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Текущая директория: /usr/lib/node_modules/bitgo/node_modules/@noble/curves/src
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[DIR] ..
[FILE] _shortw_utils.ts
[DIR] abstract
[FILE] bls12-381.ts
[FILE] bn254.ts
[FILE] ed25519.ts
[FILE] ed448.ts
[FILE] index.ts
[FILE] jubjub.ts
[FILE] misc.ts
[FILE] nist.ts
[FILE] p256.ts
[FILE] p384.ts
[FILE] p521.ts
[FILE] package.json
[FILE] pasta.ts
[FILE] secp256k1.ts
[FILE] utils.ts
Просмотр файла: secp256k1.ts

/**
 * SECG secp256k1. See [pdf](https://www.secg.org/sec2-v2.pdf).
 *
 * Belongs to Koblitz curves: it has efficiently-computable GLV endomorphism ψ,
 * check out {@link EndomorphismOpts}. Seems to be rigid (not backdoored).
 * @module
 */
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { sha256 } from '@noble/hashes/sha2.js';
import { randomBytes } from '@noble/hashes/utils.js';
import { createCurve, type CurveFnWithCreate } from './_shortw_utils.ts';
import type { CurveLengths } from './abstract/curve.ts';
import {
  createHasher,
  type H2CHasher,
  type H2CMethod,
  isogenyMap,
} from './abstract/hash-to-curve.ts';
import { Field, mapHashToField, mod, pow2 } from './abstract/modular.ts';
import {
  _normFnElement,
  type EndomorphismOpts,
  mapToCurveSimpleSWU,
  type WeierstrassPoint as PointType,
  type WeierstrassOpts,
  type WeierstrassPointCons,
} from './abstract/weierstrass.ts';
import type { Hex, PrivKey } from './utils.ts';
import {
  bytesToNumberBE,
  concatBytes,
  ensureBytes,
  inRange,
  numberToBytesBE,
  utf8ToBytes,
} from './utils.ts';

// Seems like generator was produced from some seed:
// `Point.BASE.multiply(Point.Fn.inv(2n, N)).toAffine().x`
// // gives short x 0x3b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63n
const secp256k1_CURVE: WeierstrassOpts<bigint> = {
  p: BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f'),
  n: BigInt('0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141'),
  h: BigInt(1),
  a: BigInt(0),
  b: BigInt(7),
  Gx: BigInt('0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798'),
  Gy: BigInt('0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8'),
};

const secp256k1_ENDO: EndomorphismOpts = {
  beta: BigInt('0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee'),
  basises: [
    [BigInt('0x3086d221a7d46bcde86c90e49284eb15'), -BigInt('0xe4437ed6010e88286f547fa90abfe4c3')],
    [BigInt('0x114ca50f7a8e2f3f657c1108d9d44cfd8'), BigInt('0x3086d221a7d46bcde86c90e49284eb15')],
  ],
};

const _0n = /* @__PURE__ */ BigInt(0);
const _1n = /* @__PURE__ */ BigInt(1);
const _2n = /* @__PURE__ */ BigInt(2);

/**
 * √n = n^((p+1)/4) for fields p = 3 mod 4. We unwrap the loop and multiply bit-by-bit.
 * (P+1n/4n).toString(2) would produce bits [223x 1, 0, 22x 1, 4x 0, 11, 00]
 */
function sqrtMod(y: bigint): bigint {
  const P = secp256k1_CURVE.p;
  // prettier-ignore
  const _3n = BigInt(3), _6n = BigInt(6), _11n = BigInt(11), _22n = BigInt(22);
  // prettier-ignore
  const _23n = BigInt(23), _44n = BigInt(44), _88n = BigInt(88);
  const b2 = (y * y * y) % P; // x^3, 11
  const b3 = (b2 * b2 * y) % P; // x^7
  const b6 = (pow2(b3, _3n, P) * b3) % P;
  const b9 = (pow2(b6, _3n, P) * b3) % P;
  const b11 = (pow2(b9, _2n, P) * b2) % P;
  const b22 = (pow2(b11, _11n, P) * b11) % P;
  const b44 = (pow2(b22, _22n, P) * b22) % P;
  const b88 = (pow2(b44, _44n, P) * b44) % P;
  const b176 = (pow2(b88, _88n, P) * b88) % P;
  const b220 = (pow2(b176, _44n, P) * b44) % P;
  const b223 = (pow2(b220, _3n, P) * b3) % P;
  const t1 = (pow2(b223, _23n, P) * b22) % P;
  const t2 = (pow2(t1, _6n, P) * b2) % P;
  const root = pow2(t2, _2n, P);
  if (!Fpk1.eql(Fpk1.sqr(root), y)) throw new Error('Cannot find square root');
  return root;
}

const Fpk1 = Field(secp256k1_CURVE.p, { sqrt: sqrtMod });

/**
 * secp256k1 curve, ECDSA and ECDH methods.
 *
 * Field: `2n**256n - 2n**32n - 2n**9n - 2n**8n - 2n**7n - 2n**6n - 2n**4n - 1n`
 *
 * @example
 * ```js
 * import { secp256k1 } from '@noble/curves/secp256k1';
 * const { secretKey, publicKey } = secp256k1.keygen();
 * const msg = new TextEncoder().encode('hello');
 * const sig = secp256k1.sign(msg, secretKey);
 * const isValid = secp256k1.verify(sig, msg, publicKey) === true;
 * ```
 */
export const secp256k1: CurveFnWithCreate = createCurve(
  { ...secp256k1_CURVE, Fp: Fpk1, lowS: true, endo: secp256k1_ENDO },
  sha256
);

// Schnorr signatures are superior to ECDSA from above. Below is Schnorr-specific BIP0340 code.
// https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki
/** An object mapping tags to their tagged hash prefix of [SHA256(tag) | SHA256(tag)] */
const TAGGED_HASH_PREFIXES: { [tag: string]: Uint8Array } = {};
function taggedHash(tag: string, ...messages: Uint8Array[]): Uint8Array {
  let tagP = TAGGED_HASH_PREFIXES[tag];
  if (tagP === undefined) {
    const tagH = sha256(utf8ToBytes(tag));
    tagP = concatBytes(tagH, tagH);
    TAGGED_HASH_PREFIXES[tag] = tagP;
  }
  return sha256(concatBytes(tagP, ...messages));
}

// ECDSA compact points are 33-byte. Schnorr is 32: we strip first byte 0x02 or 0x03
const pointToBytes = (point: PointType<bigint>) => point.toBytes(true).slice(1);
const Pointk1 = /* @__PURE__ */ (() => secp256k1.Point)();
const hasEven = (y: bigint) => y % _2n === _0n;

// Calculate point, scalar and bytes
function schnorrGetExtPubKey(priv: PrivKey) {
  const { Fn, BASE } = Pointk1;
  const d_ = _normFnElement(Fn, priv);
  const p = BASE.multiply(d_); // P = d'⋅G; 0 < d' < n check is done inside
  const scalar = hasEven(p.y) ? d_ : Fn.neg(d_);
  return { scalar, bytes: pointToBytes(p) };
}
/**
 * lift_x from BIP340. Convert 32-byte x coordinate to elliptic curve point.
 * @returns valid point checked for being on-curve
 */
function lift_x(x: bigint): PointType<bigint> {
  const Fp = Fpk1;
  if (!Fp.isValidNot0(x)) throw new Error('invalid x: Fail if x ≥ p');
  const xx = Fp.create(x * x);
  const c = Fp.create(xx * x + BigInt(7)); // Let c = x³ + 7 mod p.
  let y = Fp.sqrt(c); // Let y = c^(p+1)/4 mod p. Same as sqrt().
  // Return the unique point P such that x(P) = x and
  // y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.
  if (!hasEven(y)) y = Fp.neg(y);
  const p = Pointk1.fromAffine({ x, y });
  p.assertValidity();
  return p;
}
const num = bytesToNumberBE;
/**
 * Create tagged hash, convert it to bigint, reduce modulo-n.
 */
function challenge(...args: Uint8Array[]): bigint {
  return Pointk1.Fn.create(num(taggedHash('BIP0340/challenge', ...args)));
}

/**
 * Schnorr public key is just `x` coordinate of Point as per BIP340.
 */
function schnorrGetPublicKey(secretKey: Hex): Uint8Array {
  return schnorrGetExtPubKey(secretKey).bytes; // d'=int(sk). Fail if d'=0 or d'≥n. Ret bytes(d'⋅G)
}

/**
 * Creates Schnorr signature as per BIP340. Verifies itself before returning anything.
 * auxRand is optional and is not the sole source of k generation: bad CSPRNG won't be dangerous.
 */
function schnorrSign(message: Hex, secretKey: PrivKey, auxRand: Hex = randomBytes(32)): Uint8Array {
  const { Fn } = Pointk1;
  const m = ensureBytes('message', message);
  const { bytes: px, scalar: d } = schnorrGetExtPubKey(secretKey); // checks for isWithinCurveOrder
  const a = ensureBytes('auxRand', auxRand, 32); // Auxiliary random data a: a 32-byte array
  const t = Fn.toBytes(d ^ num(taggedHash('BIP0340/aux', a))); // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
  const rand = taggedHash('BIP0340/nonce', t, px, m); // Let rand = hash/nonce(t || bytes(P) || m)
  // Let k' = int(rand) mod n. Fail if k' = 0. Let R = k'⋅G
  const { bytes: rx, scalar: k } = schnorrGetExtPubKey(rand);
  const e = challenge(rx, px, m); // Let e = int(hash/challenge(bytes(R) || bytes(P) || m)) mod n.
  const sig = new Uint8Array(64); // Let sig = bytes(R) || bytes((k + ed) mod n).
  sig.set(rx, 0);
  sig.set(Fn.toBytes(Fn.create(k + e * d)), 32);
  // If Verify(bytes(P), m, sig) (see below) returns failure, abort
  if (!schnorrVerify(sig, m, px)) throw new Error('sign: Invalid signature produced');
  return sig;
}

/**
 * Verifies Schnorr signature.
 * Will swallow errors & return false except for initial type validation of arguments.
 */
function schnorrVerify(signature: Hex, message: Hex, publicKey: Hex): boolean {
  const { Fn, BASE } = Pointk1;
  const sig = ensureBytes('signature', signature, 64);
  const m = ensureBytes('message', message);
  const pub = ensureBytes('publicKey', publicKey, 32);
  try {
    const P = lift_x(num(pub)); // P = lift_x(int(pk)); fail if that fails
    const r = num(sig.subarray(0, 32)); // Let r = int(sig[0:32]); fail if r ≥ p.
    if (!inRange(r, _1n, secp256k1_CURVE.p)) return false;
    const s = num(sig.subarray(32, 64)); // Let s = int(sig[32:64]); fail if s ≥ n.
    if (!inRange(s, _1n, secp256k1_CURVE.n)) return false;
    // int(challenge(bytes(r)||bytes(P)||m))%n
    const e = challenge(Fn.toBytes(r), pointToBytes(P), m);
    // R = s⋅G - e⋅P, where -eP == (n-e)P
    const R = BASE.multiplyUnsafe(s).add(P.multiplyUnsafe(Fn.neg(e)));
    const { x, y } = R.toAffine();
    // Fail if is_infinite(R) / not has_even_y(R) / x(R) ≠ r.
    if (R.is0() || !hasEven(y) || x !== r) return false;
    return true;
  } catch (error) {
    return false;
  }
}

export type SecpSchnorr = {
  keygen: (seed?: Uint8Array) => { secretKey: Uint8Array; publicKey: Uint8Array };
  getPublicKey: typeof schnorrGetPublicKey;
  sign: typeof schnorrSign;
  verify: typeof schnorrVerify;
  Point: WeierstrassPointCons<bigint>;
  utils: {
    randomSecretKey: (seed?: Uint8Array) => Uint8Array;
    pointToBytes: (point: PointType<bigint>) => Uint8Array;
    lift_x: typeof lift_x;
    taggedHash: typeof taggedHash;

    /** @deprecated use `randomSecretKey` */
    randomPrivateKey: (seed?: Uint8Array) => Uint8Array;
    /** @deprecated use `utils` */
    numberToBytesBE: typeof numberToBytesBE;
    /** @deprecated use `utils` */
    bytesToNumberBE: typeof bytesToNumberBE;
    /** @deprecated use `modular` */
    mod: typeof mod;
  };
  lengths: CurveLengths;
};
/**
 * Schnorr signatures over secp256k1.
 * https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki
 * @example
 * ```js
 * import { schnorr } from '@noble/curves/secp256k1';
 * const { secretKey, publicKey } = schnorr.keygen();
 * // const publicKey = schnorr.getPublicKey(secretKey);
 * const msg = new TextEncoder().encode('hello');
 * const sig = schnorr.sign(msg, secretKey);
 * const isValid = schnorr.verify(sig, msg, publicKey);
 * ```
 */
export const schnorr: SecpSchnorr = /* @__PURE__ */ (() => {
  const size = 32;
  const seedLength = 48;
  const randomSecretKey = (seed = randomBytes(seedLength)): Uint8Array => {
    return mapHashToField(seed, secp256k1_CURVE.n);
  };
  // TODO: remove
  secp256k1.utils.randomSecretKey;
  function keygen(seed?: Uint8Array) {
    const secretKey = randomSecretKey(seed);
    return { secretKey, publicKey: schnorrGetPublicKey(secretKey) };
  }
  return {
    keygen,
    getPublicKey: schnorrGetPublicKey,
    sign: schnorrSign,
    verify: schnorrVerify,
    Point: Pointk1,
    utils: {
      randomSecretKey: randomSecretKey,
      randomPrivateKey: randomSecretKey,
      taggedHash,

      // TODO: remove
      lift_x,
      pointToBytes,
      numberToBytesBE,
      bytesToNumberBE,
      mod,
    },
    lengths: {
      secretKey: size,
      publicKey: size,
      publicKeyHasPrefix: false,
      signature: size * 2,
      seed: seedLength,
    },
  };
})();

const isoMap = /* @__PURE__ */ (() =>
  isogenyMap(
    Fpk1,
    [
      // xNum
      [
        '0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa8c7',
        '0x7d3d4c80bc321d5b9f315cea7fd44c5d595d2fc0bf63b92dfff1044f17c6581',
        '0x534c328d23f234e6e2a413deca25caece4506144037c40314ecbd0b53d9dd262',
        '0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa88c',
      ],
      // xDen
      [
        '0xd35771193d94918a9ca34ccbb7b640dd86cd409542f8487d9fe6b745781eb49b',
        '0xedadc6f64383dc1df7c4b2d51b54225406d36b641f5e41bbc52a56612a8c6d14',
        '0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
      ],
      // yNum
      [
        '0x4bda12f684bda12f684bda12f684bda12f684bda12f684bda12f684b8e38e23c',
        '0xc75e0c32d5cb7c0fa9d0a54b12a0a6d5647ab046d686da6fdffc90fc201d71a3',
        '0x29a6194691f91a73715209ef6512e576722830a201be2018a765e85a9ecee931',
        '0x2f684bda12f684bda12f684bda12f684bda12f684bda12f684bda12f38e38d84',
      ],
      // yDen
      [
        '0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffff93b',
        '0x7a06534bb8bdb49fd5e9e6632722c2989467c1bfc8e8d978dfb425d2685c2573',
        '0x6484aa716545ca2cf3a70c3fa8fe337e0a3d21162f0d6299a7bf8192bfd2a76f',
        '0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
      ],
    ].map((i) => i.map((j) => BigInt(j))) as [bigint[], bigint[], bigint[], bigint[]]
  ))();
const mapSWU = /* @__PURE__ */ (() =>
  mapToCurveSimpleSWU(Fpk1, {
    A: BigInt('0x3f8731abdd661adca08a5558f0f5d272e953d363cb6f0e5d405447c01a444533'),
    B: BigInt('1771'),
    Z: Fpk1.create(BigInt('-11')),
  }))();

/** Hashing / encoding to secp256k1 points / field. RFC 9380 methods. */
export const secp256k1_hasher: H2CHasher<bigint> = /* @__PURE__ */ (() =>
  createHasher(
    secp256k1.Point,
    (scalars: bigint[]) => {
      const { x, y } = mapSWU(Fpk1.create(scalars[0]));
      return isoMap(x, y);
    },
    {
      DST: 'secp256k1_XMD:SHA-256_SSWU_RO_',
      encodeDST: 'secp256k1_XMD:SHA-256_SSWU_NU_',
      p: Fpk1.ORDER,
      m: 1,
      k: 128,
      expand: 'xmd',
      hash: sha256,
    }
  ))();

/** @deprecated use `import { secp256k1_hasher } from '@noble/curves/secp256k1.js';` */
export const hashToCurve: H2CMethod<bigint> = /* @__PURE__ */ (() =>
  secp256k1_hasher.hashToCurve)();

/** @deprecated use `import { secp256k1_hasher } from '@noble/curves/secp256k1.js';` */
export const encodeToCurve: H2CMethod<bigint> = /* @__PURE__ */ (() =>
  secp256k1_hasher.encodeToCurve)();
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