const R = Point.BASE.multiply(r); // R = rG
const k = hashDomainToScalar((0, utils_js_1.concatBytes)(R.toRawBytes(), pointBytes, message), context); // k = hash(R+P+msg)
const k = hashDomainToScalar(ut.concatBytes(R.toRawBytes(), pointBytes, message), context); // k = hash(R+P+msg)
const s = mod.mod(r + k * scalar, CURVE_ORDER); // s = r + kp

@@ -573,7 +558,7 @@ return new Signature(R, s).toRawBytes();

const SB = ExtendedPoint.BASE.multiplyUnsafe(s);
const k = hashDomainToScalar((0, utils_js_1.concatBytes)(r.toRawBytes(), publicKey.toRawBytes(), message), context);
const k = hashDomainToScalar(ut.concatBytes(r.toRawBytes(), publicKey.toRawBytes(), message), context);
const kA = ExtendedPoint.fromAffine(publicKey).multiplyUnsafe(k);
const RkA = ExtendedPoint.fromAffine(r).add(kA);
// [8][S]B = [8]R + [8][k]A'
return RkA.subtract(SB).multiplyUnsafe(CURVE.h).equals(ExtendedPoint.ZERO);
return RkA.subtract(SB).clearCofactor().equals(ExtendedPoint.ZERO);
}

@@ -584,8 +569,6 @@ // Enable precomputes. Slows down first publicKey computation by 20ms.

getExtendedPublicKey,
mod: modP,
invert: Fp.invert,
/**
* Not needed for ed25519 private keys. Needed if you use scalars directly (rare).
*/
hashToPrivateScalar: (hash) => (0, utils_js_1.hashToPrivateScalar)(hash, CURVE_ORDER, true),
hashToPrivateScalar: (hash) => ut.hashToPrivateScalar(hash, CURVE_ORDER, true),
/**

@@ -595,3 +578,3 @@ * ed25519 private keys are uniform 32-bit strings. We do not need to check for

*/
randomPrivateKey: () => randomBytes(fieldLen),
randomPrivateKey: () => randomBytes(Fp.BYTES),
/**

@@ -598,0 +581,0 @@ * We're doing scalar multiplication (used in getPublicKey etc) with precomputed BASE_POINT

49

lib/abstract/modular.js

@@ -64,2 +64,3 @@ "use strict";

while (a !== _0n) {
// JIT applies optimization if those two lines follow each other
const q = b / a;

@@ -79,3 +80,4 @@ const r = b % a;

// Tonelli-Shanks algorithm
// https://eprint.iacr.org/2012/685.pdf (page 12)
// Paper 1: https://eprint.iacr.org/2012/685.pdf (page 12)
// Paper 2: Square Roots from 1; 24, 51, 10 to Dan Shanks
function tonelliShanks(P) {

@@ -90,3 +92,3 @@ // Legendre constant: used to calculate Legendre symbol (a | p),

// Step 1: By factoring out powers of 2 from p - 1,
// find q and s such that p - 1 = q2s with q odd
// find q and s such that p - 1 = q*(2^s) with q odd
for (Q = P - _1n, S = 0; Q % _2n === _0n; Q /= _2n, S++)

@@ -110,27 +112,28 @@ ;

return function tonelliSlow(Fp, n) {
// Step 0: Check that n is indeed a square: (n | p) must be ≡ 1
if (Fp.pow(n, legendreC) !== Fp.ONE)
// Step 0: Check that n is indeed a square: (n | p) should not be ≡ -1
if (Fp.pow(n, legendreC) === Fp.negate(Fp.ONE))
throw new Error('Cannot find square root');
let s = S;
let c = pow(Z, Q, P);
let r = Fp.pow(n, Q1div2);
let t = Fp.pow(n, Q);
let t2 = Fp.ZERO;
while (!Fp.equals(Fp.sub(t, Fp.ONE), Fp.ZERO)) {
t2 = Fp.square(t);
let i;
for (i = 1; i < s; i++) {
// stop if t2-1 == 0
if (Fp.equals(Fp.sub(t2, Fp.ONE), Fp.ZERO))
let r = S;
// TODO: will fail at Fp2/etc
let g = Fp.pow(Fp.mul(Fp.ONE, Z), Q); // will update both x and b
let x = Fp.pow(n, Q1div2); // first guess at the square root
let b = Fp.pow(n, Q); // first guess at the fudge factor
while (!Fp.equals(b, Fp.ONE)) {
if (Fp.equals(b, Fp.ZERO))
return Fp.ZERO; // https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm (4. If t = 0, return r = 0)
// Find m such b^(2^m)==1
let m = 1;
for (let t2 = Fp.square(b); m < r; m++) {
if (Fp.equals(t2, Fp.ONE))
break;
// t2 *= t2
t2 = Fp.square(t2);
t2 = Fp.square(t2); // t2 *= t2
}
let b = pow(c, BigInt(1 << (s - i - 1)), P);
r = Fp.mul(r, b);
c = mod(b * b, P);
t = Fp.mul(t, c);
s = i;
// NOTE: r-m-1 can be bigger than 32, need to convert to bigint before shift, otherwise there will be overflow
const ge = Fp.pow(g, _1n << BigInt(r - m - 1)); // ge = 2^(r-m-1)
g = Fp.square(ge); // g = ge * ge
x = Fp.mul(x, ge); // x *= ge
b = Fp.mul(b, g); // b *= g
r = m;
}
return r;
return x;
};

@@ -137,0 +140,0 @@ }

2

lib/abstract/montgomery.js

@@ -17,3 +17,3 @@ "use strict";

continue; // Optional
if (!Number.isSafeInteger(curve[i]))
if (!(0, utils_js_1.isPositiveInt)(curve[i]))
throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);

@@ -20,0 +20,0 @@ }

8

lib/abstract/utils.d.ts

@@ -25,2 +25,3 @@ /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */

};
export declare function isPositiveInt(num: any): num is number;
export declare function validateOpts<FP, T>(curve: BasicCurve<FP> & T): Readonly<{

@@ -45,10 +46,11 @@ readonly nBitLength: number;

/**
* FIPS 186 B.4.1-compliant "constant-time" private key generation utility.
* Can take (n+8) or more bytes of uniform input e.g. from CSPRNG or KDF
* and convert them into private scalar, with the modulo bias being neglible.
* As per FIPS 186 B.4.1.
* Needs at least 40 bytes of input for 32-byte private key.
* https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
* @param hash hash output from sha512, or a similar function
* @param hash hash output from SHA3 or a similar function
* @returns valid private scalar
*/
export declare function hashToPrivateScalar(hash: Hex, CURVE_ORDER: bigint, isLE?: boolean): bigint;
export declare function hashToPrivateScalar(hash: Hex, groupOrder: bigint, isLE?: boolean): bigint;
export declare function equalBytes(b1: Uint8Array, b2: Uint8Array): boolean;

@@ -55,0 +57,0 @@ export declare function bitLen(n: bigint): number;

36

lib/abstract/utils.js
"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
exports.bitMask = exports.bitSet = exports.bitGet = exports.bitLen = exports.equalBytes = exports.hashToPrivateScalar = exports.nLength = exports.concatBytes = exports.ensureBytes = exports.numberToBytesLE = exports.numberToBytesBE = exports.bytesToNumberLE = exports.bytesToNumberBE = exports.hexToBytes = exports.hexToNumber = exports.numberToHexUnpadded = exports.bytesToHex = exports.validateOpts = void 0;
exports.bitMask = exports.bitSet = exports.bitGet = exports.bitLen = exports.equalBytes = exports.hashToPrivateScalar = exports.nLength = exports.concatBytes = exports.ensureBytes = exports.numberToBytesLE = exports.numberToBytesBE = exports.bytesToNumberLE = exports.bytesToNumberBE = exports.hexToBytes = exports.hexToNumber = exports.numberToHexUnpadded = exports.bytesToHex = exports.validateOpts = exports.isPositiveInt = void 0;
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */

@@ -9,7 +9,13 @@ const mod = require("./modular.js");

const _2n = BigInt(2);
// Bans floats and integers above 2^53-1
function isPositiveInt(num) {
return typeof num === 'number' && Number.isSafeInteger(num) && num > 0;
}
exports.isPositiveInt = isPositiveInt;
function validateOpts(curve) {
mod.validateField(curve.Fp);
for (const i of ['n', 'h']) {
if (typeof curve[i] !== 'bigint')
throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
const val = curve[i];
if (typeof val !== 'bigint')
throw new Error(`Invalid curve param ${i}=${val} (${typeof val})`);
}

@@ -21,6 +27,7 @@ if (!curve.Fp.isValid(curve.Gx))

for (const i of ['nBitLength', 'nByteLength']) {
if (curve[i] === undefined)
const val = curve[i];
if (val === undefined)
continue; // Optional
if (!Number.isSafeInteger(curve[i]))
throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
if (!isPositiveInt(val))
throw new Error(`Invalid curve param ${i}=${val} (${typeof val})`);
}

@@ -124,17 +131,18 @@ // Set defaults

/**
* FIPS 186 B.4.1-compliant "constant-time" private key generation utility.
* Can take (n+8) or more bytes of uniform input e.g. from CSPRNG or KDF
* and convert them into private scalar, with the modulo bias being neglible.
* As per FIPS 186 B.4.1.
* Needs at least 40 bytes of input for 32-byte private key.
* https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
* @param hash hash output from sha512, or a similar function
* @param hash hash output from SHA3 or a similar function
* @returns valid private scalar
*/
function hashToPrivateScalar(hash, CURVE_ORDER, isLE = false) {
function hashToPrivateScalar(hash, groupOrder, isLE = false) {
hash = ensureBytes(hash);
const orderLen = nLength(CURVE_ORDER).nByteLength;
const minLen = orderLen + 8;
if (orderLen < 16 || hash.length < minLen || hash.length > 1024)
throw new Error('Expected valid bytes of private key as per FIPS 186');
const hashLen = hash.length;
const minLen = nLength(groupOrder).nByteLength + 8;
if (minLen < 24 || hashLen < minLen || hashLen > 1024)
throw new Error(`hashToPrivateScalar: expected ${minLen}-1024 bytes of input, got ${hashLen}`);
const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);
return mod.mod(num, CURVE_ORDER - _1n) + _1n;
return mod.mod(num, groupOrder - _1n) + _1n;
}

@@ -141,0 +149,0 @@ exports.hashToPrivateScalar = hashToPrivateScalar;

16

lib/abstract/weierstrass.d.ts
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import * as mod from './modular.js';
import * as ut from './utils.js';
import { Hex, PrivKey } from './utils.js';
import * as utils from './utils.js';
import { htfOpts } from './hash-to-curve.js';

@@ -17,6 +17,7 @@ import { Group, GroupConstructor } from './group.js';

};
export declare type BasicCurve<T> = utils.BasicCurve<T> & {
export declare type BasicCurve<T> = ut.BasicCurve<T> & {
a: T;
b: T;
normalizePrivateKey?: (key: PrivKey) => PrivKey;
wrapPrivateKey?: boolean;
endo?: EndomorphismOpts;

@@ -32,3 +33,3 @@ isTorsionFree?: (c: ProjectiveConstructor<T>, point: ProjectivePointType<T>) => boolean;

declare type Entropy = Hex | true;
declare type SignOpts = {
export declare type SignOpts = {
lowS?: boolean;

@@ -132,3 +133,3 @@ extraEntropy?: Entropy;

lowS?: boolean;
hash: utils.CHash;
hash: ut.CHash;
hmac: HmacFnSync;

@@ -151,3 +152,3 @@ randomBytes: (bytesLength?: number) => Uint8Array;

readonly b: bigint;
readonly normalizePrivateKey?: ((key: PrivKey) => PrivKey) | undefined;
readonly normalizePrivateKey?: ((key: ut.PrivKey) => ut.PrivKey) | undefined;
readonly endo?: EndomorphismOpts | undefined;

@@ -162,3 +163,3 @@ readonly isTorsionFree?: ((c: ProjectiveConstructor<bigint>, point: ProjectivePointType<bigint>) => boolean) | undefined;

lowS: boolean;
readonly hash: utils.CHash;
readonly hash: ut.CHash;
readonly hmac: HmacFnSync;

@@ -173,2 +174,3 @@ readonly randomBytes: (bytesLength?: number | undefined) => Uint8Array;

sign: (msgHash: Hex, privKey: PrivKey, opts?: SignOpts) => SignatureType;
signUnhashed: (msg: Uint8Array, privKey: PrivKey, opts?: SignOpts) => SignatureType;
verify: (signature: Hex | SignatureType, msgHash: Hex, publicKey: PubKey, opts?: {

@@ -181,4 +183,2 @@ lowS?: boolean;

utils: {
mod: (a: bigint, b?: bigint) => bigint;
invert: (number: bigint, modulo?: bigint) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -185,0 +185,0 @@ _bigintToString: (num: bigint) => string;

373

lib/abstract/weierstrass.js

@@ -6,4 +6,2 @@ "use strict";

exports.mapToCurveSimpleSWU = exports.SWUFpSqrtRatio = exports.weierstrass = exports.weierstrassPoints = void 0;
// TODO: sync vs async naming
// TODO: default randomBytes
// Differences from @noble/secp256k1 1.7:

@@ -14,8 +12,9 @@ // 1. Different double() formula (but same addition)

// 4. DRBG supports outputLen bigger than outputLen of hmac
// 5. Support for different hash functions
const mod = require("./modular.js");
const ut = require("./utils.js");
const utils_js_1 = require("./utils.js");
const utils = require("./utils.js");
const hash_to_curve_js_1 = require("./hash-to-curve.js");
const group_js_1 = require("./group.js");
// DER encoding utilities
// ASN.1 DER encoding utilities
class DERError extends Error {

@@ -26,42 +25,40 @@ constructor(message) {

}
function sliceDER(s) {
// Proof: any([(i>=0x80) == (int(hex(i).replace('0x', '').zfill(2)[0], 16)>=8) for i in range(0, 256)])
// Padding done by numberToHex
return Number.parseInt(s[0], 16) >= 8 ? '00' + s : s;
}
function parseDERInt(data) {
if (data.length < 2 || data[0] !== 0x02) {
throw new DERError(`Invalid signature integer tag: ${(0, utils_js_1.bytesToHex)(data)}`);
}
const len = data[1];
const res = data.subarray(2, len + 2);
if (!len || res.length !== len) {
throw new DERError(`Invalid signature integer: wrong length`);
}
// Strange condition, its not about length, but about first bytes of number.
if (res[0] === 0x00 && res[1] <= 0x7f) {
throw new DERError('Invalid signature integer: trailing length');
}
return { data: (0, utils_js_1.bytesToNumberBE)(res), left: data.subarray(len + 2) };
}
function parseDERSignature(data) {
if (data.length < 2 || data[0] != 0x30) {
throw new DERError(`Invalid signature tag: ${(0, utils_js_1.bytesToHex)(data)}`);
}
if (data[1] !== data.length - 2) {
throw new DERError('Invalid signature: incorrect length');
}
const { data: r, left: sBytes } = parseDERInt(data.subarray(2));
const { data: s, left: rBytesLeft } = parseDERInt(sBytes);
if (rBytesLeft.length) {
throw new DERError(`Invalid signature: left bytes after parsing: ${(0, utils_js_1.bytesToHex)(rBytesLeft)}`);
}
return { r, s };
}
// Be friendly to bad ECMAScript parsers by not using bigint literals like 123n
const _0n = BigInt(0);
const _1n = BigInt(1);
const _3n = BigInt(3);
const DER = {
slice(s) {
// Proof: any([(i>=0x80) == (int(hex(i).replace('0x', '').zfill(2)[0], 16)>=8) for i in range(0, 256)])
// Padding done by numberToHex
return Number.parseInt(s[0], 16) >= 8 ? '00' + s : s;
},
parseInt(data) {
if (data.length < 2 || data[0] !== 0x02) {
throw new DERError(`Invalid signature integer tag: ${(0, utils_js_1.bytesToHex)(data)}`);
}
const len = data[1];
const res = data.subarray(2, len + 2);
if (!len || res.length !== len) {
throw new DERError(`Invalid signature integer: wrong length`);
}
// Strange condition, its not about length, but about first bytes of number.
if (res[0] === 0x00 && res[1] <= 0x7f) {
throw new DERError('Invalid signature integer: trailing length');
}
return { data: ut.bytesToNumberBE(res), left: data.subarray(len + 2) };
},
parseSig(data) {
if (data.length < 2 || data[0] != 0x30) {
throw new DERError(`Invalid signature tag: ${(0, utils_js_1.bytesToHex)(data)}`);
}
if (data[1] !== data.length - 2) {
throw new DERError('Invalid signature: incorrect length');
}
const { data: r, left: sBytes } = DER.parseInt(data.subarray(2));
const { data: s, left: rBytesLeft } = DER.parseInt(sBytes);
if (rBytesLeft.length) {
throw new DERError(`Invalid signature: left bytes after parsing: ${(0, utils_js_1.bytesToHex)(rBytesLeft)}`);
}
return { r, s };
},
};
function validatePointOpts(curve) {
const opts = utils.validateOpts(curve);
const opts = ut.validateOpts(curve);
const Fp = opts.Fp;

@@ -99,17 +96,9 @@ for (const i of ['a', 'b']) {

}
// Be friendly to bad ECMAScript parsers by not using bigint literals like 123n
const _0n = BigInt(0);
const _1n = BigInt(1);
const _3n = BigInt(3);
function weierstrassPoints(opts) {
const CURVE = validatePointOpts(opts);
const Fp = CURVE.Fp;
// Lengths
// All curves has same field / group length as for now, but it can be different for other curves
const { nByteLength, nBitLength } = CURVE;
const groupLen = nByteLength;
// Not using ** operator with bigints for old engines.
// 2n ** (8n * 32n) == 2n << (8n * 32n - 1n)
//const FIELD_MASK = _2n << (_8n * BigInt(fieldLen) - _1n);
// function numToFieldStr(num: bigint): string {
// if (typeof num !== 'bigint') throw new Error('Expected bigint');
// if (!(_0n <= num && num < FIELD_MASK)) throw new Error(`Expected number < 2^${fieldLen * 8}`);
// return num.toString(16).padStart(2 * fieldLen, '0');
// }
const { Fp } = CURVE; // All curves has same field / group length as for now, but they can differ
/**

@@ -125,14 +114,22 @@ * y² = x³ + ax + b: Short weierstrass curve formula

}
// Valid group elements reside in range 1..n-1
function isWithinCurveOrder(num) {
return _0n < num && num < CURVE.n;
}
/**
* Validates if a private key is valid and converts it to bigint form.
* Supports two options, that are passed when CURVE is initialized:
* - `normalizePrivateKey()` executed before all checks
* - `wrapPrivateKey` when true, executed after most checks, but before `0 < key < n`
*/
function normalizePrivateKey(key) {
if (typeof CURVE.normalizePrivateKey === 'function') {
key = CURVE.normalizePrivateKey(key);
}
const { normalizePrivateKey: custom, nByteLength: groupLen, wrapPrivateKey, n: order } = CURVE;
if (typeof custom === 'function')
key = custom(key);
let num;
if (typeof key === 'bigint') {
// Curve order check is done below
num = key;
}
else if (typeof key === 'number' && Number.isSafeInteger(key) && key > 0) {
else if (ut.isPositiveInt(key)) {
num = BigInt(key);

@@ -143,3 +140,4 @@ }

throw new Error(`Expected ${groupLen} bytes of private key`);
num = (0, utils_js_1.hexToNumber)(key);
// Validates individual octets
num = ut.hexToNumber(key);
}

@@ -149,3 +147,3 @@ else if (key instanceof Uint8Array) {

throw new Error(`Expected ${groupLen} bytes of private key`);
num = (0, utils_js_1.bytesToNumberBE)(key);
num = ut.bytesToNumberBE(key);
}

@@ -155,4 +153,5 @@ else {

}
if (CURVE.wrapPrivateKey)
num = mod.mod(num, CURVE.n);
// Useful for curves with cofactor != 1
if (wrapPrivateKey)
num = mod.mod(num, order);
if (!isWithinCurveOrder(num))

@@ -162,4 +161,8 @@ throw new Error('Expected private key: 0 < key < n');

}
/**
* Validates if a scalar ("private number") is valid.
* Scalars are valid only if they are less than curve order.
*/
function normalizeScalar(num) {
if (typeof num === 'number' && Number.isSafeInteger(num) && num > 0)
if (ut.isPositiveInt(num))
return BigInt(num);

@@ -192,3 +195,3 @@ if (typeof num === 'bigint' && isWithinCurveOrder(num))

* Takes a bunch of Projective Points but executes only one
* invert on all of them. invert is very slow operation,
* inversion on all of them. Inversion is very slow operation,
* so this improves performance massively.

@@ -200,2 +203,5 @@ */

}
/**
* Optimization: converts a list of projective points to a list of identical points with Z=1.
*/
static normalizeZ(points) {

@@ -221,5 +227,2 @@ return ProjectivePoint.toAffineBatch(points).map(ProjectivePoint.fromAffine);

}
doubleAdd() {
return this.add(this);
}
// Renes-Costello-Batina exception-free doubling formula.

@@ -429,16 +432,15 @@ // There is 30% faster Jacobian formula, but it is not complete.

isTorsionFree() {
if (CURVE.h === _1n)
return true; // No subgroups, always torsion fee
if (CURVE.isTorsionFree)
return CURVE.isTorsionFree(ProjectivePoint, this);
// is multiplyUnsafe(CURVE.n) is always ok, same as for edwards?
throw new Error('Unsupported!');
const { h: cofactor, isTorsionFree } = CURVE;
if (cofactor === _1n)
return true; // No subgroups, always torsion-free
if (isTorsionFree)
return isTorsionFree(ProjectivePoint, this);
throw new Error('isTorsionFree() has not been declared for the elliptic curve');
}
// Clear cofactor of G1
// https://eprint.iacr.org/2019/403
clearCofactor() {
if (CURVE.h === _1n)
const { h: cofactor, clearCofactor } = CURVE;
if (cofactor === _1n)
return this; // Fast-path
if (CURVE.clearCofactor)
return CURVE.clearCofactor(ProjectivePoint, this);
if (clearCofactor)
return clearCofactor(ProjectivePoint, this);
return this.multiplyUnsafe(CURVE.h);

@@ -449,3 +451,4 @@ }

ProjectivePoint.ZERO = new ProjectivePoint(Fp.ZERO, Fp.ONE, Fp.ZERO);
const wnaf = (0, group_js_1.wNAF)(ProjectivePoint, CURVE.endo ? nBitLength / 2 : nBitLength);
const _bits = CURVE.nBitLength;
const wnaf = (0, group_js_1.wNAF)(ProjectivePoint, CURVE.endo ? Math.ceil(_bits / 2) : _bits);
function assertPrjPoint(other) {

@@ -481,3 +484,3 @@ if (!(other instanceof ProjectivePoint))

static fromHex(hex) {
const { x, y } = CURVE.fromBytes((0, utils_js_1.ensureBytes)(hex));
const { x, y } = CURVE.fromBytes(ut.ensureBytes(hex));
const point = new Point(x, y);

@@ -504,3 +507,3 @@ point.assertValidity();

return;
throw new Error('Point is infinity');
throw new Error('Point at infinity');
}

@@ -510,9 +513,9 @@ // Some 3rd-party test vectors require different wording between here & `fromCompressedHex`

const { x, y } = this;
// Check if x, y are valid field elements
if (!Fp.isValid(x) || !Fp.isValid(y))
throw new Error(msg);
const left = Fp.square(y);
const right = weierstrassEquation(x);
const left = Fp.square(y); // y²
const right = weierstrassEquation(x); // x³ + ax + b
if (!Fp.equals(left, right))
throw new Error(msg);
// TODO: flag to disable this?
if (!this.isTorsionFree())

@@ -530,11 +533,12 @@ throw new Error('Point must be of prime-order subgroup');

}
toProj() {
return ProjectivePoint.fromAffine(this);
}
// Adds point to itself
double() {
return ProjectivePoint.fromAffine(this).double().toAffine();
return this.toProj().double().toAffine();
}
// Adds point to other point
add(other) {
return ProjectivePoint.fromAffine(this).add(ProjectivePoint.fromAffine(other)).toAffine();
return this.toProj().add(ProjectivePoint.fromAffine(other)).toAffine();
}
// Subtracts other point from the point
subtract(other) {

@@ -544,12 +548,12 @@ return this.add(other.negate());

multiply(scalar) {
return ProjectivePoint.fromAffine(this).multiply(scalar, this).toAffine();
return this.toProj().multiply(scalar, this).toAffine();
}
multiplyUnsafe(scalar) {
return ProjectivePoint.fromAffine(this).multiplyUnsafe(scalar).toAffine();
return this.toProj().multiplyUnsafe(scalar).toAffine();
}
clearCofactor() {
return ProjectivePoint.fromAffine(this).clearCofactor().toAffine();
return this.toProj().clearCofactor().toAffine();
}
isTorsionFree() {
return ProjectivePoint.fromAffine(this).isTorsionFree();
return this.toProj().isTorsionFree();
}

@@ -563,3 +567,3 @@ /**

multiplyAndAddUnsafe(Q, a, b) {
const P = ProjectivePoint.fromAffine(this);
const P = this.toProj();
const aP = a === _0n || a === _1n || this !== Point.BASE ? P.multiplyUnsafe(a) : P.multiply(a);

@@ -573,18 +577,19 @@ const bQ = ProjectivePoint.fromAffine(Q).multiplyUnsafe(b);

static hashToCurve(msg, options) {
if (!CURVE.mapToCurve)
throw new Error('No mapToCurve defined for curve');
msg = (0, utils_js_1.ensureBytes)(msg);
const { mapToCurve } = CURVE;
if (!mapToCurve)
throw new Error('CURVE.mapToCurve() has not been defined');
msg = ut.ensureBytes(msg);
const u = (0, hash_to_curve_js_1.hash_to_field)(msg, 2, { ...CURVE.htfDefaults, ...options });
const { x: x0, y: y0 } = CURVE.mapToCurve(u[0]);
const { x: x1, y: y1 } = CURVE.mapToCurve(u[1]);
const p = new Point(x0, y0).add(new Point(x1, y1)).clearCofactor();
return p;
const { x: x0, y: y0 } = mapToCurve(u[0]);
const { x: x1, y: y1 } = mapToCurve(u[1]);
return new Point(x0, y0).add(new Point(x1, y1)).clearCofactor();
}
// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-3
static encodeToCurve(msg, options) {
if (!CURVE.mapToCurve)
throw new Error('No mapToCurve defined for curve');
msg = (0, utils_js_1.ensureBytes)(msg);
const { mapToCurve } = CURVE;
if (!mapToCurve)
throw new Error('CURVE.mapToCurve() has not been defined');
msg = ut.ensureBytes(msg);
const u = (0, hash_to_curve_js_1.hash_to_field)(msg, 1, { ...CURVE.htfDefaults, ...options });
const { x, y } = CURVE.mapToCurve(u[0]);
const { x, y } = mapToCurve(u[0]);
return new Point(x, y).clearCofactor();

@@ -594,7 +599,7 @@ }

/**
* Base point aka generator. public_key = Point.BASE * private_key
* Base point aka generator. Any public_key = Point.BASE * private_key
*/
Point.BASE = new Point(CURVE.Gx, CURVE.Gy);
/**
* Identity point aka point at infinity. point = point + zero_point
* Identity point aka point at infinity. p - p = zero_p; p + zero_p = p
*/

@@ -612,4 +617,4 @@ Point.ZERO = new Point(Fp.ZERO, Fp.ZERO);

function validateOpts(curve) {
const opts = utils.validateOpts(curve);
if (typeof opts.hash !== 'function' || !Number.isSafeInteger(opts.hash.outputLen))
const opts = ut.validateOpts(curve);
if (typeof opts.hash !== 'function' || !ut.isPositiveInt(opts.hash.outputLen))
throw new Error('Invalid hash function');

@@ -670,3 +675,3 @@ if (typeof opts.hmac !== 'function')

}
return (0, utils_js_1.concatBytes)(...out);
return ut.concatBytes(...out);
}

@@ -678,4 +683,4 @@ }

const Fp = CURVE.Fp;
const compressedLen = Fp.BYTES + 1; // 33
const uncompressedLen = 2 * Fp.BYTES + 1; // 65
const compressedLen = Fp.BYTES + 1; // e.g. 33 for 32
const uncompressedLen = 2 * Fp.BYTES + 1; // e.g. 65 for 32
function isValidFieldElement(num) {

@@ -688,7 +693,9 @@ // 0 is disallowed by arbitrary reasons. Probably because infinity point?

toBytes(c, point, isCompressed) {
const x = Fp.toBytes(point.x);
const cat = ut.concatBytes;
if (isCompressed) {
return (0, utils_js_1.concatBytes)(new Uint8Array([point.hasEvenY() ? 0x02 : 0x03]), Fp.toBytes(point.x));
return cat(Uint8Array.from([point.hasEvenY() ? 0x02 : 0x03]), x);
}
else {
return (0, utils_js_1.concatBytes)(new Uint8Array([0x04]), Fp.toBytes(point.x), Fp.toBytes(point.y));
return cat(Uint8Array.from([0x04]), x, Fp.toBytes(point.y));
}

@@ -701,3 +708,3 @@ },

if (len === compressedLen && (header === 0x02 || header === 0x03)) {
const x = (0, utils_js_1.bytesToNumberBE)(bytes.subarray(1));
const x = ut.bytesToNumberBE(bytes.subarray(1));
if (!isValidFieldElement(x))

@@ -755,13 +762,14 @@ throw new Error('Point is not on curve');

}
function bits2int_2(bytes) {
const delta = bytes.length * 8 - CURVE.nBitLength;
const num = ut.bytesToNumberBE(bytes);
return delta > 0 ? num >> BigInt(delta) : num;
}
// Ensures ECDSA message hashes are 32 bytes and < curve order
function _truncateHash(hash, truncateOnly = false) {
const { n, nBitLength } = CURVE;
const byteLength = hash.length;
const delta = byteLength * 8 - nBitLength; // size of curve.n (252 bits)
let h = (0, utils_js_1.bytesToNumberBE)(hash);
if (delta > 0)
h = h >> BigInt(delta);
if (!truncateOnly && h >= n)
h -= n;
return h;
const h = bits2int_2(hash);
if (truncateOnly)
return h;
const { n } = CURVE;
return h >= n ? h - n : h;
}

@@ -779,3 +787,3 @@ const truncateHash = CURVE.truncateHash || _truncateHash;

}
// pair (32 bytes of r, 32 bytes of s)
// pair (bytes of r, bytes of s)
static fromCompact(hex) {

@@ -787,5 +795,7 @@ const arr = hex instanceof Uint8Array;

const str = arr ? (0, utils_js_1.bytesToHex)(hex) : hex;
if (str.length !== 128)
throw new Error(`${name}: Expected 64-byte hex`);
return new Signature((0, utils_js_1.hexToNumber)(str.slice(0, 64)), (0, utils_js_1.hexToNumber)(str.slice(64, 128)));
const gl = CURVE.nByteLength * 2; // group length in hex, not ui8a
if (str.length !== 2 * gl)
throw new Error(`${name}: Expected ${gl / 2}-byte hex`);
const slice = (from, to) => ut.hexToNumber(str.slice(from, to));
return new Signature(slice(0, gl), slice(gl, 2 * gl));
}

@@ -798,3 +808,3 @@ // DER encoded ECDSA signature

throw new TypeError(`Signature.fromDER: Expected string or Uint8Array`);
const { r, s } = parseDERSignature(arr ? hex : (0, utils_js_1.hexToBytes)(hex));
const { r, s } = DER.parseSig(arr ? hex : ut.hexToBytes(hex));
return new Signature(r, s);

@@ -815,2 +825,3 @@ }

* https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm#Public_key_recovery
* It's also possible to recover key without bit: try all 4 bit values and check for sig match.
*

@@ -831,7 +842,10 @@ * ```

throw new Error('Cannot recover: recovery bit is not present');
if (recovery !== 0 && recovery !== 1)
if (![0, 1, 2, 3].includes(recovery))
throw new Error('Cannot recover: invalid recovery bit');
const h = truncateHash((0, utils_js_1.ensureBytes)(msgHash));
const h = truncateHash(ut.ensureBytes(msgHash));
const { n } = CURVE;
const rinv = mod.invert(r, n);
const radj = recovery === 2 || recovery === 3 ? r + n : r;
if (radj >= Fp.ORDER)
throw new Error('Cannot recover: bit 2/3 is invalid with current r');
const rinv = mod.invert(radj, n);
// Q = u1⋅G + u2⋅R

@@ -841,4 +855,4 @@ const u1 = mod.mod(-h * rinv, n);

const prefix = recovery & 1 ? '03' : '02';
const R = Point.fromHex(prefix + numToFieldStr(r));
const Q = Point.BASE.multiplyAndAddUnsafe(R, u1, u2);
const R = Point.fromHex(prefix + numToFieldStr(radj));
const Q = Point.BASE.multiplyAndAddUnsafe(R, u1, u2); // unsafe is fine: no priv data leaked
if (!Q)

@@ -863,18 +877,19 @@ throw new Error('Cannot recover: point at infinify');

// DER-encoded
toDERRawBytes(isCompressed = false) {
return (0, utils_js_1.hexToBytes)(this.toDERHex(isCompressed));
toDERRawBytes() {
return ut.hexToBytes(this.toDERHex());
}
toDERHex(isCompressed = false) {
const sHex = sliceDER((0, utils_js_1.numberToHexUnpadded)(this.s));
if (isCompressed)
return sHex;
const rHex = sliceDER((0, utils_js_1.numberToHexUnpadded)(this.r));
const rLen = (0, utils_js_1.numberToHexUnpadded)(rHex.length / 2);
const sLen = (0, utils_js_1.numberToHexUnpadded)(sHex.length / 2);
const length = (0, utils_js_1.numberToHexUnpadded)(rHex.length / 2 + sHex.length / 2 + 4);
toDERHex() {
const { numberToHexUnpadded: toHex } = ut;
const sHex = DER.slice(toHex(this.s));
const rHex = DER.slice(toHex(this.r));
const sHexL = sHex.length / 2;
const rHexL = rHex.length / 2;
const sLen = toHex(sHexL);
const rLen = toHex(rHexL);
const length = toHex(rHexL + sHexL + 4);
return `30${length}02${rLen}${rHex}02${sLen}${sHex}`;
}
// 32 bytes of r, then 32 bytes of s
// padded bytes of r, then padded bytes of s
toCompactRawBytes() {
return (0, utils_js_1.hexToBytes)(this.toCompactHex());
return ut.hexToBytes(this.toCompactHex());
}

@@ -886,4 +901,2 @@ toCompactHex() {

const utils = {
mod: (n, modulo = Fp.ORDER) => mod.mod(n, modulo),
invert: Fp.invert,
isValidPrivateKey(privateKey) {

@@ -908,3 +921,3 @@ try {

*/
hashToPrivateKey: (hash) => numToField((0, utils_js_1.hashToPrivateScalar)(hash, CURVE_ORDER)),
hashToPrivateKey: (hash) => numToField(ut.hashToPrivateScalar(hash, CURVE_ORDER)),
/**

@@ -931,6 +944,6 @@ * Produces cryptographically secure private key from random of size (nBitLength+64)

/**
* Computes public key for a private key.
* Computes public key for a private key. Checks for validity of the private key.
* @param privateKey private key
* @param isCompressed whether to return compact, or full key
* @returns Public key, full by default; short when isCompressed=true
* @param isCompressed whether to return compact (default), or full key
* @returns Public key, full when isCompressed=false; short when isCompressed=true
*/

@@ -956,8 +969,8 @@ function getPublicKey(privateKey, isCompressed = false) {

/**
* ECDH (Elliptic Curve Diffie Hellman) implementation.
* 1. Checks for validity of private key
* 2. Checks for the public key of being on-curve
* ECDH (Elliptic Curve Diffie Hellman).
* Computes shared public key from private key and public key.
* Checks: 1) private key validity 2) shared key is on-curve
* @param privateA private key
* @param publicB different public key
* @param isCompressed whether to return compact (33-byte), or full (65-byte) key
* @param isCompressed whether to return compact (default), or full key
* @returns shared public key

@@ -976,4 +989,17 @@ */

function bits2int(bytes) {
const slice = bytes.length > Fp.BYTES ? bytes.slice(0, Fp.BYTES) : bytes;
return (0, utils_js_1.bytesToNumberBE)(slice);
const { nByteLength } = CURVE;
if (!(bytes instanceof Uint8Array))
throw new Error('Expected Uint8Array');
const slice = bytes.length > nByteLength ? bytes.slice(0, nByteLength) : bytes;
// const slice = bytes; nByteLength; nBitLength;
let num = ut.bytesToNumberBE(slice);
// const { nBitLength } = CURVE;
// const delta = (bytes.length * 8) - nBitLength;
// if (delta > 0) {
// // console.log('bits=', bytes.length*8, 'CURVE n=', nBitLength, 'delta=', delta);
// // console.log(bytes.length, nBitLength, delta);
// // console.log(bytes, new Error().stack);
// num >>= BigInt(delta);
// }
return num;
}

@@ -986,3 +1012,3 @@ function bits2octets(bytes) {

function int2octets(num) {
return numToField(num); // prohibits >32 bytes
return numToField(num); // prohibits >nByteLength bytes
}

@@ -995,3 +1021,3 @@ // Steps A, D of RFC6979 3.2

// Step A is ignored, since we already provide hash instead of msg
const h1 = numToField(truncateHash((0, utils_js_1.ensureBytes)(msgHash)));
const h1 = numToField(truncateHash(ut.ensureBytes(msgHash)));
const d = normalizePrivateKey(privateKey);

@@ -1004,3 +1030,3 @@ // K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1) || k')

extraEntropy = CURVE.randomBytes(Fp.BYTES);
const e = (0, utils_js_1.ensureBytes)(extraEntropy);
const e = ut.ensureBytes(extraEntropy);
if (e.length !== Fp.BYTES)

@@ -1013,3 +1039,3 @@ throw new Error(`sign: Expected ${Fp.BYTES} bytes of extra data`);

// V, 0x00 are done in HmacDRBG constructor.
const seed = (0, utils_js_1.concatBytes)(...seedArgs);
const seed = ut.concatBytes(...seedArgs);
const m = bits2int(h1);

@@ -1038,6 +1064,7 @@ return { seed, m, d };

return;
// s = (1/k * (m + dr) mod n
// s = (m + dr)/k mod n where x/k == x*inv(k)
const s = mod.mod(kinv * mod.mod(m + mod.mod(d * r, n), n), n);
if (s === _0n)
return;
// recovery bit is usually 0 or 1; rarely it's 2 or 3, when q.x > n
let recovery = (q.x === r ? 0 : 2) | Number(q.y & _1n);

@@ -1051,7 +1078,14 @@ let normS = s;

}
const defaultSigOpts = { lowS: CURVE.lowS };
/**
* Signs message hash (not message: you need to hash it by yourself).
* ```
* sign(m, d, k) where
* (x, y) = G × k
* r = x mod n
* s = (m + dr)/k mod n
* ```
* @param opts `lowS, extraEntropy`
*/
function sign(msgHash, privKey, opts = { lowS: CURVE.lowS }) {
function sign(msgHash, privKey, opts = defaultSigOpts) {
// Steps A, D of RFC6979 3.2.

@@ -1068,2 +1102,8 @@ const { seed, m, d } = initSigArgs(msgHash, privKey, opts.extraEntropy);

}
/**
* Signs a message (not message hash).
*/
function signUnhashed(msg, privKey, opts = defaultSigOpts) {
return sign(CURVE.hash(ut.ensureBytes(msg)), privKey, opts);
}
// Enable precomputes. Slows down first publicKey computation by 20ms.

@@ -1101,3 +1141,3 @@ Point.BASE._setWindowSize(8);

}
msgHash = (0, utils_js_1.ensureBytes)(msgHash);
msgHash = ut.ensureBytes(msgHash);
}

@@ -1136,2 +1176,3 @@ catch (error) {

sign,
signUnhashed,
verify,

@@ -1138,0 +1179,0 @@ Point,

1

lib/bls12-381.d.ts

@@ -0,1 +1,2 @@

/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { CurveFn } from './abstract/bls.js';

@@ -2,0 +3,0 @@ import * as mod from './abstract/modular.js';

21

lib/bls12-381.js
"use strict";
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
Object.defineProperty(exports, "__esModule", { value: true });
exports.bls12_381 = void 0;
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// The pairing-friendly Barreto-Lynn-Scott elliptic curve construction allows to:
// - Construct zk-SNARKs at the 128-bit security
// - Use threshold signatures, which allows a user to sign lots of messages with one signature and verify them swiftly in a batch, using Boneh-Lynn-Shacham signature scheme.
// Differences from @noble/bls12-381 1.4:
// - PointG1 -> G1.Point
// - PointG2 -> G2.Point
// - PointG2.fromSignature -> Signature.decode
// - PointG2.toSignature -> Signature.encode
// - Fixed Fp2 ORDER
// - Points now have only two coordinates
const sha256_1 = require("@noble/hashes/sha256");

@@ -13,9 +23,2 @@ const utils_1 = require("@noble/hashes/utils");

const hash_to_curve_js_1 = require("./abstract/hash-to-curve.js");
// Differences from bls12-381:
// - PointG1 -> G1.Point
// - PointG2 -> G2.Point
// - PointG2.fromSignature -> Signature.decode
// - PointG2.toSignature -> Signature.encode
// - Fixed Fp2 ORDER
// Points now have only two coordinates
// CURVE FIELDS

@@ -104,2 +107,4 @@ // Finite field over p.

sqrt: (num) => {
if (Fp2.equals(num, Fp2.ZERO))
return Fp2.ZERO; // Algo doesn't handles this case
// TODO: Optimize this line. It's extremely slow.

@@ -106,0 +111,0 @@ // Speeding this up would boost aggregateSignatures.

10

lib/ed25519.js

@@ -228,3 +228,3 @@ "use strict";

const MAX_255B = BigInt('0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff');
const bytes255ToNumberLE = (bytes) => exports.ed25519.utils.mod((0, utils_js_1.bytesToNumberLE)(bytes) & MAX_255B);
const bytes255ToNumberLE = (bytes) => exports.ed25519.CURVE.Fp.create((0, utils_js_1.bytesToNumberLE)(bytes) & MAX_255B);
// Computes Elligator map for Ristretto

@@ -235,3 +235,3 @@ // https://ristretto.group/formulas/elligator.html

const P = exports.ed25519.CURVE.Fp.ORDER;
const { mod } = exports.ed25519.utils;
const mod = exports.ed25519.CURVE.Fp.create;
const r = mod(SQRT_M1 * r0 * r0); // 1

@@ -294,3 +294,3 @@ const Ns = mod((r + _1n) * ONE_MINUS_D_SQ); // 2

const P = exports.ed25519.CURVE.Fp.ORDER;
const { mod } = exports.ed25519.utils;
const mod = exports.ed25519.CURVE.Fp.create;
const emsg = 'RistrettoPoint.fromHex: the hex is not valid encoding of RistrettoPoint';

@@ -327,3 +327,3 @@ const s = bytes255ToNumberLE(hex);

const P = exports.ed25519.CURVE.Fp.ORDER;
const { mod } = exports.ed25519.utils;
const mod = exports.ed25519.CURVE.Fp.create;
const u1 = mod(mod(z + y) * mod(z - y)); // 1

@@ -366,3 +366,3 @@ const u2 = mod(x * y); // 2

const b = other.ep;
const { mod } = exports.ed25519.utils;
const mod = exports.ed25519.CURVE.Fp.create;
// (x1 * y2 == y1 * x2) | (y1 * y2 == x1 * x2)

@@ -369,0 +369,0 @@ const one = mod(a.x * b.y) === mod(a.y * b.x);

3

lib/ed448.js

@@ -132,3 +132,4 @@ "use strict";

Fp,
// Subgroup order: how many points ed448 has; 2n**446n - 13818066809895115352007386748515426880336692474882178609894547503885n
// Subgroup order: how many points curve has;
// 2n**446n - 13818066809895115352007386748515426880336692474882178609894547503885n
n: BigInt('181709681073901722637330951972001133588410340171829515070372549795146003961539585716195755291692375963310293709091662304773755859649779'),

@@ -135,0 +136,0 @@ nBitLength: 456,

101

lib/esm/abstract/bls.js

@@ -1,19 +0,9 @@

/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// Barreto-Lynn-Scott Curves. A family of pairing friendly curves, with embedding degree = 12 or 24
// NOTE: only 12 supported for now
// Constructed from pair of weierstrass curves, based pairing logic
import * as mod from './modular.js';
import { ensureBytes, numberToBytesBE, bytesToNumberBE, bitLen, bitGet } from './utils.js';
// Types
import { hexToBytes, bytesToHex } from './utils.js';
import { stringToBytes, hash_to_field, expand_message_xmd } from './hash-to-curve.js';
import * as ut from './utils.js';
import { stringToBytes, hash_to_field as hashToField, expand_message_xmd as expandMessageXMD, } from './hash-to-curve.js';
import { weierstrassPoints } from './weierstrass.js';
export function bls(CURVE) {
// Fields looks pretty specific for curve, so for now we need to pass them with options
const Fp = CURVE.Fp;
const Fr = CURVE.Fr;
const Fp2 = CURVE.Fp2;
const Fp6 = CURVE.Fp6;
const Fp12 = CURVE.Fp12;
const BLS_X_LEN = bitLen(CURVE.x);
const { Fp, Fr, Fp2, Fp6, Fp12 } = CURVE;
const BLS_X_LEN = ut.bitLen(CURVE.x);
const groupLen = 32; // TODO: calculate; hardcoded for now
// Pre-compute coefficients for sparse multiplication

@@ -42,3 +32,3 @@ // Point addition and point double calculations is reused for coefficients

Rz = Fp2.mul(t0, t4); // T0 * T4
if (bitGet(CURVE.x, i)) {
if (ut.bitGet(CURVE.x, i)) {
// Addition

@@ -64,2 +54,3 @@ let t0 = Fp2.sub(Ry, Fp2.mul(Qy, Rz)); // Ry - Qy * Rz

function millerLoop(ell, g1) {
const { x } = CURVE;
const Px = g1[0];

@@ -71,3 +62,3 @@ const Py = g1[1];

f12 = Fp12.multiplyBy014(f12, E[0], Fp2.mul(E[1], Px), Fp2.mul(E[2], Py));
if (bitGet(CURVE.x, i)) {
if (ut.bitGet(x, i)) {
j += 1;

@@ -82,50 +73,13 @@ const F = ell[j];

}
// bls12-381 is a construction of two curves:
// 1. Fp: (x, y)
// 2. Fp₂: ((x₁, x₂+i), (y₁, y₂+i)) - (complex numbers)
//
// Bilinear Pairing (ate pairing) is used to combine both elements into a paired one:
// Fp₁₂ = e(Fp, Fp2)
// where Fp₁₂ = 12-degree polynomial
// Pairing is used to verify signatures.
//
// We are using Fp for private keys (shorter) and Fp2 for signatures (longer).
// Some projects may prefer to swap this relation, it is not supported for now.
const htfDefaults = { ...CURVE.htfDefaults };
function isWithinCurveOrder(num) {
return 0 < num && num < CURVE.r;
}
const utils = {
hexToBytes: hexToBytes,
bytesToHex: bytesToHex,
mod: mod.mod,
stringToBytes,
hexToBytes: ut.hexToBytes,
bytesToHex: ut.bytesToHex,
stringToBytes: stringToBytes,
// TODO: do we need to export it here?
hashToField: (msg, count, options = {}) => hash_to_field(msg, count, { ...CURVE.htfDefaults, ...options }),
expandMessageXMD: (msg, DST, lenInBytes, H = CURVE.hash) => expand_message_xmd(msg, DST, lenInBytes, H),
/**
* Can take 40 or more bytes of uniform input e.g. from CSPRNG or KDF
* and convert them into private key, with the modulo bias being negligible.
* As per FIPS 186 B.1.1.
* https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
* @param hash hash output from sha512, or a similar function
* @returns valid private key
*/
hashToPrivateKey: (hash) => {
hash = ensureBytes(hash);
if (hash.length < 40 || hash.length > 1024)
throw new Error('Expected 40-1024 bytes of private key as per FIPS 186');
// hashToPrivateScalar(hash, CURVE.r)
// NOTE: doesn't add +/-1
const num = mod.mod(bytesToNumberBE(hash), CURVE.r);
// This should never happen
if (num === 0n || num === 1n)
throw new Error('Invalid private key');
return numberToBytesBE(num, 32);
},
randomBytes: (bytesLength = 32) => CURVE.randomBytes(bytesLength),
// NIST SP 800-56A rev 3, section 5.6.1.2.2
// https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
randomPrivateKey: () => utils.hashToPrivateKey(utils.randomBytes(40)),
getDSTLabel: () => htfDefaults.DST,
hashToField: (msg, count, options = {}) => hashToField(msg, count, { ...CURVE.htfDefaults, ...options }),
expandMessageXMD: (msg, DST, lenInBytes, H = CURVE.hash) => expandMessageXMD(msg, DST, lenInBytes, H),
hashToPrivateKey: (hash) => Fr.toBytes(ut.hashToPrivateScalar(hash, CURVE.r)),
randomBytes: (bytesLength = groupLen) => CURVE.randomBytes(bytesLength),
randomPrivateKey: () => utils.hashToPrivateKey(utils.randomBytes(groupLen + 8)),
getDSTLabel: () => CURVE.htfDefaults.DST,
setDSTLabel(newLabel) {

@@ -136,22 +90,5 @@ // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-3.1

}
htfDefaults.DST = newLabel;
CURVE.htfDefaults.DST = newLabel;
},
};
function normalizePrivKey(key) {
let int;
if (key instanceof Uint8Array && key.length === 32)
int = bytesToNumberBE(key);
else if (typeof key === 'string' && key.length === 64)
int = BigInt(`0x${key}`);
else if (typeof key === 'number' && key > 0 && Number.isSafeInteger(key))
int = BigInt(key);
else if (typeof key === 'bigint' && key > 0n)
int = key;
else
throw new TypeError('Expected valid private key');
int = mod.mod(int, CURVE.r);
if (!isWithinCurveOrder(int))
throw new Error('Private key must be 0 < key < CURVE.r');
return int;
}
// Point on G1 curve: (x, y)

@@ -210,3 +147,3 @@ const G1 = weierstrassPoints({

msgPoint.assertValidity();
const sigPoint = msgPoint.multiply(normalizePrivKey(privateKey));
const sigPoint = msgPoint.multiply(G1.normalizePrivateKey(privateKey));
if (message instanceof G2.Point)

@@ -213,0 +150,0 @@ return sigPoint;

197

lib/esm/abstract/edwards.js
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// Twisted Edwards curve. The formula is: ax² + y² = 1 + dx²y²
// Differences from @noble/ed25519 1.7:
// 1. Different field element lengths in ed448:
// 1. Variable field element lengths between EDDSA/ECDH:
// EDDSA (RFC8032) is 456 bits / 57 bytes, ECDH (RFC7748) is 448 bits / 56 bytes
// 2. Different addition formula (doubling is same)
// 3. uvRatio differs between curves (half-expected, not only pow fn changes)
// 4. Point decompression code is different too (unexpected), now using generalized formula
// 4. Point decompression code is different (unexpected), now using generalized formula
// 5. Domain function was no-op for ed25519, but adds some data even with empty context for ed448
import * as mod from './modular.js';
import { bytesToHex, concatBytes, ensureBytes, numberToBytesLE, bytesToNumberLE, hashToPrivateScalar, validateOpts as utilOpts, } from './utils.js'; // TODO: import * as u from './utils.js'?
import * as ut from './utils.js';
import { ensureBytes } from './utils.js';
import { wNAF } from './group.js';
import { hash_to_field, validateHTFOpts } from './hash-to-curve.js';
import { hash_to_field as hashToField, validateHTFOpts } from './hash-to-curve.js';
// Be friendly to bad ECMAScript parsers by not using bigint literals like 123n

@@ -19,10 +20,10 @@ const _0n = BigInt(0);

const _8n = BigInt(8);
// Should be separate from overrides, since overrides can use information about curve (for example nBits)
function validateOpts(curve) {
const opts = utilOpts(curve);
if (typeof opts.hash !== 'function' || !Number.isSafeInteger(opts.hash.outputLen))
const opts = ut.validateOpts(curve);
if (typeof opts.hash !== 'function' || !ut.isPositiveInt(opts.hash.outputLen))
throw new Error('Invalid hash function');
for (const i of ['a', 'd']) {
if (typeof opts[i] !== 'bigint')
throw new Error(`Invalid curve param ${i}=${opts[i]} (${typeof opts[i]})`);
const val = opts[i];
if (typeof val !== 'bigint')
throw new Error(`Invalid curve param ${i}=${val} (${typeof val})`);
}

@@ -33,9 +34,3 @@ for (const fn of ['randomBytes']) {

}
for (const fn of [
'adjustScalarBytes',
'domain',
'uvRatio',
'mapToCurve',
'clearCofactor',
]) {
for (const fn of ['adjustScalarBytes', 'domain', 'uvRatio', 'mapToCurve']) {
if (opts[fn] === undefined)

@@ -56,8 +51,3 @@ continue; // Optional

const CURVE_ORDER = CURVE.n;
const fieldLen = Fp.BYTES; // 32 (length of one field element)
if (fieldLen > 2048)
throw new Error('Field lengths over 2048 are not supported');
const groupLen = CURVE.nByteLength;
// (2n ** 256n).toString(16);
const maxGroupElement = _2n ** BigInt(groupLen * 8); // previous POW_2_256
const maxGroupElement = _2n ** BigInt(CURVE.nByteLength * 8);
// Function overrides

@@ -67,20 +57,18 @@ const { randomBytes } = CURVE;

// sqrt(u/v)
function _uvRatio(u, v) {
try {
const value = Fp.sqrt(u * Fp.invert(v));
return { isValid: true, value };
}
catch (e) {
return { isValid: false, value: _0n };
}
}
const uvRatio = CURVE.uvRatio || _uvRatio;
const _adjustScalarBytes = (bytes) => bytes; // NOOP
const adjustScalarBytes = CURVE.adjustScalarBytes || _adjustScalarBytes;
function _domain(data, ctx, phflag) {
if (ctx.length || phflag)
throw new Error('Contexts/pre-hash are not supported');
return data;
}
const domain = CURVE.domain || _domain; // NOOP
const uvRatio = CURVE.uvRatio ||
((u, v) => {
try {
return { isValid: true, value: Fp.sqrt(u * Fp.invert(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
/**

@@ -222,6 +210,4 @@ * Extended Point works in extended coordinates: (x, y, z, t) ∋ (x=x/z, y=y/z, t=xy).

// an exposed private key e.g. sig verification.
// Allows scalar bigger than curve order, but less than 2^256
multiplyUnsafe(scalar) {
let n = normalizeScalar(scalar, CURVE_ORDER, false);
const G = ExtendedPoint.BASE;
const P0 = ExtendedPoint.ZERO;

@@ -232,6 +218,9 @@ if (n === _0n)

return this;
if (this.equals(G))
if (this.equals(ExtendedPoint.BASE))
return this.wNAF(n);
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.

@@ -241,5 +230,6 @@ isSmallOrder() {

}
// Multiplies point by a very big scalar n and checks if the result is 0.
// Multiplies point by curve order (very big scalar CURVE.n) and checks if the result is 0.
// Returns `false` is the point is dirty.
isTorsionFree() {
return this.multiplyUnsafe(CURVE_ORDER).equals(ExtendedPoint.ZERO);
return wnaf.unsafeLadder(this, CURVE_ORDER).equals(ExtendedPoint.ZERO);
}

@@ -263,9 +253,6 @@ // Converts Extended point to default (x, y) coordinates.

clearCofactor() {
if (CURVE.h === _1n)
return this; // Fast-path
// clear_cofactor(P) := h_eff * P
// hEff = h for ed25519/ed448. Maybe worth moving to params?
if (CURVE.clearCofactor)
return CURVE.clearCofactor(ExtendedPoint, this);
return this.multiplyUnsafe(CURVE.h);
const { h: cofactor } = CURVE;
if (cofactor === _1n)
return this;
return this.multiplyUnsafe(cofactor);
}

@@ -275,3 +262,3 @@ }

ExtendedPoint.ZERO = new ExtendedPoint(_0n, _1n, _1n, _0n);
const wnaf = wNAF(ExtendedPoint, groupLen * 8);
const wnaf = wNAF(ExtendedPoint, CURVE.nByteLength * 8);
function assertExtPoint(other) {

@@ -300,3 +287,4 @@ if (!(other instanceof ExtendedPoint))

const { d, a } = CURVE;
hex = ensureBytes(hex, fieldLen);
const len = Fp.BYTES;
hex = ensureBytes(hex, len);
// 1. First, interpret the string as an integer in little-endian

@@ -308,9 +296,9 @@ // representation. Bit 255 of this number is the least significant

const normed = hex.slice();
const lastByte = hex[fieldLen - 1];
normed[fieldLen - 1] = lastByte & ~0x80;
const y = bytesToNumberLE(normed);
const lastByte = hex[len - 1];
normed[len - 1] = lastByte & ~0x80;
const y = ut.bytesToNumberLE(normed);
if (strict && y >= Fp.ORDER)
throw new Error('Expected 0 < hex < P');
if (!strict && y >= maxGroupElement)
throw new Error('Expected 0 < hex < 2**256');
throw new Error('Expected 0 < hex < CURVE.n');
// 2. To recover the x-coordinate, the curve equation implies

@@ -347,4 +335,4 @@ // Ed25519: x² = (y² - 1) / (d y² + 1) (mod p).

toRawBytes() {
const bytes = numberToBytesLE(this.y, fieldLen);
bytes[fieldLen - 1] |= this.x & _1n ? 0x80 : 0;
const bytes = ut.numberToBytesLE(this.y, Fp.BYTES);
bytes[Fp.BYTES - 1] |= this.x & _1n ? 0x80 : 0;
return bytes;

@@ -354,4 +342,6 @@ }

toHex() {
return bytesToHex(this.toRawBytes());
return ut.bytesToHex(this.toRawBytes());
}
// Determines if point is in prime-order subgroup.
// Returns `false` is the point is dirty.
isTorsionFree() {

@@ -391,8 +381,8 @@ return ExtendedPoint.fromAffine(this).isTorsionFree();

static hashToCurve(msg, options) {
if (!CURVE.mapToCurve)
const { mapToCurve, htfDefaults } = CURVE;
if (!mapToCurve)
throw new Error('No mapToCurve defined for curve');
msg = ensureBytes(msg);
const u = hash_to_field(msg, 2, { ...CURVE.htfDefaults, ...options });
const { x: x0, y: y0 } = CURVE.mapToCurve(u[0]);
const { x: x1, y: y1 } = CURVE.mapToCurve(u[1]);
const u = hashToField(ensureBytes(msg), 2, { ...htfDefaults, ...options });
const { x: x0, y: y0 } = mapToCurve(u[0]);
const { x: x1, y: y1 } = mapToCurve(u[1]);
const p = new Point(x0, y0).add(new Point(x1, y1)).clearCofactor();

@@ -403,7 +393,7 @@ return p;

static encodeToCurve(msg, options) {
if (!CURVE.mapToCurve)
const { mapToCurve, htfDefaults } = CURVE;
if (!mapToCurve)
throw new Error('No mapToCurve defined for curve');
msg = ensureBytes(msg);
const u = hash_to_field(msg, 1, { ...CURVE.htfDefaults, ...options });
const { x, y } = CURVE.mapToCurve(u[0]);
const u = hashToField(ensureBytes(msg), 1, { ...htfDefaults, ...options });
const { x, y } = mapToCurve(u[0]);
return new Point(x, y).clearCofactor();

@@ -428,5 +418,6 @@ }

static fromHex(hex) {
const bytes = ensureBytes(hex, 2 * fieldLen);
const r = Point.fromHex(bytes.slice(0, fieldLen), false);
const s = bytesToNumberLE(bytes.slice(fieldLen, 2 * fieldLen));
const len = Fp.BYTES;
const bytes = ensureBytes(hex, 2 * len);
const r = Point.fromHex(bytes.slice(0, len), false);
const s = ut.bytesToNumberLE(bytes.slice(len, 2 * len));
return new Signature(r, s);

@@ -443,11 +434,11 @@ }

toRawBytes() {
return concatBytes(this.r.toRawBytes(), numberToBytesLE(this.s, fieldLen));
return ut.concatBytes(this.r.toRawBytes(), ut.numberToBytesLE(this.s, Fp.BYTES));
}
toHex() {
return bytesToHex(this.toRawBytes());
return ut.bytesToHex(this.toRawBytes());
}
}
// Little-endian SHA512 with modulo n
function modlLE(hash) {
return mod.mod(bytesToNumberLE(hash), CURVE_ORDER);
function modnLE(hash) {
return mod.mod(ut.bytesToNumberLE(hash), CURVE_ORDER);
}

@@ -463,3 +454,3 @@ /**

throw new TypeError('Specify max value');
if (typeof num === 'number' && Number.isSafeInteger(num))
if (ut.isPositiveInt(num))
num = BigInt(num);

@@ -476,32 +467,26 @@ if (typeof num === 'bigint' && num < max) {

}
throw new TypeError('Expected valid scalar: 0 < scalar < max');
throw new TypeError(`Expected valid scalar: 0 < scalar < ${max}`);
}
function checkPrivateKey(key) {
/** Convenience method that creates public key and other stuff. RFC8032 5.1.5 */
function getExtendedPublicKey(key) {
const groupLen = CURVE.nByteLength;
// Normalize bigint / number / string to Uint8Array
key =
typeof key === 'bigint' || typeof key === 'number'
? numberToBytesLE(normalizeScalar(key, maxGroupElement), groupLen)
: ensureBytes(key);
if (key.length !== groupLen)
throw new Error(`Expected ${groupLen} bytes, got ${key.length}`);
return key;
}
// Takes 64 bytes
function getKeyFromHash(hashed) {
// First 32 bytes of 64b uniformingly random input are taken,
// clears 3 bits of it to produce a random field element.
const keyb = typeof key === 'bigint' || typeof key === 'number'
? ut.numberToBytesLE(normalizeScalar(key, maxGroupElement), groupLen)
: key;
// Hash private key with curve's hash function to produce uniformingly random input
// We check byte lengths e.g.: ensureBytes(64, hash(ensureBytes(32, key)))
const hashed = ensureBytes(CURVE.hash(ensureBytes(keyb, groupLen)), 2 * groupLen);
// First half's bits are cleared to produce a random field element.
const head = adjustScalarBytes(hashed.slice(0, groupLen));
// Second 32 bytes is called key prefix (5.1.6)
// Second half is called key prefix (5.1.6)
const prefix = hashed.slice(groupLen, 2 * groupLen);
// The actual private scalar
const scalar = modlLE(head);
const scalar = modnLE(head);
// Point on Edwards curve aka public key
const point = Point.BASE.multiply(scalar);
// Uint8Array representation
const pointBytes = point.toRawBytes();
return { head, prefix, scalar, point, pointBytes };
}
/** Convenience method that creates public key and other stuff. RFC8032 5.1.5 */
function getExtendedPublicKey(key) {
return getKeyFromHash(CURVE.hash(checkPrivateKey(key)));
}
/**

@@ -518,3 +503,3 @@ * Calculates ed25519 public key. RFC8032 5.1.5

context = ensureBytes(context);
return modlLE(CURVE.hash(domain(message, context, !!CURVE.preHash)));
return modnLE(CURVE.hash(domain(message, context, !!CURVE.preHash)));
}

@@ -527,5 +512,5 @@ /** Signs message with privateKey. RFC8032 5.1.6 */

const { prefix, scalar, pointBytes } = getExtendedPublicKey(privateKey);
const r = hashDomainToScalar(concatBytes(prefix, message), context);
const r = hashDomainToScalar(ut.concatBytes(prefix, message), context);
const R = Point.BASE.multiply(r); // R = rG
const k = hashDomainToScalar(concatBytes(R.toRawBytes(), pointBytes, message), context); // k = hash(R+P+msg)
const k = hashDomainToScalar(ut.concatBytes(R.toRawBytes(), pointBytes, message), context); // k = hash(R+P+msg)
const s = mod.mod(r + k * scalar, CURVE_ORDER); // s = r + kp

@@ -569,7 +554,7 @@ return new Signature(R, s).toRawBytes();

const SB = ExtendedPoint.BASE.multiplyUnsafe(s);
const k = hashDomainToScalar(concatBytes(r.toRawBytes(), publicKey.toRawBytes(), message), context);
const k = hashDomainToScalar(ut.concatBytes(r.toRawBytes(), publicKey.toRawBytes(), message), context);
const kA = ExtendedPoint.fromAffine(publicKey).multiplyUnsafe(k);
const RkA = ExtendedPoint.fromAffine(r).add(kA);
// [8][S]B = [8]R + [8][k]A'
return RkA.subtract(SB).multiplyUnsafe(CURVE.h).equals(ExtendedPoint.ZERO);
return RkA.subtract(SB).clearCofactor().equals(ExtendedPoint.ZERO);
}

@@ -580,8 +565,6 @@ // Enable precomputes. Slows down first publicKey computation by 20ms.

getExtendedPublicKey,
mod: modP,
invert: Fp.invert,
/**
* Not needed for ed25519 private keys. Needed if you use scalars directly (rare).
*/
hashToPrivateScalar: (hash) => hashToPrivateScalar(hash, CURVE_ORDER, true),
hashToPrivateScalar: (hash) => ut.hashToPrivateScalar(hash, CURVE_ORDER, true),
/**

@@ -591,3 +574,3 @@ * ed25519 private keys are uniform 32-bit strings. We do not need to check for

*/
randomPrivateKey: () => randomBytes(fieldLen),
randomPrivateKey: () => randomBytes(Fp.BYTES),
/**

@@ -594,0 +577,0 @@ * We're doing scalar multiplication (used in getPublicKey etc) with precomputed BASE_POINT

49

lib/esm/abstract/modular.js

@@ -58,2 +58,3 @@ /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */

while (a !== _0n) {
// JIT applies optimization if those two lines follow each other
const q = b / a;

@@ -72,3 +73,4 @@ const r = b % a;

// Tonelli-Shanks algorithm
// https://eprint.iacr.org/2012/685.pdf (page 12)
// Paper 1: https://eprint.iacr.org/2012/685.pdf (page 12)
// Paper 2: Square Roots from 1; 24, 51, 10 to Dan Shanks
export function tonelliShanks(P) {

@@ -83,3 +85,3 @@ // Legendre constant: used to calculate Legendre symbol (a | p),

// Step 1: By factoring out powers of 2 from p - 1,
// find q and s such that p - 1 = q2s with q odd
// find q and s such that p - 1 = q*(2^s) with q odd
for (Q = P - _1n, S = 0; Q % _2n === _0n; Q /= _2n, S++)

@@ -103,27 +105,28 @@ ;

return function tonelliSlow(Fp, n) {
// Step 0: Check that n is indeed a square: (n | p) must be ≡ 1
if (Fp.pow(n, legendreC) !== Fp.ONE)
// Step 0: Check that n is indeed a square: (n | p) should not be ≡ -1
if (Fp.pow(n, legendreC) === Fp.negate(Fp.ONE))
throw new Error('Cannot find square root');
let s = S;
let c = pow(Z, Q, P);
let r = Fp.pow(n, Q1div2);
let t = Fp.pow(n, Q);
let t2 = Fp.ZERO;
while (!Fp.equals(Fp.sub(t, Fp.ONE), Fp.ZERO)) {
t2 = Fp.square(t);
let i;
for (i = 1; i < s; i++) {
// stop if t2-1 == 0
if (Fp.equals(Fp.sub(t2, Fp.ONE), Fp.ZERO))
let r = S;
// TODO: will fail at Fp2/etc
let g = Fp.pow(Fp.mul(Fp.ONE, Z), Q); // will update both x and b
let x = Fp.pow(n, Q1div2); // first guess at the square root
let b = Fp.pow(n, Q); // first guess at the fudge factor
while (!Fp.equals(b, Fp.ONE)) {
if (Fp.equals(b, Fp.ZERO))
return Fp.ZERO; // https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm (4. If t = 0, return r = 0)
// Find m such b^(2^m)==1
let m = 1;
for (let t2 = Fp.square(b); m < r; m++) {
if (Fp.equals(t2, Fp.ONE))
break;
// t2 *= t2
t2 = Fp.square(t2);
t2 = Fp.square(t2); // t2 *= t2
}
let b = pow(c, BigInt(1 << (s - i - 1)), P);
r = Fp.mul(r, b);
c = mod(b * b, P);
t = Fp.mul(t, c);
s = i;
// NOTE: r-m-1 can be bigger than 32, need to convert to bigint before shift, otherwise there will be overflow
const ge = Fp.pow(g, _1n << BigInt(r - m - 1)); // ge = 2^(r-m-1)
g = Fp.square(ge); // g = ge * ge
x = Fp.mul(x, ge); // x *= ge
b = Fp.mul(b, g); // b *= g
r = m;
}
return r;
return x;
};

@@ -130,0 +133,0 @@ }

6

lib/esm/abstract/montgomery.js
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import * as mod from './modular.js';
import { ensureBytes, numberToBytesLE, bytesToNumberLE,
// nLength,
} from './utils.js';
import { ensureBytes, numberToBytesLE, bytesToNumberLE, isPositiveInt } from './utils.js';
const _0n = BigInt(0);

@@ -16,3 +14,3 @@ const _1n = BigInt(1);

continue; // Optional
if (!Number.isSafeInteger(curve[i]))
if (!isPositiveInt(curve[i]))
throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);

@@ -19,0 +17,0 @@ }

33

lib/esm/abstract/utils.js

@@ -6,7 +6,12 @@ /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */

const _2n = BigInt(2);
// Bans floats and integers above 2^53-1
export function isPositiveInt(num) {
return typeof num === 'number' && Number.isSafeInteger(num) && num > 0;
}
export function validateOpts(curve) {
mod.validateField(curve.Fp);
for (const i of ['n', 'h']) {
if (typeof curve[i] !== 'bigint')
throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
const val = curve[i];
if (typeof val !== 'bigint')
throw new Error(`Invalid curve param ${i}=${val} (${typeof val})`);
}

@@ -18,6 +23,7 @@ if (!curve.Fp.isValid(curve.Gx))

for (const i of ['nBitLength', 'nByteLength']) {
if (curve[i] === undefined)
const val = curve[i];
if (val === undefined)
continue; // Optional
if (!Number.isSafeInteger(curve[i]))
throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
if (!isPositiveInt(val))
throw new Error(`Invalid curve param ${i}=${val} (${typeof val})`);
}

@@ -109,17 +115,18 @@ // Set defaults

/**
* FIPS 186 B.4.1-compliant "constant-time" private key generation utility.
* Can take (n+8) or more bytes of uniform input e.g. from CSPRNG or KDF
* and convert them into private scalar, with the modulo bias being neglible.
* As per FIPS 186 B.4.1.
* Needs at least 40 bytes of input for 32-byte private key.
* https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
* @param hash hash output from sha512, or a similar function
* @param hash hash output from SHA3 or a similar function
* @returns valid private scalar
*/
export function hashToPrivateScalar(hash, CURVE_ORDER, isLE = false) {
export function hashToPrivateScalar(hash, groupOrder, isLE = false) {
hash = ensureBytes(hash);
const orderLen = nLength(CURVE_ORDER).nByteLength;
const minLen = orderLen + 8;
if (orderLen < 16 || hash.length < minLen || hash.length > 1024)
throw new Error('Expected valid bytes of private key as per FIPS 186');
const hashLen = hash.length;
const minLen = nLength(groupOrder).nByteLength + 8;
if (minLen < 24 || hashLen < minLen || hashLen > 1024)
throw new Error(`hashToPrivateScalar: expected ${minLen}-1024 bytes of input, got ${hashLen}`);
const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);
return mod.mod(num, CURVE_ORDER - _1n) + _1n;
return mod.mod(num, groupOrder - _1n) + _1n;
}

@@ -126,0 +133,0 @@ export function equalBytes(b1, b2) {

375

lib/esm/abstract/weierstrass.js
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// Short Weierstrass curve. The formula is: y² = x³ + ax + b
// TODO: sync vs async naming
// TODO: default randomBytes
// Differences from @noble/secp256k1 1.7:

@@ -10,8 +8,9 @@ // 1. Different double() formula (but same addition)

// 4. DRBG supports outputLen bigger than outputLen of hmac
// 5. Support for different hash functions
import * as mod from './modular.js';
import { bytesToHex, bytesToNumberBE, concatBytes, ensureBytes, hexToBytes, hexToNumber, numberToHexUnpadded, hashToPrivateScalar, } from './utils.js';
import * as utils from './utils.js';
import * as ut from './utils.js';
import { bytesToHex } from './utils.js';
import { hash_to_field, validateHTFOpts } from './hash-to-curve.js';
import { wNAF } from './group.js';
// DER encoding utilities
// ASN.1 DER encoding utilities
class DERError extends Error {

@@ -22,42 +21,40 @@ constructor(message) {

}
function sliceDER(s) {
// Proof: any([(i>=0x80) == (int(hex(i).replace('0x', '').zfill(2)[0], 16)>=8) for i in range(0, 256)])
// Padding done by numberToHex
return Number.parseInt(s[0], 16) >= 8 ? '00' + s : s;
}
function parseDERInt(data) {
if (data.length < 2 || data[0] !== 0x02) {
throw new DERError(`Invalid signature integer tag: ${bytesToHex(data)}`);
}
const len = data[1];
const res = data.subarray(2, len + 2);
if (!len || res.length !== len) {
throw new DERError(`Invalid signature integer: wrong length`);
}
// Strange condition, its not about length, but about first bytes of number.
if (res[0] === 0x00 && res[1] <= 0x7f) {
throw new DERError('Invalid signature integer: trailing length');
}
return { data: bytesToNumberBE(res), left: data.subarray(len + 2) };
}
function parseDERSignature(data) {
if (data.length < 2 || data[0] != 0x30) {
throw new DERError(`Invalid signature tag: ${bytesToHex(data)}`);
}
if (data[1] !== data.length - 2) {
throw new DERError('Invalid signature: incorrect length');
}
const { data: r, left: sBytes } = parseDERInt(data.subarray(2));
const { data: s, left: rBytesLeft } = parseDERInt(sBytes);
if (rBytesLeft.length) {
throw new DERError(`Invalid signature: left bytes after parsing: ${bytesToHex(rBytesLeft)}`);
}
return { r, s };
}
// Be friendly to bad ECMAScript parsers by not using bigint literals like 123n
const _0n = BigInt(0);
const _1n = BigInt(1);
const _3n = BigInt(3);
const DER = {
slice(s) {
// Proof: any([(i>=0x80) == (int(hex(i).replace('0x', '').zfill(2)[0], 16)>=8) for i in range(0, 256)])
// Padding done by numberToHex
return Number.parseInt(s[0], 16) >= 8 ? '00' + s : s;
},
parseInt(data) {
if (data.length < 2 || data[0] !== 0x02) {
throw new DERError(`Invalid signature integer tag: ${bytesToHex(data)}`);
}
const len = data[1];
const res = data.subarray(2, len + 2);
if (!len || res.length !== len) {
throw new DERError(`Invalid signature integer: wrong length`);
}
// Strange condition, its not about length, but about first bytes of number.
if (res[0] === 0x00 && res[1] <= 0x7f) {
throw new DERError('Invalid signature integer: trailing length');
}
return { data: ut.bytesToNumberBE(res), left: data.subarray(len + 2) };
},
parseSig(data) {
if (data.length < 2 || data[0] != 0x30) {
throw new DERError(`Invalid signature tag: ${bytesToHex(data)}`);
}
if (data[1] !== data.length - 2) {
throw new DERError('Invalid signature: incorrect length');
}
const { data: r, left: sBytes } = DER.parseInt(data.subarray(2));
const { data: s, left: rBytesLeft } = DER.parseInt(sBytes);
if (rBytesLeft.length) {
throw new DERError(`Invalid signature: left bytes after parsing: ${bytesToHex(rBytesLeft)}`);
}
return { r, s };
},
};
function validatePointOpts(curve) {
const opts = utils.validateOpts(curve);
const opts = ut.validateOpts(curve);
const Fp = opts.Fp;

@@ -95,17 +92,9 @@ for (const i of ['a', 'b']) {

}
// Be friendly to bad ECMAScript parsers by not using bigint literals like 123n
const _0n = BigInt(0);
const _1n = BigInt(1);
const _3n = BigInt(3);
export function weierstrassPoints(opts) {
const CURVE = validatePointOpts(opts);
const Fp = CURVE.Fp;
// Lengths
// All curves has same field / group length as for now, but it can be different for other curves
const { nByteLength, nBitLength } = CURVE;
const groupLen = nByteLength;
// Not using ** operator with bigints for old engines.
// 2n ** (8n * 32n) == 2n << (8n * 32n - 1n)
//const FIELD_MASK = _2n << (_8n * BigInt(fieldLen) - _1n);
// function numToFieldStr(num: bigint): string {
// if (typeof num !== 'bigint') throw new Error('Expected bigint');
// if (!(_0n <= num && num < FIELD_MASK)) throw new Error(`Expected number < 2^${fieldLen * 8}`);
// return num.toString(16).padStart(2 * fieldLen, '0');
// }
const { Fp } = CURVE; // All curves has same field / group length as for now, but they can differ
/**

@@ -121,14 +110,22 @@ * y² = x³ + ax + b: Short weierstrass curve formula

}
// Valid group elements reside in range 1..n-1
function isWithinCurveOrder(num) {
return _0n < num && num < CURVE.n;
}
/**
* Validates if a private key is valid and converts it to bigint form.
* Supports two options, that are passed when CURVE is initialized:
* - `normalizePrivateKey()` executed before all checks
* - `wrapPrivateKey` when true, executed after most checks, but before `0 < key < n`
*/
function normalizePrivateKey(key) {
if (typeof CURVE.normalizePrivateKey === 'function') {
key = CURVE.normalizePrivateKey(key);
}
const { normalizePrivateKey: custom, nByteLength: groupLen, wrapPrivateKey, n: order } = CURVE;
if (typeof custom === 'function')
key = custom(key);
let num;
if (typeof key === 'bigint') {
// Curve order check is done below
num = key;
}
else if (typeof key === 'number' && Number.isSafeInteger(key) && key > 0) {
else if (ut.isPositiveInt(key)) {
num = BigInt(key);

@@ -139,3 +136,4 @@ }

throw new Error(`Expected ${groupLen} bytes of private key`);
num = hexToNumber(key);
// Validates individual octets
num = ut.hexToNumber(key);
}

@@ -145,3 +143,3 @@ else if (key instanceof Uint8Array) {

throw new Error(`Expected ${groupLen} bytes of private key`);
num = bytesToNumberBE(key);
num = ut.bytesToNumberBE(key);
}

@@ -151,4 +149,5 @@ else {

}
if (CURVE.wrapPrivateKey)
num = mod.mod(num, CURVE.n);
// Useful for curves with cofactor != 1
if (wrapPrivateKey)
num = mod.mod(num, order);
if (!isWithinCurveOrder(num))

@@ -158,4 +157,8 @@ throw new Error('Expected private key: 0 < key < n');

}
/**
* Validates if a scalar ("private number") is valid.
* Scalars are valid only if they are less than curve order.
*/
function normalizeScalar(num) {
if (typeof num === 'number' && Number.isSafeInteger(num) && num > 0)
if (ut.isPositiveInt(num))
return BigInt(num);

@@ -188,3 +191,3 @@ if (typeof num === 'bigint' && isWithinCurveOrder(num))

* Takes a bunch of Projective Points but executes only one
* invert on all of them. invert is very slow operation,
* inversion on all of them. Inversion is very slow operation,
* so this improves performance massively.

@@ -196,2 +199,5 @@ */

}
/**
* Optimization: converts a list of projective points to a list of identical points with Z=1.
*/
static normalizeZ(points) {

@@ -217,5 +223,2 @@ return ProjectivePoint.toAffineBatch(points).map(ProjectivePoint.fromAffine);

}
doubleAdd() {
return this.add(this);
}
// Renes-Costello-Batina exception-free doubling formula.

@@ -425,16 +428,15 @@ // There is 30% faster Jacobian formula, but it is not complete.

isTorsionFree() {
if (CURVE.h === _1n)
return true; // No subgroups, always torsion fee
if (CURVE.isTorsionFree)
return CURVE.isTorsionFree(ProjectivePoint, this);
// is multiplyUnsafe(CURVE.n) is always ok, same as for edwards?
throw new Error('Unsupported!');
const { h: cofactor, isTorsionFree } = CURVE;
if (cofactor === _1n)
return true; // No subgroups, always torsion-free
if (isTorsionFree)
return isTorsionFree(ProjectivePoint, this);
throw new Error('isTorsionFree() has not been declared for the elliptic curve');
}
// Clear cofactor of G1
// https://eprint.iacr.org/2019/403
clearCofactor() {
if (CURVE.h === _1n)
const { h: cofactor, clearCofactor } = CURVE;
if (cofactor === _1n)
return this; // Fast-path
if (CURVE.clearCofactor)
return CURVE.clearCofactor(ProjectivePoint, this);
if (clearCofactor)
return clearCofactor(ProjectivePoint, this);
return this.multiplyUnsafe(CURVE.h);

@@ -445,3 +447,4 @@ }

ProjectivePoint.ZERO = new ProjectivePoint(Fp.ZERO, Fp.ONE, Fp.ZERO);
const wnaf = wNAF(ProjectivePoint, CURVE.endo ? nBitLength / 2 : nBitLength);
const _bits = CURVE.nBitLength;
const wnaf = wNAF(ProjectivePoint, CURVE.endo ? Math.ceil(_bits / 2) : _bits);
function assertPrjPoint(other) {

@@ -477,3 +480,3 @@ if (!(other instanceof ProjectivePoint))

static fromHex(hex) {
const { x, y } = CURVE.fromBytes(ensureBytes(hex));
const { x, y } = CURVE.fromBytes(ut.ensureBytes(hex));
const point = new Point(x, y);

@@ -500,3 +503,3 @@ point.assertValidity();

return;
throw new Error('Point is infinity');
throw new Error('Point at infinity');
}

@@ -506,9 +509,9 @@ // Some 3rd-party test vectors require different wording between here & `fromCompressedHex`

const { x, y } = this;
// Check if x, y are valid field elements
if (!Fp.isValid(x) || !Fp.isValid(y))
throw new Error(msg);
const left = Fp.square(y);
const right = weierstrassEquation(x);
const left = Fp.square(y); // y²
const right = weierstrassEquation(x); // x³ + ax + b
if (!Fp.equals(left, right))
throw new Error(msg);
// TODO: flag to disable this?
if (!this.isTorsionFree())

@@ -526,11 +529,12 @@ throw new Error('Point must be of prime-order subgroup');

}
toProj() {
return ProjectivePoint.fromAffine(this);
}
// Adds point to itself
double() {
return ProjectivePoint.fromAffine(this).double().toAffine();
return this.toProj().double().toAffine();
}
// Adds point to other point
add(other) {
return ProjectivePoint.fromAffine(this).add(ProjectivePoint.fromAffine(other)).toAffine();
return this.toProj().add(ProjectivePoint.fromAffine(other)).toAffine();
}
// Subtracts other point from the point
subtract(other) {

@@ -540,12 +544,12 @@ return this.add(other.negate());

multiply(scalar) {
return ProjectivePoint.fromAffine(this).multiply(scalar, this).toAffine();
return this.toProj().multiply(scalar, this).toAffine();
}
multiplyUnsafe(scalar) {
return ProjectivePoint.fromAffine(this).multiplyUnsafe(scalar).toAffine();
return this.toProj().multiplyUnsafe(scalar).toAffine();
}
clearCofactor() {
return ProjectivePoint.fromAffine(this).clearCofactor().toAffine();
return this.toProj().clearCofactor().toAffine();
}
isTorsionFree() {
return ProjectivePoint.fromAffine(this).isTorsionFree();
return this.toProj().isTorsionFree();
}

@@ -559,3 +563,3 @@ /**

multiplyAndAddUnsafe(Q, a, b) {
const P = ProjectivePoint.fromAffine(this);
const P = this.toProj();
const aP = a === _0n || a === _1n || this !== Point.BASE ? P.multiplyUnsafe(a) : P.multiply(a);

@@ -569,18 +573,19 @@ const bQ = ProjectivePoint.fromAffine(Q).multiplyUnsafe(b);

static hashToCurve(msg, options) {
if (!CURVE.mapToCurve)
throw new Error('No mapToCurve defined for curve');
msg = ensureBytes(msg);
const { mapToCurve } = CURVE;
if (!mapToCurve)
throw new Error('CURVE.mapToCurve() has not been defined');
msg = ut.ensureBytes(msg);
const u = hash_to_field(msg, 2, { ...CURVE.htfDefaults, ...options });
const { x: x0, y: y0 } = CURVE.mapToCurve(u[0]);
const { x: x1, y: y1 } = CURVE.mapToCurve(u[1]);
const p = new Point(x0, y0).add(new Point(x1, y1)).clearCofactor();
return p;
const { x: x0, y: y0 } = mapToCurve(u[0]);
const { x: x1, y: y1 } = mapToCurve(u[1]);
return new Point(x0, y0).add(new Point(x1, y1)).clearCofactor();
}
// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-3
static encodeToCurve(msg, options) {
if (!CURVE.mapToCurve)
throw new Error('No mapToCurve defined for curve');
msg = ensureBytes(msg);
const { mapToCurve } = CURVE;
if (!mapToCurve)
throw new Error('CURVE.mapToCurve() has not been defined');
msg = ut.ensureBytes(msg);
const u = hash_to_field(msg, 1, { ...CURVE.htfDefaults, ...options });
const { x, y } = CURVE.mapToCurve(u[0]);
const { x, y } = mapToCurve(u[0]);
return new Point(x, y).clearCofactor();

@@ -590,7 +595,7 @@ }

/**
* Base point aka generator. public_key = Point.BASE * private_key
* Base point aka generator. Any public_key = Point.BASE * private_key
*/
Point.BASE = new Point(CURVE.Gx, CURVE.Gy);
/**
* Identity point aka point at infinity. point = point + zero_point
* Identity point aka point at infinity. p - p = zero_p; p + zero_p = p
*/

@@ -607,4 +612,4 @@ Point.ZERO = new Point(Fp.ZERO, Fp.ZERO);

function validateOpts(curve) {
const opts = utils.validateOpts(curve);
if (typeof opts.hash !== 'function' || !Number.isSafeInteger(opts.hash.outputLen))
const opts = ut.validateOpts(curve);
if (typeof opts.hash !== 'function' || !ut.isPositiveInt(opts.hash.outputLen))
throw new Error('Invalid hash function');

@@ -665,3 +670,3 @@ if (typeof opts.hmac !== 'function')

}
return concatBytes(...out);
return ut.concatBytes(...out);
}

@@ -673,4 +678,4 @@ }

const Fp = CURVE.Fp;
const compressedLen = Fp.BYTES + 1; // 33
const uncompressedLen = 2 * Fp.BYTES + 1; // 65
const compressedLen = Fp.BYTES + 1; // e.g. 33 for 32
const uncompressedLen = 2 * Fp.BYTES + 1; // e.g. 65 for 32
function isValidFieldElement(num) {

@@ -683,7 +688,9 @@ // 0 is disallowed by arbitrary reasons. Probably because infinity point?

toBytes(c, point, isCompressed) {
const x = Fp.toBytes(point.x);
const cat = ut.concatBytes;
if (isCompressed) {
return concatBytes(new Uint8Array([point.hasEvenY() ? 0x02 : 0x03]), Fp.toBytes(point.x));
return cat(Uint8Array.from([point.hasEvenY() ? 0x02 : 0x03]), x);
}
else {
return concatBytes(new Uint8Array([0x04]), Fp.toBytes(point.x), Fp.toBytes(point.y));
return cat(Uint8Array.from([0x04]), x, Fp.toBytes(point.y));
}

@@ -696,3 +703,3 @@ },

if (len === compressedLen && (header === 0x02 || header === 0x03)) {
const x = bytesToNumberBE(bytes.subarray(1));
const x = ut.bytesToNumberBE(bytes.subarray(1));
if (!isValidFieldElement(x))

@@ -750,13 +757,14 @@ throw new Error('Point is not on curve');

}
function bits2int_2(bytes) {
const delta = bytes.length * 8 - CURVE.nBitLength;
const num = ut.bytesToNumberBE(bytes);
return delta > 0 ? num >> BigInt(delta) : num;
}
// Ensures ECDSA message hashes are 32 bytes and < curve order
function _truncateHash(hash, truncateOnly = false) {
const { n, nBitLength } = CURVE;
const byteLength = hash.length;
const delta = byteLength * 8 - nBitLength; // size of curve.n (252 bits)
let h = bytesToNumberBE(hash);
if (delta > 0)
h = h >> BigInt(delta);
if (!truncateOnly && h >= n)
h -= n;
return h;
const h = bits2int_2(hash);
if (truncateOnly)
return h;
const { n } = CURVE;
return h >= n ? h - n : h;
}

@@ -774,3 +782,3 @@ const truncateHash = CURVE.truncateHash || _truncateHash;

}
// pair (32 bytes of r, 32 bytes of s)
// pair (bytes of r, bytes of s)
static fromCompact(hex) {

@@ -782,5 +790,7 @@ const arr = hex instanceof Uint8Array;

const str = arr ? bytesToHex(hex) : hex;
if (str.length !== 128)
throw new Error(`${name}: Expected 64-byte hex`);
return new Signature(hexToNumber(str.slice(0, 64)), hexToNumber(str.slice(64, 128)));
const gl = CURVE.nByteLength * 2; // group length in hex, not ui8a
if (str.length !== 2 * gl)
throw new Error(`${name}: Expected ${gl / 2}-byte hex`);
const slice = (from, to) => ut.hexToNumber(str.slice(from, to));
return new Signature(slice(0, gl), slice(gl, 2 * gl));
}

@@ -793,3 +803,3 @@ // DER encoded ECDSA signature

throw new TypeError(`Signature.fromDER: Expected string or Uint8Array`);
const { r, s } = parseDERSignature(arr ? hex : hexToBytes(hex));
const { r, s } = DER.parseSig(arr ? hex : ut.hexToBytes(hex));
return new Signature(r, s);

@@ -810,2 +820,3 @@ }

* https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm#Public_key_recovery
* It's also possible to recover key without bit: try all 4 bit values and check for sig match.
*

@@ -826,7 +837,10 @@ * ```

throw new Error('Cannot recover: recovery bit is not present');
if (recovery !== 0 && recovery !== 1)
if (![0, 1, 2, 3].includes(recovery))
throw new Error('Cannot recover: invalid recovery bit');
const h = truncateHash(ensureBytes(msgHash));
const h = truncateHash(ut.ensureBytes(msgHash));
const { n } = CURVE;
const rinv = mod.invert(r, n);
const radj = recovery === 2 || recovery === 3 ? r + n : r;
if (radj >= Fp.ORDER)
throw new Error('Cannot recover: bit 2/3 is invalid with current r');
const rinv = mod.invert(radj, n);
// Q = u1⋅G + u2⋅R

@@ -836,4 +850,4 @@ const u1 = mod.mod(-h * rinv, n);

const prefix = recovery & 1 ? '03' : '02';
const R = Point.fromHex(prefix + numToFieldStr(r));
const Q = Point.BASE.multiplyAndAddUnsafe(R, u1, u2);
const R = Point.fromHex(prefix + numToFieldStr(radj));
const Q = Point.BASE.multiplyAndAddUnsafe(R, u1, u2); // unsafe is fine: no priv data leaked
if (!Q)

@@ -858,18 +872,19 @@ throw new Error('Cannot recover: point at infinify');

// DER-encoded
toDERRawBytes(isCompressed = false) {
return hexToBytes(this.toDERHex(isCompressed));
toDERRawBytes() {
return ut.hexToBytes(this.toDERHex());
}
toDERHex(isCompressed = false) {
const sHex = sliceDER(numberToHexUnpadded(this.s));
if (isCompressed)
return sHex;
const rHex = sliceDER(numberToHexUnpadded(this.r));
const rLen = numberToHexUnpadded(rHex.length / 2);
const sLen = numberToHexUnpadded(sHex.length / 2);
const length = numberToHexUnpadded(rHex.length / 2 + sHex.length / 2 + 4);
toDERHex() {
const { numberToHexUnpadded: toHex } = ut;
const sHex = DER.slice(toHex(this.s));
const rHex = DER.slice(toHex(this.r));
const sHexL = sHex.length / 2;
const rHexL = rHex.length / 2;
const sLen = toHex(sHexL);
const rLen = toHex(rHexL);
const length = toHex(rHexL + sHexL + 4);
return `30${length}02${rLen}${rHex}02${sLen}${sHex}`;
}
// 32 bytes of r, then 32 bytes of s
// padded bytes of r, then padded bytes of s
toCompactRawBytes() {
return hexToBytes(this.toCompactHex());
return ut.hexToBytes(this.toCompactHex());
}

@@ -881,4 +896,2 @@ toCompactHex() {

const utils = {
mod: (n, modulo = Fp.ORDER) => mod.mod(n, modulo),
invert: Fp.invert,
isValidPrivateKey(privateKey) {

@@ -903,3 +916,3 @@ try {

*/
hashToPrivateKey: (hash) => numToField(hashToPrivateScalar(hash, CURVE_ORDER)),
hashToPrivateKey: (hash) => numToField(ut.hashToPrivateScalar(hash, CURVE_ORDER)),
/**

@@ -926,6 +939,6 @@ * Produces cryptographically secure private key from random of size (nBitLength+64)

/**
* Computes public key for a private key.
* Computes public key for a private key. Checks for validity of the private key.
* @param privateKey private key
* @param isCompressed whether to return compact, or full key
* @returns Public key, full by default; short when isCompressed=true
* @param isCompressed whether to return compact (default), or full key
* @returns Public key, full when isCompressed=false; short when isCompressed=true
*/

@@ -951,8 +964,8 @@ function getPublicKey(privateKey, isCompressed = false) {

/**
* ECDH (Elliptic Curve Diffie Hellman) implementation.
* 1. Checks for validity of private key
* 2. Checks for the public key of being on-curve
* ECDH (Elliptic Curve Diffie Hellman).
* Computes shared public key from private key and public key.
* Checks: 1) private key validity 2) shared key is on-curve
* @param privateA private key
* @param publicB different public key
* @param isCompressed whether to return compact (33-byte), or full (65-byte) key
* @param isCompressed whether to return compact (default), or full key
* @returns shared public key

@@ -971,4 +984,17 @@ */

function bits2int(bytes) {
const slice = bytes.length > Fp.BYTES ? bytes.slice(0, Fp.BYTES) : bytes;
return bytesToNumberBE(slice);
const { nByteLength } = CURVE;
if (!(bytes instanceof Uint8Array))
throw new Error('Expected Uint8Array');
const slice = bytes.length > nByteLength ? bytes.slice(0, nByteLength) : bytes;
// const slice = bytes; nByteLength; nBitLength;
let num = ut.bytesToNumberBE(slice);
// const { nBitLength } = CURVE;
// const delta = (bytes.length * 8) - nBitLength;
// if (delta > 0) {
// // console.log('bits=', bytes.length*8, 'CURVE n=', nBitLength, 'delta=', delta);
// // console.log(bytes.length, nBitLength, delta);
// // console.log(bytes, new Error().stack);
// num >>= BigInt(delta);
// }
return num;
}

@@ -981,3 +1007,3 @@ function bits2octets(bytes) {

function int2octets(num) {
return numToField(num); // prohibits >32 bytes
return numToField(num); // prohibits >nByteLength bytes
}

@@ -990,3 +1016,3 @@ // Steps A, D of RFC6979 3.2

// Step A is ignored, since we already provide hash instead of msg
const h1 = numToField(truncateHash(ensureBytes(msgHash)));
const h1 = numToField(truncateHash(ut.ensureBytes(msgHash)));
const d = normalizePrivateKey(privateKey);

@@ -999,3 +1025,3 @@ // K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1) || k')

extraEntropy = CURVE.randomBytes(Fp.BYTES);
const e = ensureBytes(extraEntropy);
const e = ut.ensureBytes(extraEntropy);
if (e.length !== Fp.BYTES)

@@ -1008,3 +1034,3 @@ throw new Error(`sign: Expected ${Fp.BYTES} bytes of extra data`);

// V, 0x00 are done in HmacDRBG constructor.
const seed = concatBytes(...seedArgs);
const seed = ut.concatBytes(...seedArgs);
const m = bits2int(h1);

@@ -1033,6 +1059,7 @@ return { seed, m, d };

return;
// s = (1/k * (m + dr) mod n
// s = (m + dr)/k mod n where x/k == x*inv(k)
const s = mod.mod(kinv * mod.mod(m + mod.mod(d * r, n), n), n);
if (s === _0n)
return;
// recovery bit is usually 0 or 1; rarely it's 2 or 3, when q.x > n
let recovery = (q.x === r ? 0 : 2) | Number(q.y & _1n);

@@ -1046,7 +1073,14 @@ let normS = s;

}
const defaultSigOpts = { lowS: CURVE.lowS };
/**
* Signs message hash (not message: you need to hash it by yourself).
* ```
* sign(m, d, k) where
* (x, y) = G × k
* r = x mod n
* s = (m + dr)/k mod n
* ```
* @param opts `lowS, extraEntropy`
*/
function sign(msgHash, privKey, opts = { lowS: CURVE.lowS }) {
function sign(msgHash, privKey, opts = defaultSigOpts) {
// Steps A, D of RFC6979 3.2.

@@ -1063,2 +1097,8 @@ const { seed, m, d } = initSigArgs(msgHash, privKey, opts.extraEntropy);

}
/**
* Signs a message (not message hash).
*/
function signUnhashed(msg, privKey, opts = defaultSigOpts) {
return sign(CURVE.hash(ut.ensureBytes(msg)), privKey, opts);
}
// Enable precomputes. Slows down first publicKey computation by 20ms.

@@ -1096,3 +1136,3 @@ Point.BASE._setWindowSize(8);

}
msgHash = ensureBytes(msgHash);
msgHash = ut.ensureBytes(msgHash);
}

@@ -1131,2 +1171,3 @@ catch (error) {

sign,
signUnhashed,
verify,

@@ -1133,0 +1174,0 @@ Point,

19

lib/esm/bls12-381.js
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// The pairing-friendly Barreto-Lynn-Scott elliptic curve construction allows to:
// - Construct zk-SNARKs at the 128-bit security
// - Use threshold signatures, which allows a user to sign lots of messages with one signature and verify them swiftly in a batch, using Boneh-Lynn-Shacham signature scheme.
// Differences from @noble/bls12-381 1.4:
// - PointG1 -> G1.Point
// - PointG2 -> G2.Point
// - PointG2.fromSignature -> Signature.decode
// - PointG2.toSignature -> Signature.encode
// - Fixed Fp2 ORDER
// - Points now have only two coordinates
import { sha256 } from '@noble/hashes/sha256';

@@ -10,9 +20,2 @@ import { randomBytes } from '@noble/hashes/utils';

import { isogenyMap } from './abstract/hash-to-curve.js';
// Differences from bls12-381:
// - PointG1 -> G1.Point
// - PointG2 -> G2.Point
// - PointG2.fromSignature -> Signature.decode
// - PointG2.toSignature -> Signature.encode
// - Fixed Fp2 ORDER
// Points now have only two coordinates
// CURVE FIELDS

@@ -101,2 +104,4 @@ // Finite field over p.

sqrt: (num) => {
if (Fp2.equals(num, Fp2.ZERO))
return Fp2.ZERO; // Algo doesn't handles this case
// TODO: Optimize this line. It's extremely slow.

@@ -103,0 +108,0 @@ // Speeding this up would boost aggregateSignatures.

10

lib/esm/ed25519.js

@@ -225,3 +225,3 @@ /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */

const MAX_255B = BigInt('0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff');
const bytes255ToNumberLE = (bytes) => ed25519.utils.mod(bytesToNumberLE(bytes) & MAX_255B);
const bytes255ToNumberLE = (bytes) => ed25519.CURVE.Fp.create(bytesToNumberLE(bytes) & MAX_255B);
// Computes Elligator map for Ristretto

@@ -232,3 +232,3 @@ // https://ristretto.group/formulas/elligator.html

const P = ed25519.CURVE.Fp.ORDER;
const { mod } = ed25519.utils;
const mod = ed25519.CURVE.Fp.create;
const r = mod(SQRT_M1 * r0 * r0); // 1

@@ -291,3 +291,3 @@ const Ns = mod((r + _1n) * ONE_MINUS_D_SQ); // 2

const P = ed25519.CURVE.Fp.ORDER;
const { mod } = ed25519.utils;
const mod = ed25519.CURVE.Fp.create;
const emsg = 'RistrettoPoint.fromHex: the hex is not valid encoding of RistrettoPoint';

@@ -324,3 +324,3 @@ const s = bytes255ToNumberLE(hex);

const P = ed25519.CURVE.Fp.ORDER;
const { mod } = ed25519.utils;
const mod = ed25519.CURVE.Fp.create;
const u1 = mod(mod(z + y) * mod(z - y)); // 1

@@ -363,3 +363,3 @@ const u2 = mod(x * y); // 2

const b = other.ep;
const { mod } = ed25519.utils;
const mod = ed25519.CURVE.Fp.create;
// (x1 * y2 == y1 * x2) | (y1 * y2 == x1 * x2)

@@ -366,0 +366,0 @@ const one = mod(a.x * b.y) === mod(a.y * b.x);

3

lib/esm/ed448.js

@@ -129,3 +129,4 @@ /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */

Fp,
// Subgroup order: how many points ed448 has; 2n**446n - 13818066809895115352007386748515426880336692474882178609894547503885n
// Subgroup order: how many points curve has;
// 2n**446n - 13818066809895115352007386748515426880336692474882178609894547503885n
n: BigInt('181709681073901722637330951972001133588410340171829515070372549795146003961539585716195755291692375963310293709091662304773755859649779'),

@@ -132,0 +133,0 @@ nBitLength: 456,

9

lib/esm/jubjub.js
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { sha256 } from '@noble/hashes/sha256';
import { sha512 } from '@noble/hashes/sha512';
import { concatBytes, randomBytes, utf8ToBytes } from '@noble/hashes/utils';

@@ -10,2 +10,3 @@ import { twistedEdwards } from './abstract/edwards.js';

* https://neuromancer.sk/std/other/JubJub
* jubjub does not use EdDSA, so `hash`/sha512 params are passed because interface expects them.
*/

@@ -17,5 +18,5 @@ export const jubjub = twistedEdwards({

// Finite field 𝔽p over which we'll do calculations
// Same value as bls12-381 Fr (not Fp)
Fp: Fp(BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001')),
// Subgroup order: how many points ed25519 has
// 2n ** 252n + 27742317777372353535851937790883648493n;
// Subgroup order: how many points curve has
n: BigInt('0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7'),

@@ -27,3 +28,3 @@ // Cofactor

Gy: BigInt('0x1d523cf1ddab1a1793132e78c866c0c33e26ba5cc220fed7cc3f870e59d292aa'),
hash: sha256,
hash: sha512,
randomBytes,

@@ -30,0 +31,0 @@ });

47

lib/esm/secp256k1.js

@@ -10,6 +10,4 @@ /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */

/**
* secp256k1 belongs to Koblitz curves: it has
* efficiently computable Frobenius endomorphism.
* Endomorphism improves efficiency:
* Uses 2x less RAM, speeds up precomputation by 2x and ECDH / sign key recovery by 20%.
* secp256k1 belongs to Koblitz curves: it has efficiently computable endomorphism.
* Endomorphism uses 2x less RAM, speeds up precomputation by 2x and ECDH / key recovery by 20%.
* Should always be used for Projective's double-and-add multiplication.

@@ -115,3 +113,3 @@ * For affines cached multiplication, it trades off 1/2 init time & 1/3 ram for 20% perf hit.

const b2 = a1;
const POW_2_128 = BigInt('0x100000000000000000000000000000000');
const POW_2_128 = BigInt('0x100000000000000000000000000000000'); // (2n**128n).toString(16)
const c1 = divNearest(b2 * k, n);

@@ -160,18 +158,16 @@ const c2 = divNearest(-b1 * k, n);

// Schnorr is 32 bytes
if (bytes.length === 32) {
const x = bytesToNumberBE(bytes);
if (!isValidFieldElement(x))
throw new Error('Point is not on curve');
const y2 = secp256k1.utils._weierstrassEquation(x); // y² = x³ + ax + b
let y = sqrtMod(y2); // y = y² ^ (p+1)/4
const isYOdd = (y & _1n) === _1n;
// Schnorr
if (isYOdd)
y = secp256k1.CURVE.Fp.negate(y);
const point = new secp256k1.Point(x, y);
point.assertValidity();
return point;
}
// Do we need that in schnorr at all?
return secp256k1.Point.fromHex(publicKey);
if (bytes.length !== 32)
throw new Error('Schnorr pubkeys must be 32 bytes');
const x = bytesToNumberBE(bytes);
if (!isValidFieldElement(x))
throw new Error('Point is not on curve');
const y2 = secp256k1.utils._weierstrassEquation(x); // y² = x³ + ax + b
let y = sqrtMod(y2); // y = y² ^ (p+1)/4
const isYOdd = (y & _1n) === _1n;
// Schnorr
if (isYOdd)
y = secp256k1.CURVE.Fp.negate(y);
const point = new secp256k1.Point(x, y);
point.assertValidity();
return point;
}

@@ -212,6 +208,7 @@ }

const bytes = ensureBytes(hex);
if (bytes.length !== 64)
throw new TypeError(`SchnorrSignature.fromHex: expected 64 bytes, not ${bytes.length}`);
const r = bytesToNumberBE(bytes.subarray(0, 32));
const s = bytesToNumberBE(bytes.subarray(32, 64));
const len = 32; // group length
if (bytes.length !== 2 * len)
throw new TypeError(`SchnorrSignature.fromHex: expected ${2 * len} bytes, not ${bytes.length}`);
const r = bytesToNumberBE(bytes.subarray(0, len));
const s = bytesToNumberBE(bytes.subarray(len, 2 * len));
return new SchnorrSignature(r, s);

@@ -218,0 +215,0 @@ }

5

lib/esm/stark.js

@@ -124,3 +124,4 @@ /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */

const sha256mask = 2n ** 256n;
const limit = sha256mask - starkCurve.utils.mod(sha256mask, starkCurve.CURVE.n);
const Fn = Fp(CURVE.n);
const limit = sha256mask - Fn.create(sha256mask);
for (let i = 0;; i++) {

@@ -130,3 +131,3 @@ const key = hashKeyWithIndex(_seed, i);

if (key < limit)
return starkCurve.utils.mod(key, starkCurve.CURVE.n).toString(16);
return Fn.create(key).toString(16);
}

@@ -133,0 +134,0 @@ }

1

lib/jubjub.d.ts
/**
* jubjub Twisted Edwards curve.
* https://neuromancer.sk/std/other/JubJub
* jubjub does not use EdDSA, so `hash`/sha512 params are passed because interface expects them.
*/

@@ -5,0 +6,0 @@ export declare const jubjub: import("./abstract/edwards.js").CurveFn;

9

lib/jubjub.js

@@ -5,3 +5,3 @@ "use strict";

/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
const sha256_1 = require("@noble/hashes/sha256");
const sha512_1 = require("@noble/hashes/sha512");
const utils_1 = require("@noble/hashes/utils");

@@ -14,2 +14,3 @@ const edwards_js_1 = require("./abstract/edwards.js");

* https://neuromancer.sk/std/other/JubJub
* jubjub does not use EdDSA, so `hash`/sha512 params are passed because interface expects them.
*/

@@ -21,5 +22,5 @@ exports.jubjub = (0, edwards_js_1.twistedEdwards)({

// Finite field 𝔽p over which we'll do calculations
// Same value as bls12-381 Fr (not Fp)
Fp: (0, modular_js_1.Fp)(BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001')),
// Subgroup order: how many points ed25519 has
// 2n ** 252n + 27742317777372353535851937790883648493n;
// Subgroup order: how many points curve has
n: BigInt('0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7'),

@@ -31,3 +32,3 @@ // Cofactor

Gy: BigInt('0x1d523cf1ddab1a1793132e78c866c0c33e26ba5cc220fed7cc3f870e59d292aa'),
hash: sha256_1.sha256,
hash: sha512_1.sha512,
randomBytes: utils_1.randomBytes,

@@ -34,0 +35,0 @@ });

16

lib/p192.d.ts

@@ -41,6 +41,4 @@ export declare const P192: Readonly<{

getSharedSecret: (privateA: import("./abstract/utils.js").PrivKey, publicB: import("./abstract/weierstrass.js").PubKey, isCompressed?: boolean | undefined) => Uint8Array;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: {
lowS?: boolean | undefined;
extraEntropy?: (true | import("./abstract/utils.js").Hex) | undefined;
} | undefined) => import("./abstract/weierstrass.js").SignatureType;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
signUnhashed: (msg: Uint8Array, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
verify: (signature: import("./abstract/utils.js").Hex | import("./abstract/weierstrass.js").SignatureType, msgHash: import("./abstract/utils.js").Hex, publicKey: import("./abstract/weierstrass.js").PubKey, opts?: {

@@ -53,4 +51,2 @@ lowS?: boolean | undefined;

utils: {
mod: (a: bigint, b?: bigint | undefined) => bigint;
invert: (number: bigint, modulo?: bigint | undefined) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -108,6 +104,4 @@ _bigintToString: (num: bigint) => string;

getSharedSecret: (privateA: import("./abstract/utils.js").PrivKey, publicB: import("./abstract/weierstrass.js").PubKey, isCompressed?: boolean | undefined) => Uint8Array;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: {
lowS?: boolean | undefined;
extraEntropy?: (true | import("./abstract/utils.js").Hex) | undefined;
} | undefined) => import("./abstract/weierstrass.js").SignatureType;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
signUnhashed: (msg: Uint8Array, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
verify: (signature: import("./abstract/utils.js").Hex | import("./abstract/weierstrass.js").SignatureType, msgHash: import("./abstract/utils.js").Hex, publicKey: import("./abstract/weierstrass.js").PubKey, opts?: {

@@ -120,4 +114,2 @@ lowS?: boolean | undefined;

utils: {
mod: (a: bigint, b?: bigint | undefined) => bigint;
invert: (number: bigint, modulo?: bigint | undefined) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -124,0 +116,0 @@ _bigintToString: (num: bigint) => string;

16

lib/p224.d.ts

@@ -41,6 +41,4 @@ export declare const P224: Readonly<{

getSharedSecret: (privateA: import("./abstract/utils.js").PrivKey, publicB: import("./abstract/weierstrass.js").PubKey, isCompressed?: boolean | undefined) => Uint8Array;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: {
lowS?: boolean | undefined;
extraEntropy?: (true | import("./abstract/utils.js").Hex) | undefined;
} | undefined) => import("./abstract/weierstrass.js").SignatureType;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
signUnhashed: (msg: Uint8Array, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
verify: (signature: import("./abstract/utils.js").Hex | import("./abstract/weierstrass.js").SignatureType, msgHash: import("./abstract/utils.js").Hex, publicKey: import("./abstract/weierstrass.js").PubKey, opts?: {

@@ -53,4 +51,2 @@ lowS?: boolean | undefined;

utils: {
mod: (a: bigint, b?: bigint | undefined) => bigint;
invert: (number: bigint, modulo?: bigint | undefined) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -108,6 +104,4 @@ _bigintToString: (num: bigint) => string;

getSharedSecret: (privateA: import("./abstract/utils.js").PrivKey, publicB: import("./abstract/weierstrass.js").PubKey, isCompressed?: boolean | undefined) => Uint8Array;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: {
lowS?: boolean | undefined;
extraEntropy?: (true | import("./abstract/utils.js").Hex) | undefined;
} | undefined) => import("./abstract/weierstrass.js").SignatureType;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
signUnhashed: (msg: Uint8Array, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
verify: (signature: import("./abstract/utils.js").Hex | import("./abstract/weierstrass.js").SignatureType, msgHash: import("./abstract/utils.js").Hex, publicKey: import("./abstract/weierstrass.js").PubKey, opts?: {

@@ -120,4 +114,2 @@ lowS?: boolean | undefined;

utils: {
mod: (a: bigint, b?: bigint | undefined) => bigint;
invert: (number: bigint, modulo?: bigint | undefined) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -124,0 +116,0 @@ _bigintToString: (num: bigint) => string;

16

lib/p256.d.ts

@@ -41,6 +41,4 @@ export declare const P256: Readonly<{

getSharedSecret: (privateA: import("./abstract/utils.js").PrivKey, publicB: import("./abstract/weierstrass.js").PubKey, isCompressed?: boolean | undefined) => Uint8Array;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: {
lowS?: boolean | undefined;
extraEntropy?: (true | import("./abstract/utils.js").Hex) | undefined;
} | undefined) => import("./abstract/weierstrass.js").SignatureType;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
signUnhashed: (msg: Uint8Array, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
verify: (signature: import("./abstract/utils.js").Hex | import("./abstract/weierstrass.js").SignatureType, msgHash: import("./abstract/utils.js").Hex, publicKey: import("./abstract/weierstrass.js").PubKey, opts?: {

@@ -53,4 +51,2 @@ lowS?: boolean | undefined;

utils: {
mod: (a: bigint, b?: bigint | undefined) => bigint;
invert: (number: bigint, modulo?: bigint | undefined) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -108,6 +104,4 @@ _bigintToString: (num: bigint) => string;

getSharedSecret: (privateA: import("./abstract/utils.js").PrivKey, publicB: import("./abstract/weierstrass.js").PubKey, isCompressed?: boolean | undefined) => Uint8Array;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: {
lowS?: boolean | undefined;
extraEntropy?: (true | import("./abstract/utils.js").Hex) | undefined;
} | undefined) => import("./abstract/weierstrass.js").SignatureType;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
signUnhashed: (msg: Uint8Array, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
verify: (signature: import("./abstract/utils.js").Hex | import("./abstract/weierstrass.js").SignatureType, msgHash: import("./abstract/utils.js").Hex, publicKey: import("./abstract/weierstrass.js").PubKey, opts?: {

@@ -120,4 +114,2 @@ lowS?: boolean | undefined;

utils: {
mod: (a: bigint, b?: bigint | undefined) => bigint;
invert: (number: bigint, modulo?: bigint | undefined) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -124,0 +116,0 @@ _bigintToString: (num: bigint) => string;

16

lib/p384.d.ts

@@ -41,6 +41,4 @@ export declare const P384: Readonly<{

getSharedSecret: (privateA: import("./abstract/utils.js").PrivKey, publicB: import("./abstract/weierstrass.js").PubKey, isCompressed?: boolean | undefined) => Uint8Array;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: {
lowS?: boolean | undefined;
extraEntropy?: (true | import("./abstract/utils.js").Hex) | undefined;
} | undefined) => import("./abstract/weierstrass.js").SignatureType;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
signUnhashed: (msg: Uint8Array, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
verify: (signature: import("./abstract/utils.js").Hex | import("./abstract/weierstrass.js").SignatureType, msgHash: import("./abstract/utils.js").Hex, publicKey: import("./abstract/weierstrass.js").PubKey, opts?: {

@@ -53,4 +51,2 @@ lowS?: boolean | undefined;

utils: {
mod: (a: bigint, b?: bigint | undefined) => bigint;
invert: (number: bigint, modulo?: bigint | undefined) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -108,6 +104,4 @@ _bigintToString: (num: bigint) => string;

getSharedSecret: (privateA: import("./abstract/utils.js").PrivKey, publicB: import("./abstract/weierstrass.js").PubKey, isCompressed?: boolean | undefined) => Uint8Array;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: {
lowS?: boolean | undefined;
extraEntropy?: (true | import("./abstract/utils.js").Hex) | undefined;
} | undefined) => import("./abstract/weierstrass.js").SignatureType;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
signUnhashed: (msg: Uint8Array, privKey: import("./abstract/utils.js").PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
verify: (signature: import("./abstract/utils.js").Hex | import("./abstract/weierstrass.js").SignatureType, msgHash: import("./abstract/utils.js").Hex, publicKey: import("./abstract/weierstrass.js").PubKey, opts?: {

@@ -120,4 +114,2 @@ lowS?: boolean | undefined;

utils: {
mod: (a: bigint, b?: bigint | undefined) => bigint;
invert: (number: bigint, modulo?: bigint | undefined) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -124,0 +116,0 @@ _bigintToString: (num: bigint) => string;

16

lib/p521.d.ts

@@ -42,6 +42,4 @@ import { PrivKey } from './abstract/utils.js';

getSharedSecret: (privateA: PrivKey, publicB: import("./abstract/weierstrass.js").PubKey, isCompressed?: boolean | undefined) => Uint8Array;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: PrivKey, opts?: {
lowS?: boolean | undefined;
extraEntropy?: (true | import("./abstract/utils.js").Hex) | undefined;
} | undefined) => import("./abstract/weierstrass.js").SignatureType;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
signUnhashed: (msg: Uint8Array, privKey: PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
verify: (signature: import("./abstract/utils.js").Hex | import("./abstract/weierstrass.js").SignatureType, msgHash: import("./abstract/utils.js").Hex, publicKey: import("./abstract/weierstrass.js").PubKey, opts?: {

@@ -54,4 +52,2 @@ lowS?: boolean | undefined;

utils: {
mod: (a: bigint, b?: bigint | undefined) => bigint;
invert: (number: bigint, modulo?: bigint | undefined) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -109,6 +105,4 @@ _bigintToString: (num: bigint) => string;

getSharedSecret: (privateA: PrivKey, publicB: import("./abstract/weierstrass.js").PubKey, isCompressed?: boolean | undefined) => Uint8Array;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: PrivKey, opts?: {
lowS?: boolean | undefined;
extraEntropy?: (true | import("./abstract/utils.js").Hex) | undefined;
} | undefined) => import("./abstract/weierstrass.js").SignatureType;
sign: (msgHash: import("./abstract/utils.js").Hex, privKey: PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
signUnhashed: (msg: Uint8Array, privKey: PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
verify: (signature: import("./abstract/utils.js").Hex | import("./abstract/weierstrass.js").SignatureType, msgHash: import("./abstract/utils.js").Hex, publicKey: import("./abstract/weierstrass.js").PubKey, opts?: {

@@ -121,4 +115,2 @@ lowS?: boolean | undefined;

utils: {
mod: (a: bigint, b?: bigint | undefined) => bigint;
invert: (number: bigint, modulo?: bigint | undefined) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -125,0 +117,0 @@ _bigintToString: (num: bigint) => string;

8

lib/secp256k1.d.ts

@@ -43,6 +43,4 @@ import { PointType } from './abstract/weierstrass.js';

getSharedSecret: (privateA: PrivKey, publicB: import("./abstract/weierstrass.js").PubKey, isCompressed?: boolean | undefined) => Uint8Array;
sign: (msgHash: Hex, privKey: PrivKey, opts?: {
lowS?: boolean | undefined;
extraEntropy?: (true | Hex) | undefined;
} | undefined) => import("./abstract/weierstrass.js").SignatureType;
sign: (msgHash: Hex, privKey: PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
signUnhashed: (msg: Uint8Array, privKey: PrivKey, opts?: import("./abstract/weierstrass.js").SignOpts | undefined) => import("./abstract/weierstrass.js").SignatureType;
verify: (signature: Hex | import("./abstract/weierstrass.js").SignatureType, msgHash: Hex, publicKey: import("./abstract/weierstrass.js").PubKey, opts?: {

@@ -55,4 +53,2 @@ lowS?: boolean | undefined;

utils: {
mod: (a: bigint, b?: bigint | undefined) => bigint;
invert: (number: bigint, modulo?: bigint | undefined) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -59,0 +55,0 @@ _bigintToString: (num: bigint) => string;

47

lib/secp256k1.js

@@ -13,6 +13,4 @@ "use strict";

/**
* secp256k1 belongs to Koblitz curves: it has
* efficiently computable Frobenius endomorphism.
* Endomorphism improves efficiency:
* Uses 2x less RAM, speeds up precomputation by 2x and ECDH / sign key recovery by 20%.
* secp256k1 belongs to Koblitz curves: it has efficiently computable endomorphism.
* Endomorphism uses 2x less RAM, speeds up precomputation by 2x and ECDH / key recovery by 20%.
* Should always be used for Projective's double-and-add multiplication.

@@ -118,3 +116,3 @@ * For affines cached multiplication, it trades off 1/2 init time & 1/3 ram for 20% perf hit.

const b2 = a1;
const POW_2_128 = BigInt('0x100000000000000000000000000000000');
const POW_2_128 = BigInt('0x100000000000000000000000000000000'); // (2n**128n).toString(16)
const c1 = divNearest(b2 * k, n);

@@ -163,18 +161,16 @@ const c2 = divNearest(-b1 * k, n);

// Schnorr is 32 bytes
if (bytes.length === 32) {
const x = (0, utils_js_1.bytesToNumberBE)(bytes);
if (!isValidFieldElement(x))
throw new Error('Point is not on curve');
const y2 = exports.secp256k1.utils._weierstrassEquation(x); // y² = x³ + ax + b
let y = sqrtMod(y2); // y = y² ^ (p+1)/4
const isYOdd = (y & _1n) === _1n;
// Schnorr
if (isYOdd)
y = exports.secp256k1.CURVE.Fp.negate(y);
const point = new exports.secp256k1.Point(x, y);
point.assertValidity();
return point;
}
// Do we need that in schnorr at all?
return exports.secp256k1.Point.fromHex(publicKey);
if (bytes.length !== 32)
throw new Error('Schnorr pubkeys must be 32 bytes');
const x = (0, utils_js_1.bytesToNumberBE)(bytes);
if (!isValidFieldElement(x))
throw new Error('Point is not on curve');
const y2 = exports.secp256k1.utils._weierstrassEquation(x); // y² = x³ + ax + b
let y = sqrtMod(y2); // y = y² ^ (p+1)/4
const isYOdd = (y & _1n) === _1n;
// Schnorr
if (isYOdd)
y = exports.secp256k1.CURVE.Fp.negate(y);
const point = new exports.secp256k1.Point(x, y);
point.assertValidity();
return point;
}

@@ -216,6 +212,7 @@ }

const bytes = (0, utils_js_1.ensureBytes)(hex);
if (bytes.length !== 64)
throw new TypeError(`SchnorrSignature.fromHex: expected 64 bytes, not ${bytes.length}`);
const r = (0, utils_js_1.bytesToNumberBE)(bytes.subarray(0, 32));
const s = (0, utils_js_1.bytesToNumberBE)(bytes.subarray(32, 64));
const len = 32; // group length
if (bytes.length !== 2 * len)
throw new TypeError(`SchnorrSignature.fromHex: expected ${2 * len} bytes, not ${bytes.length}`);
const r = (0, utils_js_1.bytesToNumberBE)(bytes.subarray(0, len));
const s = (0, utils_js_1.bytesToNumberBE)(bytes.subarray(len, 2 * len));
return new SchnorrSignature(r, s);

@@ -222,0 +219,0 @@ }

2

lib/stark.d.ts

@@ -46,4 +46,2 @@ import { ProjectivePointType } from './abstract/weierstrass.js';

export declare const utils: {
mod: (a: bigint, b?: bigint | undefined) => bigint;
invert: (number: bigint, modulo?: bigint | undefined) => bigint;
_bigintToBytes: (num: bigint) => Uint8Array;

@@ -50,0 +48,0 @@ _bigintToString: (num: bigint) => string;

5

lib/stark.js

@@ -137,3 +137,4 @@ "use strict";

const sha256mask = 2n ** 256n;
const limit = sha256mask - exports.starkCurve.utils.mod(sha256mask, exports.starkCurve.CURVE.n);
const Fn = (0, modular_js_1.Fp)(CURVE.n);
const limit = sha256mask - Fn.create(sha256mask);
for (let i = 0;; i++) {

@@ -143,3 +144,3 @@ const key = hashKeyWithIndex(_seed, i);

if (key < limit)
return exports.starkCurve.utils.mod(key, exports.starkCurve.CURVE.n).toString(16);
return Fn.create(key).toString(16);
}

@@ -146,0 +147,0 @@ }

4

package.json
{
"name": "@noble/curves",
"version": "0.5.1",
"version": "0.5.2",
"description": "Minimal, auditable JS implementation of elliptic curve cryptography",

@@ -34,3 +34,3 @@ "files": [

"micro-bmark": "0.2.0",
"micro-should": "0.2.0",
"micro-should": "0.3.0",
"prettier": "2.6.2",

@@ -37,0 +37,0 @@ "rollup": "2.75.5",

5

README.md

@@ -204,4 +204,2 @@ # noble-curves

utils: {
mod: (a: bigint, b?: bigint) => bigint;
invert: (number: bigint, modulo?: bigint) => bigint;
randomPrivateKey: () => Uint8Array;

@@ -310,2 +308,3 @@ getExtendedPublicKey: (key: PrivKey) => {

sign: (msgHash: Hex, privKey: PrivKey, opts?: SignOpts) => SignatureType;
signUnhashed: (msg: Uint8Array, privKey: PrivKey, opts?: SignOpts) => SignatureType;
verify: (

@@ -321,4 +320,2 @@ signature: Hex | SignatureType,

utils: {
mod: (a: bigint) => bigint;
invert: (number: bigint) => bigint;
isValidPrivateKey(privateKey: PrivKey): boolean;

@@ -325,0 +322,0 @@ hashToPrivateKey: (hash: Hex) => Uint8Array;

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