@noble/curves/src/misc.ts

Audited & minimal JS implementation of elliptic curve cryptography

/**
 * Miscellaneous, rarely used curves.
 * jubjub, babyjubjub, pallas, vesta.
 * @module
 */
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { blake256 } from '@noble/hashes/blake1.js';
import { blake2s } from '@noble/hashes/blake2.js';
import { sha256, sha384, sha512 } from '@noble/hashes/sha2.js';
import { concatBytes } from '@noble/hashes/utils.js';
import {
  eddsa,
  edwards,
  type EdDSA,
  type EdwardsOpts,
  type EdwardsPoint,
} from './abstract/edwards.ts';
import { ecdsa, weierstrass, type ECDSA, type WeierstrassOpts } from './abstract/weierstrass.ts';
import { asciiToBytes } from './utils.ts';

// Jubjub curves have 𝔽p over scalar fields of other curves. They are friendly to ZK proofs.

// jubjub p = bls n, verify in bls12-381.ts
const jubjub_CURVE: EdwardsOpts = {
  p: BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001'),
  n: BigInt('0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7'),
  h: BigInt(8),
  a: BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000000'),
  d: BigInt('0x2a9318e74bfa2b48f5fd9207e6bd7fd4292d7f6d37579d2601065fd6d6343eb1'),
  Gx: BigInt('0x11dafe5d23e1218086a365b99fbf3d3be72f6afd7d1f72623e6b071492d1122b'),
  Gy: BigInt('0x1d523cf1ddab1a1793132e78c866c0c33e26ba5cc220fed7cc3f870e59d292aa'),
};
/** Curve over scalar field of bls12-381. jubjub Fp = bls n */
export const jubjub: EdDSA = /* @__PURE__ */ eddsa(edwards(jubjub_CURVE), sha512);

// babyjubjub p = bn254 n, verify in bn254.ts
const babyjubjub_CURVE: EdwardsOpts = {
  p: BigInt('0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001'),
  n: BigInt('0x30644e72e131a029b85045b68181585d59f76dc1c90770533b94bee1c9093788'),
  h: BigInt(8),
  a: BigInt('168700'),
  d: BigInt('168696'),
  Gx: BigInt('0x23343e3445b673d38bcba38f25645adb494b1255b1162bb40f41a59f4d4b45e'),
  Gy: BigInt('0xc19139cb84c680a6e14116da06056174a0cfa121e6e5c2450f87d64fc000001'),
};
/** Curve over scalar field of bn254. babyjubjub Fp = bn254 n */
export const babyjubjub: EdDSA = /* @__PURE__ */ eddsa(edwards(babyjubjub_CURVE), blake256);

const jubjub_gh_first_block = asciiToBytes(
  '096b36a5804bfacef1691e173c366a47ff5ba84a44f26ddd7e8d9f79d5b42df0'
);

// Returns point at JubJub curve which is prime order and not zero
export function jubjub_groupHash(tag: Uint8Array, personalization: Uint8Array): EdwardsPoint {
  const h = blake2s.create({ personalization, dkLen: 32 });
  h.update(jubjub_gh_first_block);
  h.update(tag);
  // NOTE: returns EdwardsPoint, in case it will be multiplied later
  let p = jubjub.Point.fromBytes(h.digest());
  // NOTE: cannot replace with isSmallOrder, returns Point*8
  p = p.multiply(jubjub_CURVE.h);
  if (p.equals(jubjub.Point.ZERO)) throw new Error('Point has small order');
  return p;
}

// No secret data is leaked here at all.
// It operates over public data:
// const G_SPEND = jubjub.findGroupHash(Uint8Array.of(), asciiToBytes('Item_G_'));
export function jubjub_findGroupHash(m: Uint8Array, personalization: Uint8Array): EdwardsPoint {
  const tag = concatBytes(m, Uint8Array.of(0));
  const hashes = [];
  for (let i = 0; i < 256; i++) {
    tag[tag.length - 1] = i;
    try {
      hashes.push(jubjub_groupHash(tag, personalization));
    } catch (e) {}
  }
  if (!hashes.length) throw new Error('findGroupHash tag overflow');
  return hashes[0];
}

const brainpoolP256r1_CURVE: WeierstrassOpts<bigint> = {
  p: BigInt('0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377'),
  a: BigInt('0x7d5a0975fc2c3057eef67530417affe7fb8055c126dc5c6ce94a4b44f330b5d9'),
  b: BigInt('0x26dc5c6ce94a4b44f330b5d9bbd77cbf958416295cf7e1ce6bccdc18ff8c07b6'),
  n: BigInt('0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7'),
  Gx: BigInt('0x8bd2aeb9cb7e57cb2c4b482ffc81b7afb9de27e1e3bd23c23a4453bd9ace3262'),
  Gy: BigInt('0x547ef835c3dac4fd97f8461a14611dc9c27745132ded8e545c1d54c72f046997'),
  h: BigInt(1),
};
/** Brainpool P256r1 with sha256, from RFC 5639. */
export const brainpoolP256r1: ECDSA = ecdsa(weierstrass(brainpoolP256r1_CURVE), sha256);

const brainpoolP384r1_CURVE: WeierstrassOpts<bigint> = {
  p: BigInt(
    '0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53'
  ),
  a: BigInt(
    '0x7bc382c63d8c150c3c72080ace05afa0c2bea28e4fb22787139165efba91f90f8aa5814a503ad4eb04a8c7dd22ce2826'
  ),
  b: BigInt(
    '0x04a8c7dd22ce28268b39b55416f0447c2fb77de107dcd2a62e880ea53eeb62d57cb4390295dbc9943ab78696fa504c11'
  ),
  n: BigInt(
    '0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565'
  ),
  Gx: BigInt(
    '0x1d1c64f068cf45ffa2a63a81b7c13f6b8847a3e77ef14fe3db7fcafe0cbd10e8e826e03436d646aaef87b2e247d4af1e'
  ),
  Gy: BigInt(
    '0x8abe1d7520f9c2a45cb1eb8e95cfd55262b70b29feec5864e19c054ff99129280e4646217791811142820341263c5315'
  ),
  h: BigInt(1),
};
/** Brainpool P384r1 with sha384, from RFC 5639. */
export const brainpoolP384r1: ECDSA = ecdsa(weierstrass(brainpoolP384r1_CURVE), sha384);

const brainpoolP512r1_CURVE: WeierstrassOpts<bigint> = {
  p: BigInt(
    '0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3'
  ),
  a: BigInt(
    '0x7830a3318b603b89e2327145ac234cc594cbdd8d3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94ca'
  ),
  b: BigInt(
    '0x3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94cadc083e67984050b75ebae5dd2809bd638016f723'
  ),
  n: BigInt(
    '0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069'
  ),
  Gx: BigInt(
    '0x81aee4bdd82ed9645a21322e9c4c6a9385ed9f70b5d916c1b43b62eef4d0098eff3b1f78e2d0d48d50d1687b93b97d5f7c6d5047406a5e688b352209bcb9f822'
  ),
  Gy: BigInt(
    '0x7dde385d566332ecc0eabfa9cf7822fdf209f70024a57b1aa000c55b881f8111b2dcde494a5f485e5bca4bd88a2763aed1ca2b2fa8f0540678cd1e0f3ad80892'
  ),
  h: BigInt(1),
};
/** Brainpool P521r1 with sha512, from RFC 5639. */
export const brainpoolP512r1: ECDSA = ecdsa(weierstrass(brainpoolP512r1_CURVE), sha512);