noble-curves/src/p521.ts

/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { createCurve } from './_shortw_utils.js';
import { sha512 } from '@noble/hashes/sha512';
import { Fp as Field } from './abstract/modular.js';
import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
import * as htf from './abstract/hash-to-curve.js';

// NIST secp521r1 aka P521
// Note that it's 521, which differs from 512 of its hash function.
// https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-521

// Field over which we'll do calculations; 2n**521n - 1n
// prettier-ignore
const P = BigInt('0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff');
const Fp = Field(P);

const CURVE_A = Fp.create(BigInt('-3'));
// prettier-ignore
const CURVE_B = BigInt('0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00');

const mapSWU = mapToCurveSimpleSWU(Fp, {
  A: CURVE_A,
  B: CURVE_B,
  Z: Fp.create(BigInt('-4')),
});

// prettier-ignore
export const P521 = createCurve({
  // Params: a, b
  a: CURVE_A,
  b: CURVE_B,
  Fp,
  // Curve order, total count of valid points in the field
  n: BigInt('0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409'),
  // Base point (x, y) aka generator point
  Gx: BigInt('0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66'),
  Gy: BigInt('0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650'),
  h: BigInt(1),
  lowS: false,
  allowedPrivateKeyLengths: [130, 131, 132] // P521 keys are variable-length. Normalize to 132b
} as const, sha512);
export const secp521r1 = P521;

const { hashToCurve, encodeToCurve } = htf.createHasher(
  secp521r1.ProjectivePoint,
  (scalars: bigint[]) => mapSWU(scalars[0]),
  {
    DST: 'P521_XMD:SHA-512_SSWU_RO_',
    encodeDST: 'P521_XMD:SHA-512_SSWU_NU_',
    p: Fp.ORDER,
    m: 1,
    k: 256,
    expand: 'xmd',
    hash: sha512,
  }
);
export { hashToCurve, encodeToCurve };