@noble/curves/src/nist.ts

Audited & minimal JS implementation of elliptic curve cryptography

/**
 * Internal module for NIST P256, P384, P521 curves.
 * Do not use for now.
 * @module
 */
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { sha256, sha384, sha512 } from '@noble/hashes/sha2.js';
import { createHasher, type H2CHasher } from './abstract/hash-to-curve.ts';
import { Field } from './abstract/modular.ts';
import { createORPF, type OPRF } from './abstract/oprf.ts';
import {
  ecdsa,
  mapToCurveSimpleSWU,
  weierstrass,
  type ECDSA,
  type WeierstrassOpts,
  type WeierstrassPointCons,
} from './abstract/weierstrass.ts';

// p = 2n**224n * (2n**32n-1n) + 2n**192n + 2n**96n - 1n
// a = Fp256.create(BigInt('-3'));
const p256_CURVE: WeierstrassOpts<bigint> = /* @__PURE__ */ (() => ({
  p: BigInt('0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff'),
  n: BigInt('0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551'),
  h: BigInt(1),
  a: BigInt('0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc'),
  b: BigInt('0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b'),
  Gx: BigInt('0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296'),
  Gy: BigInt('0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5'),
}))();

// p = 2n**384n - 2n**128n - 2n**96n + 2n**32n - 1n
const p384_CURVE: WeierstrassOpts<bigint> = /* @__PURE__ */ (() => ({
  p: BigInt(
    '0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff'
  ),
  n: BigInt(
    '0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973'
  ),
  h: BigInt(1),
  a: BigInt(
    '0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc'
  ),
  b: BigInt(
    '0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef'
  ),
  Gx: BigInt(
    '0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7'
  ),
  Gy: BigInt(
    '0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f'
  ),
}))();

// p = 2n**521n - 1n
const p521_CURVE: WeierstrassOpts<bigint> = /* @__PURE__ */ (() => ({
  p: BigInt(
    '0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff'
  ),
  n: BigInt(
    '0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409'
  ),
  h: BigInt(1),
  a: BigInt(
    '0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc'
  ),
  b: BigInt(
    '0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00'
  ),
  Gx: BigInt(
    '0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66'
  ),
  Gy: BigInt(
    '0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650'
  ),
}))();

type SwuOpts = {
  A: bigint;
  B: bigint;
  Z: bigint;
};

function createSWU(Point: WeierstrassPointCons<bigint>, opts: SwuOpts) {
  const map = mapToCurveSimpleSWU(Point.Fp, opts);
  return (scalars: bigint[]) => map(scalars[0]);
}

// NIST P256
const p256_Point = /* @__PURE__ */ weierstrass(p256_CURVE);
/**
 * NIST P256 (aka secp256r1, prime256v1) curve, ECDSA and ECDH methods.
 * Hashes inputs with sha256 by default.
 *
 * @example
 * ```js
 * import { p256 } from '@noble/curves/nist.js';
 * const { secretKey, publicKey } = p256.keygen();
 * // const publicKey = p256.getPublicKey(secretKey);
 * const msg = new TextEncoder().encode('hello noble');
 * const sig = p256.sign(msg, secretKey);
 * const isValid = p256.verify(sig, msg, publicKey);
 * // const sigKeccak = p256.sign(keccak256(msg), secretKey, { prehash: false });
 * ```
 */
export const p256: ECDSA = /* @__PURE__ */ ecdsa(p256_Point, sha256);
/** Hashing / encoding to p256 points / field. RFC 9380 methods. */
export const p256_hasher: H2CHasher<WeierstrassPointCons<bigint>> = /* @__PURE__ */ (() => {
  return createHasher(
    p256_Point,
    createSWU(p256_Point, {
      A: p256_CURVE.a,
      B: p256_CURVE.b,
      Z: p256_Point.Fp.create(BigInt('-10')),
    }),
    {
      DST: 'P256_XMD:SHA-256_SSWU_RO_',
      encodeDST: 'P256_XMD:SHA-256_SSWU_NU_',
      p: p256_CURVE.p,
      m: 1,
      k: 128,
      expand: 'xmd',
      hash: sha256,
    }
  );
})();
/** p256 OPRF, defined in RFC 9497. */
export const p256_oprf: OPRF = /* @__PURE__ */ (() =>
  createORPF({
    name: 'P256-SHA256',
    Point: p256_Point,
    hash: sha256,
    hashToGroup: p256_hasher.hashToCurve,
    hashToScalar: p256_hasher.hashToScalar,
  }))();

// NIST P384
const p384_Point = /* @__PURE__ */ weierstrass(p384_CURVE);
/** NIST P384 (aka secp384r1) curve, ECDSA and ECDH methods. Hashes inputs with sha384 by default. */
export const p384: ECDSA = /* @__PURE__ */ ecdsa(p384_Point, sha384);
/** Hashing / encoding to p384 points / field. RFC 9380 methods. */
export const p384_hasher: H2CHasher<WeierstrassPointCons<bigint>> = /* @__PURE__ */ (() => {
  return createHasher(
    p384_Point,
    createSWU(p384_Point, {
      A: p384_CURVE.a,
      B: p384_CURVE.b,
      Z: p384_Point.Fp.create(BigInt('-12')),
    }),
    {
      DST: 'P384_XMD:SHA-384_SSWU_RO_',
      encodeDST: 'P384_XMD:SHA-384_SSWU_NU_',
      p: p384_CURVE.p,
      m: 1,
      k: 192,
      expand: 'xmd',
      hash: sha384,
    }
  );
})();
/** p384 OPRF, defined in RFC 9497. */
export const p384_oprf: OPRF = /* @__PURE__ */ (() =>
  createORPF({
    name: 'P384-SHA384',
    Point: p384_Point,
    hash: sha384,
    hashToGroup: p384_hasher.hashToCurve,
    hashToScalar: p384_hasher.hashToScalar,
  }))();

// NIST P521
const Fn521 = /* @__PURE__ */ (() => Field(p521_CURVE.n, { allowedLengths: [65, 66] }))();
const p521_Point = /* @__PURE__ */ weierstrass(p521_CURVE, { Fn: Fn521 });
/** NIST P521 (aka secp521r1) curve, ECDSA and ECDH methods. Hashes inputs with sha512 by default. */
export const p521: ECDSA = /* @__PURE__ */ ecdsa(p521_Point, sha512);
/** Hashing / encoding to p521 points / field. RFC 9380 methods. */
export const p521_hasher: H2CHasher<WeierstrassPointCons<bigint>> = /* @__PURE__ */ (() => {
  return createHasher(
    p521_Point,
    createSWU(p521_Point, {
      A: p521_CURVE.a,
      B: p521_CURVE.b,
      Z: p521_Point.Fp.create(BigInt('-4')),
    }),
    {
      DST: 'P521_XMD:SHA-512_SSWU_RO_',
      encodeDST: 'P521_XMD:SHA-512_SSWU_NU_',
      p: p521_CURVE.p,
      m: 1,
      k: 256,
      expand: 'xmd',
      hash: sha512,
    }
  );
})();
/** p521 OPRF, defined in RFC 9497. */
export const p521_oprf: OPRF = /* @__PURE__ */ (() =>
  createORPF({
    name: 'P521-SHA512',
    Point: p521_Point,
    hash: sha512,
    hashToGroup: p521_hasher.hashToCurve,
    hashToScalar: p521_hasher.hashToScalar, // produces L=98 just like in RFC
  }))();