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Просмотр файла: weierstrass.js
"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
exports.DER = exports.DERErr = void 0;
exports._splitEndoScalar = _splitEndoScalar;
exports._normFnElement = _normFnElement;
exports.weierstrassN = weierstrassN;
exports.SWUFpSqrtRatio = SWUFpSqrtRatio;
exports.mapToCurveSimpleSWU = mapToCurveSimpleSWU;
exports.ecdh = ecdh;
exports.ecdsa = ecdsa;
exports.weierstrassPoints = weierstrassPoints;
exports._legacyHelperEquat = _legacyHelperEquat;
exports.weierstrass = weierstrass;
/**
* Short Weierstrass curve methods. The formula is: y² = x³ + ax + b.
*
* ### Design rationale for types
*
* * Interaction between classes from different curves should fail:
* `k256.Point.BASE.add(p256.Point.BASE)`
* * For this purpose we want to use `instanceof` operator, which is fast and works during runtime
* * Different calls of `curve()` would return different classes -
* `curve(params) !== curve(params)`: if somebody decided to monkey-patch their curve,
* it won't affect others
*
* TypeScript can't infer types for classes created inside a function. Classes is one instance
* of nominative types in TypeScript and interfaces only check for shape, so it's hard to create
* unique type for every function call.
*
* We can use generic types via some param, like curve opts, but that would:
* 1. Enable interaction between `curve(params)` and `curve(params)` (curves of same params)
* which is hard to debug.
* 2. Params can be generic and we can't enforce them to be constant value:
* if somebody creates curve from non-constant params,
* it would be allowed to interact with other curves with non-constant params
*
* @todo https://www.typescriptlang.org/docs/handbook/release-notes/typescript-2-7.html#unique-symbol
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
const hmac_js_1 = require("@noble/hashes/hmac.js");
const utils_1 = require("@noble/hashes/utils");
const utils_ts_1 = require("../utils.js");
const curve_ts_1 = require("./curve.js");
const modular_ts_1 = require("./modular.js");
// We construct basis in such way that den is always positive and equals n, but num sign depends on basis (not on secret value)
const divNearest = (num, den) => (num + (num >= 0 ? den : -den) / _2n) / den;
/**
* Splits scalar for GLV endomorphism.
*/
function _splitEndoScalar(k, basis, n) {
// Split scalar into two such that part is ~half bits: `abs(part) < sqrt(N)`
// Since part can be negative, we need to do this on point.
// TODO: verifyScalar function which consumes lambda
const [[a1, b1], [a2, b2]] = basis;
const c1 = divNearest(b2 * k, n);
const c2 = divNearest(-b1 * k, n);
// |k1|/|k2| is < sqrt(N), but can be negative.
// If we do `k1 mod N`, we'll get big scalar (`> sqrt(N)`): so, we do cheaper negation instead.
let k1 = k - c1 * a1 - c2 * a2;
let k2 = -c1 * b1 - c2 * b2;
const k1neg = k1 < _0n;
const k2neg = k2 < _0n;
if (k1neg)
k1 = -k1;
if (k2neg)
k2 = -k2;
// Double check that resulting scalar less than half bits of N: otherwise wNAF will fail.
// This should only happen on wrong basises. Also, math inside is too complex and I don't trust it.
const MAX_NUM = (0, utils_ts_1.bitMask)(Math.ceil((0, utils_ts_1.bitLen)(n) / 2)) + _1n; // Half bits of N
if (k1 < _0n || k1 >= MAX_NUM || k2 < _0n || k2 >= MAX_NUM) {
throw new Error('splitScalar (endomorphism): failed, k=' + k);
}
return { k1neg, k1, k2neg, k2 };
}
function validateSigFormat(format) {
if (!['compact', 'recovered', 'der'].includes(format))
throw new Error('Signature format must be "compact", "recovered", or "der"');
return format;
}
function validateSigOpts(opts, def) {
const optsn = {};
for (let optName of Object.keys(def)) {
// @ts-ignore
optsn[optName] = opts[optName] === undefined ? def[optName] : opts[optName];
}
(0, utils_ts_1._abool2)(optsn.lowS, 'lowS');
(0, utils_ts_1._abool2)(optsn.prehash, 'prehash');
if (optsn.format !== undefined)
validateSigFormat(optsn.format);
return optsn;
}
class DERErr extends Error {
constructor(m = '') {
super(m);
}
}
exports.DERErr = DERErr;
/**
* ASN.1 DER encoding utilities. ASN is very complex & fragile. Format:
*
* [0x30 (SEQUENCE), bytelength, 0x02 (INTEGER), intLength, R, 0x02 (INTEGER), intLength, S]
*
* Docs: https://letsencrypt.org/docs/a-warm-welcome-to-asn1-and-der/, https://luca.ntop.org/Teaching/Appunti/asn1.html
*/
exports.DER = {
// asn.1 DER encoding utils
Err: DERErr,
// Basic building block is TLV (Tag-Length-Value)
_tlv: {
encode: (tag, data) => {
const { Err: E } = exports.DER;
if (tag < 0 || tag > 256)
throw new E('tlv.encode: wrong tag');
if (data.length & 1)
throw new E('tlv.encode: unpadded data');
const dataLen = data.length / 2;
const len = (0, utils_ts_1.numberToHexUnpadded)(dataLen);
if ((len.length / 2) & 128)
throw new E('tlv.encode: long form length too big');
// length of length with long form flag
const lenLen = dataLen > 127 ? (0, utils_ts_1.numberToHexUnpadded)((len.length / 2) | 128) : '';
const t = (0, utils_ts_1.numberToHexUnpadded)(tag);
return t + lenLen + len + data;
},
// v - value, l - left bytes (unparsed)
decode(tag, data) {
const { Err: E } = exports.DER;
let pos = 0;
if (tag < 0 || tag > 256)
throw new E('tlv.encode: wrong tag');
if (data.length < 2 || data[pos++] !== tag)
throw new E('tlv.decode: wrong tlv');
const first = data[pos++];
const isLong = !!(first & 128); // First bit of first length byte is flag for short/long form
let length = 0;
if (!isLong)
length = first;
else {
// Long form: [longFlag(1bit), lengthLength(7bit), length (BE)]
const lenLen = first & 127;
if (!lenLen)
throw new E('tlv.decode(long): indefinite length not supported');
if (lenLen > 4)
throw new E('tlv.decode(long): byte length is too big'); // this will overflow u32 in js
const lengthBytes = data.subarray(pos, pos + lenLen);
if (lengthBytes.length !== lenLen)
throw new E('tlv.decode: length bytes not complete');
if (lengthBytes[0] === 0)
throw new E('tlv.decode(long): zero leftmost byte');
for (const b of lengthBytes)
length = (length << 8) | b;
pos += lenLen;
if (length < 128)
throw new E('tlv.decode(long): not minimal encoding');
}
const v = data.subarray(pos, pos + length);
if (v.length !== length)
throw new E('tlv.decode: wrong value length');
return { v, l: data.subarray(pos + length) };
},
},
// https://crypto.stackexchange.com/a/57734 Leftmost bit of first byte is 'negative' flag,
// since we always use positive integers here. It must always be empty:
// - add zero byte if exists
// - if next byte doesn't have a flag, leading zero is not allowed (minimal encoding)
_int: {
encode(num) {
const { Err: E } = exports.DER;
if (num < _0n)
throw new E('integer: negative integers are not allowed');
let hex = (0, utils_ts_1.numberToHexUnpadded)(num);
// Pad with zero byte if negative flag is present
if (Number.parseInt(hex[0], 16) & 0b1000)
hex = '00' + hex;
if (hex.length & 1)
throw new E('unexpected DER parsing assertion: unpadded hex');
return hex;
},
decode(data) {
const { Err: E } = exports.DER;
if (data[0] & 128)
throw new E('invalid signature integer: negative');
if (data[0] === 0x00 && !(data[1] & 128))
throw new E('invalid signature integer: unnecessary leading zero');
return (0, utils_ts_1.bytesToNumberBE)(data);
},
},
toSig(hex) {
// parse DER signature
const { Err: E, _int: int, _tlv: tlv } = exports.DER;
const data = (0, utils_ts_1.ensureBytes)('signature', hex);
const { v: seqBytes, l: seqLeftBytes } = tlv.decode(0x30, data);
if (seqLeftBytes.length)
throw new E('invalid signature: left bytes after parsing');
const { v: rBytes, l: rLeftBytes } = tlv.decode(0x02, seqBytes);
const { v: sBytes, l: sLeftBytes } = tlv.decode(0x02, rLeftBytes);
if (sLeftBytes.length)
throw new E('invalid signature: left bytes after parsing');
return { r: int.decode(rBytes), s: int.decode(sBytes) };
},
hexFromSig(sig) {
const { _tlv: tlv, _int: int } = exports.DER;
const rs = tlv.encode(0x02, int.encode(sig.r));
const ss = tlv.encode(0x02, int.encode(sig.s));
const seq = rs + ss;
return tlv.encode(0x30, seq);
},
};
// Be friendly to bad ECMAScript parsers by not using bigint literals
// prettier-ignore
const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3), _4n = BigInt(4);
function _normFnElement(Fn, key) {
const { BYTES: expected } = Fn;
let num;
if (typeof key === 'bigint') {
num = key;
}
else {
let bytes = (0, utils_ts_1.ensureBytes)('private key', key);
try {
num = Fn.fromBytes(bytes);
}
catch (error) {
throw new Error(`invalid private key: expected ui8a of size ${expected}, got ${typeof key}`);
}
}
if (!Fn.isValidNot0(num))
throw new Error('invalid private key: out of range [1..N-1]');
return num;
}
/**
* Creates weierstrass Point constructor, based on specified curve options.
*
* @example
```js
const opts = {
p: BigInt('0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff'),
n: BigInt('0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551'),
h: BigInt(1),
a: BigInt('0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc'),
b: BigInt('0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b'),
Gx: BigInt('0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296'),
Gy: BigInt('0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5'),
};
const p256_Point = weierstrass(opts);
```
*/
function weierstrassN(params, extraOpts = {}) {
const validated = (0, curve_ts_1._createCurveFields)('weierstrass', params, extraOpts);
const { Fp, Fn } = validated;
let CURVE = validated.CURVE;
const { h: cofactor, n: CURVE_ORDER } = CURVE;
(0, utils_ts_1._validateObject)(extraOpts, {}, {
allowInfinityPoint: 'boolean',
clearCofactor: 'function',
isTorsionFree: 'function',
fromBytes: 'function',
toBytes: 'function',
endo: 'object',
wrapPrivateKey: 'boolean',
});
const { endo } = extraOpts;
if (endo) {
// validateObject(endo, { beta: 'bigint', splitScalar: 'function' });
if (!Fp.is0(CURVE.a) || typeof endo.beta !== 'bigint' || !Array.isArray(endo.basises)) {
throw new Error('invalid endo: expected "beta": bigint and "basises": array');
}
}
const lengths = getWLengths(Fp, Fn);
function assertCompressionIsSupported() {
if (!Fp.isOdd)
throw new Error('compression is not supported: Field does not have .isOdd()');
}
// Implements IEEE P1363 point encoding
function pointToBytes(_c, point, isCompressed) {
const { x, y } = point.toAffine();
const bx = Fp.toBytes(x);
(0, utils_ts_1._abool2)(isCompressed, 'isCompressed');
if (isCompressed) {
assertCompressionIsSupported();
const hasEvenY = !Fp.isOdd(y);
return (0, utils_ts_1.concatBytes)(pprefix(hasEvenY), bx);
}
else {
return (0, utils_ts_1.concatBytes)(Uint8Array.of(0x04), bx, Fp.toBytes(y));
}
}
function pointFromBytes(bytes) {
(0, utils_ts_1._abytes2)(bytes, undefined, 'Point');
const { publicKey: comp, publicKeyUncompressed: uncomp } = lengths; // e.g. for 32-byte: 33, 65
const length = bytes.length;
const head = bytes[0];
const tail = bytes.subarray(1);
// No actual validation is done here: use .assertValidity()
if (length === comp && (head === 0x02 || head === 0x03)) {
const x = Fp.fromBytes(tail);
if (!Fp.isValid(x))
throw new Error('bad point: is not on curve, wrong x');
const y2 = weierstrassEquation(x); // y² = x³ + ax + b
let y;
try {
y = Fp.sqrt(y2); // y = y² ^ (p+1)/4
}
catch (sqrtError) {
const err = sqrtError instanceof Error ? ': ' + sqrtError.message : '';
throw new Error('bad point: is not on curve, sqrt error' + err);
}
assertCompressionIsSupported();
const isYOdd = Fp.isOdd(y); // (y & _1n) === _1n;
const isHeadOdd = (head & 1) === 1; // ECDSA-specific
if (isHeadOdd !== isYOdd)
y = Fp.neg(y);
return { x, y };
}
else if (length === uncomp && head === 0x04) {
// TODO: more checks
const L = Fp.BYTES;
const x = Fp.fromBytes(tail.subarray(0, L));
const y = Fp.fromBytes(tail.subarray(L, L * 2));
if (!isValidXY(x, y))
throw new Error('bad point: is not on curve');
return { x, y };
}
else {
throw new Error(`bad point: got length ${length}, expected compressed=${comp} or uncompressed=${uncomp}`);
}
}
const encodePoint = extraOpts.toBytes || pointToBytes;
const decodePoint = extraOpts.fromBytes || pointFromBytes;
function weierstrassEquation(x) {
const x2 = Fp.sqr(x); // x * x
const x3 = Fp.mul(x2, x); // x² * x
return Fp.add(Fp.add(x3, Fp.mul(x, CURVE.a)), CURVE.b); // x³ + a * x + b
}
// TODO: move top-level
/** Checks whether equation holds for given x, y: y² == x³ + ax + b */
function isValidXY(x, y) {
const left = Fp.sqr(y); // y²
const right = weierstrassEquation(x); // x³ + ax + b
return Fp.eql(left, right);
}
// Validate whether the passed curve params are valid.
// Test 1: equation y² = x³ + ax + b should work for generator point.
if (!isValidXY(CURVE.Gx, CURVE.Gy))
throw new Error('bad curve params: generator point');
// Test 2: discriminant Δ part should be non-zero: 4a³ + 27b² != 0.
// Guarantees curve is genus-1, smooth (non-singular).
const _4a3 = Fp.mul(Fp.pow(CURVE.a, _3n), _4n);
const _27b2 = Fp.mul(Fp.sqr(CURVE.b), BigInt(27));
if (Fp.is0(Fp.add(_4a3, _27b2)))
throw new Error('bad curve params: a or b');
/** Asserts coordinate is valid: 0 <= n < Fp.ORDER. */
function acoord(title, n, banZero = false) {
if (!Fp.isValid(n) || (banZero && Fp.is0(n)))
throw new Error(`bad point coordinate ${title}`);
return n;
}
function aprjpoint(other) {
if (!(other instanceof Point))
throw new Error('ProjectivePoint expected');
}
function splitEndoScalarN(k) {
if (!endo || !endo.basises)
throw new Error('no endo');
return _splitEndoScalar(k, endo.basises, Fn.ORDER);
}
// Memoized toAffine / validity check. They are heavy. Points are immutable.
// Converts Projective point to affine (x, y) coordinates.
// Can accept precomputed Z^-1 - for example, from invertBatch.
// (X, Y, Z) ∋ (x=X/Z, y=Y/Z)
const toAffineMemo = (0, utils_ts_1.memoized)((p, iz) => {
const { X, Y, Z } = p;
// Fast-path for normalized points
if (Fp.eql(Z, Fp.ONE))
return { x: X, y: Y };
const is0 = p.is0();
// If invZ was 0, we return zero point. However we still want to execute
// all operations, so we replace invZ with a random number, 1.
if (iz == null)
iz = is0 ? Fp.ONE : Fp.inv(Z);
const x = Fp.mul(X, iz);
const y = Fp.mul(Y, iz);
const zz = Fp.mul(Z, iz);
if (is0)
return { x: Fp.ZERO, y: Fp.ZERO };
if (!Fp.eql(zz, Fp.ONE))
throw new Error('invZ was invalid');
return { x, y };
});
// NOTE: on exception this will crash 'cached' and no value will be set.
// Otherwise true will be return
const assertValidMemo = (0, utils_ts_1.memoized)((p) => {
if (p.is0()) {
// (0, 1, 0) aka ZERO is invalid in most contexts.
// In BLS, ZERO can be serialized, so we allow it.
// (0, 0, 0) is invalid representation of ZERO.
if (extraOpts.allowInfinityPoint && !Fp.is0(p.Y))
return;
throw new Error('bad point: ZERO');
}
// Some 3rd-party test vectors require different wording between here & `fromCompressedHex`
const { x, y } = p.toAffine();
if (!Fp.isValid(x) || !Fp.isValid(y))
throw new Error('bad point: x or y not field elements');
if (!isValidXY(x, y))
throw new Error('bad point: equation left != right');
if (!p.isTorsionFree())
throw new Error('bad point: not in prime-order subgroup');
return true;
});
function finishEndo(endoBeta, k1p, k2p, k1neg, k2neg) {
k2p = new Point(Fp.mul(k2p.X, endoBeta), k2p.Y, k2p.Z);
k1p = (0, curve_ts_1.negateCt)(k1neg, k1p);
k2p = (0, curve_ts_1.negateCt)(k2neg, k2p);
return k1p.add(k2p);
}
/**
* Projective Point works in 3d / projective (homogeneous) coordinates:(X, Y, Z) ∋ (x=X/Z, y=Y/Z).
* Default Point works in 2d / affine coordinates: (x, y).
* We're doing calculations in projective, because its operations don't require costly inversion.
*/
class Point {
/** Does NOT validate if the point is valid. Use `.assertValidity()`. */
constructor(X, Y, Z) {
this.X = acoord('x', X);
this.Y = acoord('y', Y, true);
this.Z = acoord('z', Z);
Object.freeze(this);
}
static CURVE() {
return CURVE;
}
/** Does NOT validate if the point is valid. Use `.assertValidity()`. */
static fromAffine(p) {
const { x, y } = p || {};
if (!p || !Fp.isValid(x) || !Fp.isValid(y))
throw new Error('invalid affine point');
if (p instanceof Point)
throw new Error('projective point not allowed');
// (0, 0) would've produced (0, 0, 1) - instead, we need (0, 1, 0)
if (Fp.is0(x) && Fp.is0(y))
return Point.ZERO;
return new Point(x, y, Fp.ONE);
}
static fromBytes(bytes) {
const P = Point.fromAffine(decodePoint((0, utils_ts_1._abytes2)(bytes, undefined, 'point')));
P.assertValidity();
return P;
}
static fromHex(hex) {
return Point.fromBytes((0, utils_ts_1.ensureBytes)('pointHex', hex));
}
get x() {
return this.toAffine().x;
}
get y() {
return this.toAffine().y;
}
/**
*
* @param windowSize
* @param isLazy true will defer table computation until the first multiplication
* @returns
*/
precompute(windowSize = 8, isLazy = true) {
wnaf.createCache(this, windowSize);
if (!isLazy)
this.multiply(_3n); // random number
return this;
}
// TODO: return `this`
/** A point on curve is valid if it conforms to equation. */
assertValidity() {
assertValidMemo(this);
}
hasEvenY() {
const { y } = this.toAffine();
if (!Fp.isOdd)
throw new Error("Field doesn't support isOdd");
return !Fp.isOdd(y);
}
/** Compare one point to another. */
equals(other) {
aprjpoint(other);
const { X: X1, Y: Y1, Z: Z1 } = this;
const { X: X2, Y: Y2, Z: Z2 } = other;
const U1 = Fp.eql(Fp.mul(X1, Z2), Fp.mul(X2, Z1));
const U2 = Fp.eql(Fp.mul(Y1, Z2), Fp.mul(Y2, Z1));
return U1 && U2;
}
/** Flips point to one corresponding to (x, -y) in Affine coordinates. */
negate() {
return new Point(this.X, Fp.neg(this.Y), this.Z);
}
// Renes-Costello-Batina exception-free doubling formula.
// There is 30% faster Jacobian formula, but it is not complete.
// https://eprint.iacr.org/2015/1060, algorithm 3
// Cost: 8M + 3S + 3*a + 2*b3 + 15add.
double() {
const { a, b } = CURVE;
const b3 = Fp.mul(b, _3n);
const { X: X1, Y: Y1, Z: Z1 } = this;
let X3 = Fp.ZERO, Y3 = Fp.ZERO, Z3 = Fp.ZERO; // prettier-ignore
let t0 = Fp.mul(X1, X1); // step 1
let t1 = Fp.mul(Y1, Y1);
let t2 = Fp.mul(Z1, Z1);
let t3 = Fp.mul(X1, Y1);
t3 = Fp.add(t3, t3); // step 5
Z3 = Fp.mul(X1, Z1);
Z3 = Fp.add(Z3, Z3);
X3 = Fp.mul(a, Z3);
Y3 = Fp.mul(b3, t2);
Y3 = Fp.add(X3, Y3); // step 10
X3 = Fp.sub(t1, Y3);
Y3 = Fp.add(t1, Y3);
Y3 = Fp.mul(X3, Y3);
X3 = Fp.mul(t3, X3);
Z3 = Fp.mul(b3, Z3); // step 15
t2 = Fp.mul(a, t2);
t3 = Fp.sub(t0, t2);
t3 = Fp.mul(a, t3);
t3 = Fp.add(t3, Z3);
Z3 = Fp.add(t0, t0); // step 20
t0 = Fp.add(Z3, t0);
t0 = Fp.add(t0, t2);
t0 = Fp.mul(t0, t3);
Y3 = Fp.add(Y3, t0);
t2 = Fp.mul(Y1, Z1); // step 25
t2 = Fp.add(t2, t2);
t0 = Fp.mul(t2, t3);
X3 = Fp.sub(X3, t0);
Z3 = Fp.mul(t2, t1);
Z3 = Fp.add(Z3, Z3); // step 30
Z3 = Fp.add(Z3, Z3);
return new Point(X3, Y3, Z3);
}
// Renes-Costello-Batina exception-free addition formula.
// There is 30% faster Jacobian formula, but it is not complete.
// https://eprint.iacr.org/2015/1060, algorithm 1
// Cost: 12M + 0S + 3*a + 3*b3 + 23add.
add(other) {
aprjpoint(other);
const { X: X1, Y: Y1, Z: Z1 } = this;
const { X: X2, Y: Y2, Z: Z2 } = other;
let X3 = Fp.ZERO, Y3 = Fp.ZERO, Z3 = Fp.ZERO; // prettier-ignore
const a = CURVE.a;
const b3 = Fp.mul(CURVE.b, _3n);
let t0 = Fp.mul(X1, X2); // step 1
let t1 = Fp.mul(Y1, Y2);
let t2 = Fp.mul(Z1, Z2);
let t3 = Fp.add(X1, Y1);
let t4 = Fp.add(X2, Y2); // step 5
t3 = Fp.mul(t3, t4);
t4 = Fp.add(t0, t1);
t3 = Fp.sub(t3, t4);
t4 = Fp.add(X1, Z1);
let t5 = Fp.add(X2, Z2); // step 10
t4 = Fp.mul(t4, t5);
t5 = Fp.add(t0, t2);
t4 = Fp.sub(t4, t5);
t5 = Fp.add(Y1, Z1);
X3 = Fp.add(Y2, Z2); // step 15
t5 = Fp.mul(t5, X3);
X3 = Fp.add(t1, t2);
t5 = Fp.sub(t5, X3);
Z3 = Fp.mul(a, t4);
X3 = Fp.mul(b3, t2); // step 20
Z3 = Fp.add(X3, Z3);
X3 = Fp.sub(t1, Z3);
Z3 = Fp.add(t1, Z3);
Y3 = Fp.mul(X3, Z3);
t1 = Fp.add(t0, t0); // step 25
t1 = Fp.add(t1, t0);
t2 = Fp.mul(a, t2);
t4 = Fp.mul(b3, t4);
t1 = Fp.add(t1, t2);
t2 = Fp.sub(t0, t2); // step 30
t2 = Fp.mul(a, t2);
t4 = Fp.add(t4, t2);
t0 = Fp.mul(t1, t4);
Y3 = Fp.add(Y3, t0);
t0 = Fp.mul(t5, t4); // step 35
X3 = Fp.mul(t3, X3);
X3 = Fp.sub(X3, t0);
t0 = Fp.mul(t3, t1);
Z3 = Fp.mul(t5, Z3);
Z3 = Fp.add(Z3, t0); // step 40
return new Point(X3, Y3, Z3);
}
subtract(other) {
return this.add(other.negate());
}
is0() {
return this.equals(Point.ZERO);
}
/**
* Constant time multiplication.
* Uses wNAF method. Windowed method may be 10% faster,
* but takes 2x longer to generate and consumes 2x memory.
* Uses precomputes when available.
* Uses endomorphism for Koblitz curves.
* @param scalar by which the point would be multiplied
* @returns New point
*/
multiply(scalar) {
const { endo } = extraOpts;
if (!Fn.isValidNot0(scalar))
throw new Error('invalid scalar: out of range'); // 0 is invalid
let point, fake; // Fake point is used to const-time mult
const mul = (n) => wnaf.cached(this, n, (p) => (0, curve_ts_1.normalizeZ)(Point, p));
/** See docs for {@link EndomorphismOpts} */
if (endo) {
const { k1neg, k1, k2neg, k2 } = splitEndoScalarN(scalar);
const { p: k1p, f: k1f } = mul(k1);
const { p: k2p, f: k2f } = mul(k2);
fake = k1f.add(k2f);
point = finishEndo(endo.beta, k1p, k2p, k1neg, k2neg);
}
else {
const { p, f } = mul(scalar);
point = p;
fake = f;
}
// Normalize `z` for both points, but return only real one
return (0, curve_ts_1.normalizeZ)(Point, [point, fake])[0];
}
/**
* Non-constant-time multiplication. Uses double-and-add algorithm.
* It's faster, but should only be used when you don't care about
* an exposed secret key e.g. sig verification, which works over *public* keys.
*/
multiplyUnsafe(sc) {
const { endo } = extraOpts;
const p = this;
if (!Fn.isValid(sc))
throw new Error('invalid scalar: out of range'); // 0 is valid
if (sc === _0n || p.is0())
return Point.ZERO;
if (sc === _1n)
return p; // fast-path
if (wnaf.hasCache(this))
return this.multiply(sc);
if (endo) {
const { k1neg, k1, k2neg, k2 } = splitEndoScalarN(sc);
const { p1, p2 } = (0, curve_ts_1.mulEndoUnsafe)(Point, p, k1, k2); // 30% faster vs wnaf.unsafe
return finishEndo(endo.beta, p1, p2, k1neg, k2neg);
}
else {
return wnaf.unsafe(p, sc);
}
}
multiplyAndAddUnsafe(Q, a, b) {
const sum = this.multiplyUnsafe(a).add(Q.multiplyUnsafe(b));
return sum.is0() ? undefined : sum;
}
/**
* Converts Projective point to affine (x, y) coordinates.
* @param invertedZ Z^-1 (inverted zero) - optional, precomputation is useful for invertBatch
*/
toAffine(invertedZ) {
return toAffineMemo(this, invertedZ);
}
/**
* Checks whether Point is free of torsion elements (is in prime subgroup).
* Always torsion-free for cofactor=1 curves.
*/
isTorsionFree() {
const { isTorsionFree } = extraOpts;
if (cofactor === _1n)
return true;
if (isTorsionFree)
return isTorsionFree(Point, this);
return wnaf.unsafe(this, CURVE_ORDER).is0();
}
clearCofactor() {
const { clearCofactor } = extraOpts;
if (cofactor === _1n)
return this; // Fast-path
if (clearCofactor)
return clearCofactor(Point, this);
return this.multiplyUnsafe(cofactor);
}
isSmallOrder() {
// can we use this.clearCofactor()?
return this.multiplyUnsafe(cofactor).is0();
}
toBytes(isCompressed = true) {
(0, utils_ts_1._abool2)(isCompressed, 'isCompressed');
this.assertValidity();
return encodePoint(Point, this, isCompressed);
}
toHex(isCompressed = true) {
return (0, utils_ts_1.bytesToHex)(this.toBytes(isCompressed));
}
toString() {
return `<Point ${this.is0() ? 'ZERO' : this.toHex()}>`;
}
// TODO: remove
get px() {
return this.X;
}
get py() {
return this.X;
}
get pz() {
return this.Z;
}
toRawBytes(isCompressed = true) {
return this.toBytes(isCompressed);
}
_setWindowSize(windowSize) {
this.precompute(windowSize);
}
static normalizeZ(points) {
return (0, curve_ts_1.normalizeZ)(Point, points);
}
static msm(points, scalars) {
return (0, curve_ts_1.pippenger)(Point, Fn, points, scalars);
}
static fromPrivateKey(privateKey) {
return Point.BASE.multiply(_normFnElement(Fn, privateKey));
}
}
// base / generator point
Point.BASE = new Point(CURVE.Gx, CURVE.Gy, Fp.ONE);
// zero / infinity / identity point
Point.ZERO = new Point(Fp.ZERO, Fp.ONE, Fp.ZERO); // 0, 1, 0
// math field
Point.Fp = Fp;
// scalar field
Point.Fn = Fn;
const bits = Fn.BITS;
const wnaf = new curve_ts_1.wNAF(Point, extraOpts.endo ? Math.ceil(bits / 2) : bits);
Point.BASE.precompute(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
return Point;
}
// Points start with byte 0x02 when y is even; otherwise 0x03
function pprefix(hasEvenY) {
return Uint8Array.of(hasEvenY ? 0x02 : 0x03);
}
/**
* Implementation of the Shallue and van de Woestijne method for any weierstrass curve.
* TODO: check if there is a way to merge this with uvRatio in Edwards; move to modular.
* b = True and y = sqrt(u / v) if (u / v) is square in F, and
* b = False and y = sqrt(Z * (u / v)) otherwise.
* @param Fp
* @param Z
* @returns
*/
function SWUFpSqrtRatio(Fp, Z) {
// Generic implementation
const q = Fp.ORDER;
let l = _0n;
for (let o = q - _1n; o % _2n === _0n; o /= _2n)
l += _1n;
const c1 = l; // 1. c1, the largest integer such that 2^c1 divides q - 1.
// We need 2n ** c1 and 2n ** (c1-1). We can't use **; but we can use <<.
// 2n ** c1 == 2n << (c1-1)
const _2n_pow_c1_1 = _2n << (c1 - _1n - _1n);
const _2n_pow_c1 = _2n_pow_c1_1 * _2n;
const c2 = (q - _1n) / _2n_pow_c1; // 2. c2 = (q - 1) / (2^c1) # Integer arithmetic
const c3 = (c2 - _1n) / _2n; // 3. c3 = (c2 - 1) / 2 # Integer arithmetic
const c4 = _2n_pow_c1 - _1n; // 4. c4 = 2^c1 - 1 # Integer arithmetic
const c5 = _2n_pow_c1_1; // 5. c5 = 2^(c1 - 1) # Integer arithmetic
const c6 = Fp.pow(Z, c2); // 6. c6 = Z^c2
const c7 = Fp.pow(Z, (c2 + _1n) / _2n); // 7. c7 = Z^((c2 + 1) / 2)
let sqrtRatio = (u, v) => {
let tv1 = c6; // 1. tv1 = c6
let tv2 = Fp.pow(v, c4); // 2. tv2 = v^c4
let tv3 = Fp.sqr(tv2); // 3. tv3 = tv2^2
tv3 = Fp.mul(tv3, v); // 4. tv3 = tv3 * v
let tv5 = Fp.mul(u, tv3); // 5. tv5 = u * tv3
tv5 = Fp.pow(tv5, c3); // 6. tv5 = tv5^c3
tv5 = Fp.mul(tv5, tv2); // 7. tv5 = tv5 * tv2
tv2 = Fp.mul(tv5, v); // 8. tv2 = tv5 * v
tv3 = Fp.mul(tv5, u); // 9. tv3 = tv5 * u
let tv4 = Fp.mul(tv3, tv2); // 10. tv4 = tv3 * tv2
tv5 = Fp.pow(tv4, c5); // 11. tv5 = tv4^c5
let isQR = Fp.eql(tv5, Fp.ONE); // 12. isQR = tv5 == 1
tv2 = Fp.mul(tv3, c7); // 13. tv2 = tv3 * c7
tv5 = Fp.mul(tv4, tv1); // 14. tv5 = tv4 * tv1
tv3 = Fp.cmov(tv2, tv3, isQR); // 15. tv3 = CMOV(tv2, tv3, isQR)
tv4 = Fp.cmov(tv5, tv4, isQR); // 16. tv4 = CMOV(tv5, tv4, isQR)
// 17. for i in (c1, c1 - 1, ..., 2):
for (let i = c1; i > _1n; i--) {
let tv5 = i - _2n; // 18. tv5 = i - 2
tv5 = _2n << (tv5 - _1n); // 19. tv5 = 2^tv5
let tvv5 = Fp.pow(tv4, tv5); // 20. tv5 = tv4^tv5
const e1 = Fp.eql(tvv5, Fp.ONE); // 21. e1 = tv5 == 1
tv2 = Fp.mul(tv3, tv1); // 22. tv2 = tv3 * tv1
tv1 = Fp.mul(tv1, tv1); // 23. tv1 = tv1 * tv1
tvv5 = Fp.mul(tv4, tv1); // 24. tv5 = tv4 * tv1
tv3 = Fp.cmov(tv2, tv3, e1); // 25. tv3 = CMOV(tv2, tv3, e1)
tv4 = Fp.cmov(tvv5, tv4, e1); // 26. tv4 = CMOV(tv5, tv4, e1)
}
return { isValid: isQR, value: tv3 };
};
if (Fp.ORDER % _4n === _3n) {
// sqrt_ratio_3mod4(u, v)
const c1 = (Fp.ORDER - _3n) / _4n; // 1. c1 = (q - 3) / 4 # Integer arithmetic
const c2 = Fp.sqrt(Fp.neg(Z)); // 2. c2 = sqrt(-Z)
sqrtRatio = (u, v) => {
let tv1 = Fp.sqr(v); // 1. tv1 = v^2
const tv2 = Fp.mul(u, v); // 2. tv2 = u * v
tv1 = Fp.mul(tv1, tv2); // 3. tv1 = tv1 * tv2
let y1 = Fp.pow(tv1, c1); // 4. y1 = tv1^c1
y1 = Fp.mul(y1, tv2); // 5. y1 = y1 * tv2
const y2 = Fp.mul(y1, c2); // 6. y2 = y1 * c2
const tv3 = Fp.mul(Fp.sqr(y1), v); // 7. tv3 = y1^2; 8. tv3 = tv3 * v
const isQR = Fp.eql(tv3, u); // 9. isQR = tv3 == u
let y = Fp.cmov(y2, y1, isQR); // 10. y = CMOV(y2, y1, isQR)
return { isValid: isQR, value: y }; // 11. return (isQR, y) isQR ? y : y*c2
};
}
// No curves uses that
// if (Fp.ORDER % _8n === _5n) // sqrt_ratio_5mod8
return sqrtRatio;
}
/**
* Simplified Shallue-van de Woestijne-Ulas Method
* https://www.rfc-editor.org/rfc/rfc9380#section-6.6.2
*/
function mapToCurveSimpleSWU(Fp, opts) {
(0, modular_ts_1.validateField)(Fp);
const { A, B, Z } = opts;
if (!Fp.isValid(A) || !Fp.isValid(B) || !Fp.isValid(Z))
throw new Error('mapToCurveSimpleSWU: invalid opts');
const sqrtRatio = SWUFpSqrtRatio(Fp, Z);
if (!Fp.isOdd)
throw new Error('Field does not have .isOdd()');
// Input: u, an element of F.
// Output: (x, y), a point on E.
return (u) => {
// prettier-ignore
let tv1, tv2, tv3, tv4, tv5, tv6, x, y;
tv1 = Fp.sqr(u); // 1. tv1 = u^2
tv1 = Fp.mul(tv1, Z); // 2. tv1 = Z * tv1
tv2 = Fp.sqr(tv1); // 3. tv2 = tv1^2
tv2 = Fp.add(tv2, tv1); // 4. tv2 = tv2 + tv1
tv3 = Fp.add(tv2, Fp.ONE); // 5. tv3 = tv2 + 1
tv3 = Fp.mul(tv3, B); // 6. tv3 = B * tv3
tv4 = Fp.cmov(Z, Fp.neg(tv2), !Fp.eql(tv2, Fp.ZERO)); // 7. tv4 = CMOV(Z, -tv2, tv2 != 0)
tv4 = Fp.mul(tv4, A); // 8. tv4 = A * tv4
tv2 = Fp.sqr(tv3); // 9. tv2 = tv3^2
tv6 = Fp.sqr(tv4); // 10. tv6 = tv4^2
tv5 = Fp.mul(tv6, A); // 11. tv5 = A * tv6
tv2 = Fp.add(tv2, tv5); // 12. tv2 = tv2 + tv5
tv2 = Fp.mul(tv2, tv3); // 13. tv2 = tv2 * tv3
tv6 = Fp.mul(tv6, tv4); // 14. tv6 = tv6 * tv4
tv5 = Fp.mul(tv6, B); // 15. tv5 = B * tv6
tv2 = Fp.add(tv2, tv5); // 16. tv2 = tv2 + tv5
x = Fp.mul(tv1, tv3); // 17. x = tv1 * tv3
const { isValid, value } = sqrtRatio(tv2, tv6); // 18. (is_gx1_square, y1) = sqrt_ratio(tv2, tv6)
y = Fp.mul(tv1, u); // 19. y = tv1 * u -> Z * u^3 * y1
y = Fp.mul(y, value); // 20. y = y * y1
x = Fp.cmov(x, tv3, isValid); // 21. x = CMOV(x, tv3, is_gx1_square)
y = Fp.cmov(y, value, isValid); // 22. y = CMOV(y, y1, is_gx1_square)
const e1 = Fp.isOdd(u) === Fp.isOdd(y); // 23. e1 = sgn0(u) == sgn0(y)
y = Fp.cmov(Fp.neg(y), y, e1); // 24. y = CMOV(-y, y, e1)
const tv4_inv = (0, modular_ts_1.FpInvertBatch)(Fp, [tv4], true)[0];
x = Fp.mul(x, tv4_inv); // 25. x = x / tv4
return { x, y };
};
}
function getWLengths(Fp, Fn) {
return {
secretKey: Fn.BYTES,
publicKey: 1 + Fp.BYTES,
publicKeyUncompressed: 1 + 2 * Fp.BYTES,
publicKeyHasPrefix: true,
signature: 2 * Fn.BYTES,
};
}
/**
* Sometimes users only need getPublicKey, getSharedSecret, and secret key handling.
* This helper ensures no signature functionality is present. Less code, smaller bundle size.
*/
function ecdh(Point, ecdhOpts = {}) {
const { Fn } = Point;
const randomBytes_ = ecdhOpts.randomBytes || utils_ts_1.randomBytes;
const lengths = Object.assign(getWLengths(Point.Fp, Fn), { seed: (0, modular_ts_1.getMinHashLength)(Fn.ORDER) });
function isValidSecretKey(secretKey) {
try {
return !!_normFnElement(Fn, secretKey);
}
catch (error) {
return false;
}
}
function isValidPublicKey(publicKey, isCompressed) {
const { publicKey: comp, publicKeyUncompressed } = lengths;
try {
const l = publicKey.length;
if (isCompressed === true && l !== comp)
return false;
if (isCompressed === false && l !== publicKeyUncompressed)
return false;
return !!Point.fromBytes(publicKey);
}
catch (error) {
return false;
}
}
/**
* Produces cryptographically secure secret key from random of size
* (groupLen + ceil(groupLen / 2)) with modulo bias being negligible.
*/
function randomSecretKey(seed = randomBytes_(lengths.seed)) {
return (0, modular_ts_1.mapHashToField)((0, utils_ts_1._abytes2)(seed, lengths.seed, 'seed'), Fn.ORDER);
}
/**
* Computes public key for a secret key. Checks for validity of the secret key.
* @param isCompressed whether to return compact (default), or full key
* @returns Public key, full when isCompressed=false; short when isCompressed=true
*/
function getPublicKey(secretKey, isCompressed = true) {
return Point.BASE.multiply(_normFnElement(Fn, secretKey)).toBytes(isCompressed);
}
function keygen(seed) {
const secretKey = randomSecretKey(seed);
return { secretKey, publicKey: getPublicKey(secretKey) };
}
/**
* Quick and dirty check for item being public key. Does not validate hex, or being on-curve.
*/
function isProbPub(item) {
if (typeof item === 'bigint')
return false;
if (item instanceof Point)
return true;
const { secretKey, publicKey, publicKeyUncompressed } = lengths;
if (Fn.allowedLengths || secretKey === publicKey)
return undefined;
const l = (0, utils_ts_1.ensureBytes)('key', item).length;
return l === publicKey || l === publicKeyUncompressed;
}
/**
* ECDH (Elliptic Curve Diffie Hellman).
* Computes shared public key from secret key A and public key B.
* Checks: 1) secret key validity 2) shared key is on-curve.
* Does NOT hash the result.
* @param isCompressed whether to return compact (default), or full key
* @returns shared public key
*/
function getSharedSecret(secretKeyA, publicKeyB, isCompressed = true) {
if (isProbPub(secretKeyA) === true)
throw new Error('first arg must be private key');
if (isProbPub(publicKeyB) === false)
throw new Error('second arg must be public key');
const s = _normFnElement(Fn, secretKeyA);
const b = Point.fromHex(publicKeyB); // checks for being on-curve
return b.multiply(s).toBytes(isCompressed);
}
const utils = {
isValidSecretKey,
isValidPublicKey,
randomSecretKey,
// TODO: remove
isValidPrivateKey: isValidSecretKey,
randomPrivateKey: randomSecretKey,
normPrivateKeyToScalar: (key) => _normFnElement(Fn, key),
precompute(windowSize = 8, point = Point.BASE) {
return point.precompute(windowSize, false);
},
};
return Object.freeze({ getPublicKey, getSharedSecret, keygen, Point, utils, lengths });
}
/**
* Creates ECDSA signing interface for given elliptic curve `Point` and `hash` function.
* We need `hash` for 2 features:
* 1. Message prehash-ing. NOT used if `sign` / `verify` are called with `prehash: false`
* 2. k generation in `sign`, using HMAC-drbg(hash)
*
* ECDSAOpts are only rarely needed.
*
* @example
* ```js
* const p256_Point = weierstrass(...);
* const p256_sha256 = ecdsa(p256_Point, sha256);
* const p256_sha224 = ecdsa(p256_Point, sha224);
* const p256_sha224_r = ecdsa(p256_Point, sha224, { randomBytes: (length) => { ... } });
* ```
*/
function ecdsa(Point, hash, ecdsaOpts = {}) {
(0, utils_1.ahash)(hash);
(0, utils_ts_1._validateObject)(ecdsaOpts, {}, {
hmac: 'function',
lowS: 'boolean',
randomBytes: 'function',
bits2int: 'function',
bits2int_modN: 'function',
});
const randomBytes = ecdsaOpts.randomBytes || utils_ts_1.randomBytes;
const hmac = ecdsaOpts.hmac ||
((key, ...msgs) => (0, hmac_js_1.hmac)(hash, key, (0, utils_ts_1.concatBytes)(...msgs)));
const { Fp, Fn } = Point;
const { ORDER: CURVE_ORDER, BITS: fnBits } = Fn;
const { keygen, getPublicKey, getSharedSecret, utils, lengths } = ecdh(Point, ecdsaOpts);
const defaultSigOpts = {
prehash: false,
lowS: typeof ecdsaOpts.lowS === 'boolean' ? ecdsaOpts.lowS : false,
format: undefined, //'compact' as ECDSASigFormat,
extraEntropy: false,
};
const defaultSigOpts_format = 'compact';
function isBiggerThanHalfOrder(number) {
const HALF = CURVE_ORDER >> _1n;
return number > HALF;
}
function validateRS(title, num) {
if (!Fn.isValidNot0(num))
throw new Error(`invalid signature ${title}: out of range 1..Point.Fn.ORDER`);
return num;
}
function validateSigLength(bytes, format) {
validateSigFormat(format);
const size = lengths.signature;
const sizer = format === 'compact' ? size : format === 'recovered' ? size + 1 : undefined;
return (0, utils_ts_1._abytes2)(bytes, sizer, `${format} signature`);
}
/**
* ECDSA signature with its (r, s) properties. Supports compact, recovered & DER representations.
*/
class Signature {
constructor(r, s, recovery) {
this.r = validateRS('r', r); // r in [1..N-1];
this.s = validateRS('s', s); // s in [1..N-1];
if (recovery != null)
this.recovery = recovery;
Object.freeze(this);
}
static fromBytes(bytes, format = defaultSigOpts_format) {
validateSigLength(bytes, format);
let recid;
if (format === 'der') {
const { r, s } = exports.DER.toSig((0, utils_ts_1._abytes2)(bytes));
return new Signature(r, s);
}
if (format === 'recovered') {
recid = bytes[0];
format = 'compact';
bytes = bytes.subarray(1);
}
const L = Fn.BYTES;
const r = bytes.subarray(0, L);
const s = bytes.subarray(L, L * 2);
return new Signature(Fn.fromBytes(r), Fn.fromBytes(s), recid);
}
static fromHex(hex, format) {
return this.fromBytes((0, utils_ts_1.hexToBytes)(hex), format);
}
addRecoveryBit(recovery) {
return new Signature(this.r, this.s, recovery);
}
recoverPublicKey(messageHash) {
const FIELD_ORDER = Fp.ORDER;
const { r, s, recovery: rec } = this;
if (rec == null || ![0, 1, 2, 3].includes(rec))
throw new Error('recovery id invalid');
// ECDSA recovery is hard for cofactor > 1 curves.
// In sign, `r = q.x mod n`, and here we recover q.x from r.
// While recovering q.x >= n, we need to add r+n for cofactor=1 curves.
// However, for cofactor>1, r+n may not get q.x:
// r+n*i would need to be done instead where i is unknown.
// To easily get i, we either need to:
// a. increase amount of valid recid values (4, 5...); OR
// b. prohibit non-prime-order signatures (recid > 1).
const hasCofactor = CURVE_ORDER * _2n < FIELD_ORDER;
if (hasCofactor && rec > 1)
throw new Error('recovery id is ambiguous for h>1 curve');
const radj = rec === 2 || rec === 3 ? r + CURVE_ORDER : r;
if (!Fp.isValid(radj))
throw new Error('recovery id 2 or 3 invalid');
const x = Fp.toBytes(radj);
const R = Point.fromBytes((0, utils_ts_1.concatBytes)(pprefix((rec & 1) === 0), x));
const ir = Fn.inv(radj); // r^-1
const h = bits2int_modN((0, utils_ts_1.ensureBytes)('msgHash', messageHash)); // Truncate hash
const u1 = Fn.create(-h * ir); // -hr^-1
const u2 = Fn.create(s * ir); // sr^-1
// (sr^-1)R-(hr^-1)G = -(hr^-1)G + (sr^-1). unsafe is fine: there is no private data.
const Q = Point.BASE.multiplyUnsafe(u1).add(R.multiplyUnsafe(u2));
if (Q.is0())
throw new Error('point at infinify');
Q.assertValidity();
return Q;
}
// Signatures should be low-s, to prevent malleability.
hasHighS() {
return isBiggerThanHalfOrder(this.s);
}
toBytes(format = defaultSigOpts_format) {
validateSigFormat(format);
if (format === 'der')
return (0, utils_ts_1.hexToBytes)(exports.DER.hexFromSig(this));
const r = Fn.toBytes(this.r);
const s = Fn.toBytes(this.s);
if (format === 'recovered') {
if (this.recovery == null)
throw new Error('recovery bit must be present');
return (0, utils_ts_1.concatBytes)(Uint8Array.of(this.recovery), r, s);
}
return (0, utils_ts_1.concatBytes)(r, s);
}
toHex(format) {
return (0, utils_ts_1.bytesToHex)(this.toBytes(format));
}
// TODO: remove
assertValidity() { }
static fromCompact(hex) {
return Signature.fromBytes((0, utils_ts_1.ensureBytes)('sig', hex), 'compact');
}
static fromDER(hex) {
return Signature.fromBytes((0, utils_ts_1.ensureBytes)('sig', hex), 'der');
}
normalizeS() {
return this.hasHighS() ? new Signature(this.r, Fn.neg(this.s), this.recovery) : this;
}
toDERRawBytes() {
return this.toBytes('der');
}
toDERHex() {
return (0, utils_ts_1.bytesToHex)(this.toBytes('der'));
}
toCompactRawBytes() {
return this.toBytes('compact');
}
toCompactHex() {
return (0, utils_ts_1.bytesToHex)(this.toBytes('compact'));
}
}
// RFC6979: ensure ECDSA msg is X bytes and < N. RFC suggests optional truncating via bits2octets.
// FIPS 186-4 4.6 suggests the leftmost min(nBitLen, outLen) bits, which matches bits2int.
// bits2int can produce res>N, we can do mod(res, N) since the bitLen is the same.
// int2octets can't be used; pads small msgs with 0: unacceptatble for trunc as per RFC vectors
const bits2int = ecdsaOpts.bits2int ||
function bits2int_def(bytes) {
// Our custom check "just in case", for protection against DoS
if (bytes.length > 8192)
throw new Error('input is too large');
// For curves with nBitLength % 8 !== 0: bits2octets(bits2octets(m)) !== bits2octets(m)
// for some cases, since bytes.length * 8 is not actual bitLength.
const num = (0, utils_ts_1.bytesToNumberBE)(bytes); // check for == u8 done here
const delta = bytes.length * 8 - fnBits; // truncate to nBitLength leftmost bits
return delta > 0 ? num >> BigInt(delta) : num;
};
const bits2int_modN = ecdsaOpts.bits2int_modN ||
function bits2int_modN_def(bytes) {
return Fn.create(bits2int(bytes)); // can't use bytesToNumberBE here
};
// Pads output with zero as per spec
const ORDER_MASK = (0, utils_ts_1.bitMask)(fnBits);
/** Converts to bytes. Checks if num in `[0..ORDER_MASK-1]` e.g.: `[0..2^256-1]`. */
function int2octets(num) {
// IMPORTANT: the check ensures working for case `Fn.BYTES != Fn.BITS * 8`
(0, utils_ts_1.aInRange)('num < 2^' + fnBits, num, _0n, ORDER_MASK);
return Fn.toBytes(num);
}
function validateMsgAndHash(message, prehash) {
(0, utils_ts_1._abytes2)(message, undefined, 'message');
return prehash ? (0, utils_ts_1._abytes2)(hash(message), undefined, 'prehashed message') : message;
}
/**
* Steps A, D of RFC6979 3.2.
* Creates RFC6979 seed; converts msg/privKey to numbers.
* Used only in sign, not in verify.
*
* Warning: we cannot assume here that message has same amount of bytes as curve order,
* this will be invalid at least for P521. Also it can be bigger for P224 + SHA256.
*/
function prepSig(message, privateKey, opts) {
if (['recovered', 'canonical'].some((k) => k in opts))
throw new Error('sign() legacy options not supported');
const { lowS, prehash, extraEntropy } = validateSigOpts(opts, defaultSigOpts);
message = validateMsgAndHash(message, prehash); // RFC6979 3.2 A: h1 = H(m)
// We can't later call bits2octets, since nested bits2int is broken for curves
// with fnBits % 8 !== 0. Because of that, we unwrap it here as int2octets call.
// const bits2octets = (bits) => int2octets(bits2int_modN(bits))
const h1int = bits2int_modN(message);
const d = _normFnElement(Fn, privateKey); // validate secret key, convert to bigint
const seedArgs = [int2octets(d), int2octets(h1int)];
// extraEntropy. RFC6979 3.6: additional k' (optional).
if (extraEntropy != null && extraEntropy !== false) {
// K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1) || k')
// gen random bytes OR pass as-is
const e = extraEntropy === true ? randomBytes(lengths.secretKey) : extraEntropy;
seedArgs.push((0, utils_ts_1.ensureBytes)('extraEntropy', e)); // check for being bytes
}
const seed = (0, utils_ts_1.concatBytes)(...seedArgs); // Step D of RFC6979 3.2
const m = h1int; // NOTE: no need to call bits2int second time here, it is inside truncateHash!
// Converts signature params into point w r/s, checks result for validity.
// To transform k => Signature:
// q = k⋅G
// r = q.x mod n
// s = k^-1(m + rd) mod n
// Can use scalar blinding b^-1(bm + bdr) where b ∈ [1,q−1] according to
// https://tches.iacr.org/index.php/TCHES/article/view/7337/6509. We've decided against it:
// a) dependency on CSPRNG b) 15% slowdown c) doesn't really help since bigints are not CT
function k2sig(kBytes) {
// RFC 6979 Section 3.2, step 3: k = bits2int(T)
// Important: all mod() calls here must be done over N
const k = bits2int(kBytes); // mod n, not mod p
if (!Fn.isValidNot0(k))
return; // Valid scalars (including k) must be in 1..N-1
const ik = Fn.inv(k); // k^-1 mod n
const q = Point.BASE.multiply(k).toAffine(); // q = k⋅G
const r = Fn.create(q.x); // r = q.x mod n
if (r === _0n)
return;
const s = Fn.create(ik * Fn.create(m + r * d)); // Not using blinding here, see comment above
if (s === _0n)
return;
let recovery = (q.x === r ? 0 : 2) | Number(q.y & _1n); // recovery bit (2 or 3, when q.x > n)
let normS = s;
if (lowS && isBiggerThanHalfOrder(s)) {
normS = Fn.neg(s); // if lowS was passed, ensure s is always
recovery ^= 1; // // in the bottom half of N
}
return new Signature(r, normS, recovery); // use normS, not s
}
return { seed, k2sig };
}
/**
* Signs message hash with a secret key.
*
* ```
* sign(m, d) where
* k = rfc6979_hmac_drbg(m, d)
* (x, y) = G × k
* r = x mod n
* s = (m + dr) / k mod n
* ```
*/
function sign(message, secretKey, opts = {}) {
message = (0, utils_ts_1.ensureBytes)('message', message);
const { seed, k2sig } = prepSig(message, secretKey, opts); // Steps A, D of RFC6979 3.2.
const drbg = (0, utils_ts_1.createHmacDrbg)(hash.outputLen, Fn.BYTES, hmac);
const sig = drbg(seed, k2sig); // Steps B, C, D, E, F, G
return sig;
}
function tryParsingSig(sg) {
// Try to deduce format
let sig = undefined;
const isHex = typeof sg === 'string' || (0, utils_ts_1.isBytes)(sg);
const isObj = !isHex &&
sg !== null &&
typeof sg === 'object' &&
typeof sg.r === 'bigint' &&
typeof sg.s === 'bigint';
if (!isHex && !isObj)
throw new Error('invalid signature, expected Uint8Array, hex string or Signature instance');
if (isObj) {
sig = new Signature(sg.r, sg.s);
}
else if (isHex) {
try {
sig = Signature.fromBytes((0, utils_ts_1.ensureBytes)('sig', sg), 'der');
}
catch (derError) {
if (!(derError instanceof exports.DER.Err))
throw derError;
}
if (!sig) {
try {
sig = Signature.fromBytes((0, utils_ts_1.ensureBytes)('sig', sg), 'compact');
}
catch (error) {
return false;
}
}
}
if (!sig)
return false;
return sig;
}
/**
* Verifies a signature against message and public key.
* Rejects lowS signatures by default: see {@link ECDSAVerifyOpts}.
* Implements section 4.1.4 from https://www.secg.org/sec1-v2.pdf:
*
* ```
* verify(r, s, h, P) where
* u1 = hs^-1 mod n
* u2 = rs^-1 mod n
* R = u1⋅G + u2⋅P
* mod(R.x, n) == r
* ```
*/
function verify(signature, message, publicKey, opts = {}) {
const { lowS, prehash, format } = validateSigOpts(opts, defaultSigOpts);
publicKey = (0, utils_ts_1.ensureBytes)('publicKey', publicKey);
message = validateMsgAndHash((0, utils_ts_1.ensureBytes)('message', message), prehash);
if ('strict' in opts)
throw new Error('options.strict was renamed to lowS');
const sig = format === undefined
? tryParsingSig(signature)
: Signature.fromBytes((0, utils_ts_1.ensureBytes)('sig', signature), format);
if (sig === false)
return false;
try {
const P = Point.fromBytes(publicKey);
if (lowS && sig.hasHighS())
return false;
const { r, s } = sig;
const h = bits2int_modN(message); // mod n, not mod p
const is = Fn.inv(s); // s^-1 mod n
const u1 = Fn.create(h * is); // u1 = hs^-1 mod n
const u2 = Fn.create(r * is); // u2 = rs^-1 mod n
const R = Point.BASE.multiplyUnsafe(u1).add(P.multiplyUnsafe(u2)); // u1⋅G + u2⋅P
if (R.is0())
return false;
const v = Fn.create(R.x); // v = r.x mod n
return v === r;
}
catch (e) {
return false;
}
}
function recoverPublicKey(signature, message, opts = {}) {
const { prehash } = validateSigOpts(opts, defaultSigOpts);
message = validateMsgAndHash(message, prehash);
return Signature.fromBytes(signature, 'recovered').recoverPublicKey(message).toBytes();
}
return Object.freeze({
keygen,
getPublicKey,
getSharedSecret,
utils,
lengths,
Point,
sign,
verify,
recoverPublicKey,
Signature,
hash,
});
}
/** @deprecated use `weierstrass` in newer releases */
function weierstrassPoints(c) {
const { CURVE, curveOpts } = _weierstrass_legacy_opts_to_new(c);
const Point = weierstrassN(CURVE, curveOpts);
return _weierstrass_new_output_to_legacy(c, Point);
}
function _weierstrass_legacy_opts_to_new(c) {
const CURVE = {
a: c.a,
b: c.b,
p: c.Fp.ORDER,
n: c.n,
h: c.h,
Gx: c.Gx,
Gy: c.Gy,
};
const Fp = c.Fp;
let allowedLengths = c.allowedPrivateKeyLengths
? Array.from(new Set(c.allowedPrivateKeyLengths.map((l) => Math.ceil(l / 2))))
: undefined;
const Fn = (0, modular_ts_1.Field)(CURVE.n, {
BITS: c.nBitLength,
allowedLengths: allowedLengths,
modFromBytes: c.wrapPrivateKey,
});
const curveOpts = {
Fp,
Fn,
allowInfinityPoint: c.allowInfinityPoint,
endo: c.endo,
isTorsionFree: c.isTorsionFree,
clearCofactor: c.clearCofactor,
fromBytes: c.fromBytes,
toBytes: c.toBytes,
};
return { CURVE, curveOpts };
}
function _ecdsa_legacy_opts_to_new(c) {
const { CURVE, curveOpts } = _weierstrass_legacy_opts_to_new(c);
const ecdsaOpts = {
hmac: c.hmac,
randomBytes: c.randomBytes,
lowS: c.lowS,
bits2int: c.bits2int,
bits2int_modN: c.bits2int_modN,
};
return { CURVE, curveOpts, hash: c.hash, ecdsaOpts };
}
function _legacyHelperEquat(Fp, a, b) {
/**
* y² = x³ + ax + b: Short weierstrass curve formula. Takes x, returns y².
* @returns y²
*/
function weierstrassEquation(x) {
const x2 = Fp.sqr(x); // x * x
const x3 = Fp.mul(x2, x); // x² * x
return Fp.add(Fp.add(x3, Fp.mul(x, a)), b); // x³ + a * x + b
}
return weierstrassEquation;
}
function _weierstrass_new_output_to_legacy(c, Point) {
const { Fp, Fn } = Point;
function isWithinCurveOrder(num) {
return (0, utils_ts_1.inRange)(num, _1n, Fn.ORDER);
}
const weierstrassEquation = _legacyHelperEquat(Fp, c.a, c.b);
return Object.assign({}, {
CURVE: c,
Point: Point,
ProjectivePoint: Point,
normPrivateKeyToScalar: (key) => _normFnElement(Fn, key),
weierstrassEquation,
isWithinCurveOrder,
});
}
function _ecdsa_new_output_to_legacy(c, _ecdsa) {
const Point = _ecdsa.Point;
return Object.assign({}, _ecdsa, {
ProjectivePoint: Point,
CURVE: Object.assign({}, c, (0, modular_ts_1.nLength)(Point.Fn.ORDER, Point.Fn.BITS)),
});
}
// _ecdsa_legacy
function weierstrass(c) {
const { CURVE, curveOpts, hash, ecdsaOpts } = _ecdsa_legacy_opts_to_new(c);
const Point = weierstrassN(CURVE, curveOpts);
const signs = ecdsa(Point, hash, ecdsaOpts);
return _ecdsa_new_output_to_legacy(c, signs);
}
//# sourceMappingURL=weierstrass.js.mapВыполнить команду
Для локальной разработки. Не используйте в интернете!