@noble/curves/src/abstract/poseidon.ts

Audited & minimal JS implementation of elliptic curve cryptography

/**
 * Implements [Poseidon](https://www.poseidon-hash.info) ZK-friendly hash.
 *
 * There are many poseidon variants with different constants.
 * We don't provide them: you should construct them manually.
 * Check out [micro-starknet](https://github.com/paulmillr/micro-starknet) package for a proper example.
 * @module
 */
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { asafenumber, bitGet, validateObject } from '../utils.ts';
import { FpInvertBatch, FpPow, type IField, validateField } from './modular.ts';

// Grain LFSR (Linear-Feedback Shift Register): https://eprint.iacr.org/2009/109.pdf
function grainLFSR(state: number[]): () => boolean {
  let pos = 0;
  if (state.length !== 80) throw new Error('grainLFRS: wrong state length, should be 80 bits');
  const getBit = (): boolean => {
    const r = (offset: number) => state[(pos + offset) % 80];
    const bit = r(62) ^ r(51) ^ r(38) ^ r(23) ^ r(13) ^ r(0);
    state[pos] = bit;
    pos = ++pos % 80;
    return !!bit;
  };
  for (let i = 0; i < 160; i++) getBit();
  return () => {
    // https://en.wikipedia.org/wiki/Shrinking_generator
    while (true) {
      const b1 = getBit();
      const b2 = getBit();
      if (!b1) continue;
      return b2;
    }
  };
}

export type PoseidonBasicOpts = {
  Fp: IField<bigint>;
  t: number; // t = rate + capacity
  roundsFull: number;
  roundsPartial: number;
  isSboxInverse?: boolean;
};

function assertValidPosOpts(opts: PoseidonBasicOpts) {
  const { Fp, roundsFull } = opts;
  validateField(Fp);
  validateObject(
    opts,
    {
      t: 'number',
      roundsFull: 'number',
      roundsPartial: 'number',
    },
    {
      isSboxInverse: 'boolean',
    }
  );
  for (const k of ['t', 'roundsFull', 'roundsPartial'] as const) {
    asafenumber(opts[k], k);
    if (opts[k] < 1) throw new Error('invalid number ' + k);
  }
  if (roundsFull & 1) throw new Error('roundsFull is not even' + roundsFull);
}

function poseidonGrain(opts: PoseidonBasicOpts) {
  assertValidPosOpts(opts);
  const { Fp } = opts;
  const state = Array(80).fill(1);
  let pos = 0;
  const writeBits = (value: bigint, bitCount: number) => {
    for (let i = bitCount - 1; i >= 0; i--) state[pos++] = Number(bitGet(value, i));
  };
  const _0n = BigInt(0);
  const _1n = BigInt(1);
  writeBits(_1n, 2); // prime field
  writeBits(opts.isSboxInverse ? _1n : _0n, 4); // b2..b5
  writeBits(BigInt(Fp.BITS), 12); // b6..b17
  writeBits(BigInt(opts.t), 12); // b18..b29
  writeBits(BigInt(opts.roundsFull), 10); // b30..b39
  writeBits(BigInt(opts.roundsPartial), 10); // b40..b49

  const getBit = grainLFSR(state);
  return (count: number, reject: boolean): bigint[] => {
    const res: bigint[] = [];
    for (let i = 0; i < count; i++) {
      while (true) {
        let num = _0n;
        for (let i = 0; i < Fp.BITS; i++) {
          num <<= _1n;
          if (getBit()) num |= _1n;
        }
        if (reject && num >= Fp.ORDER) continue; // rejection sampling
        res.push(Fp.create(num));
        break;
      }
    }
    return res;
  };
}

export type PoseidonGrainOpts = PoseidonBasicOpts & {
  sboxPower?: number;
};

type PoseidonConstants = { mds: bigint[][]; roundConstants: bigint[][] };

// NOTE: this is not standard but used often for constant generation for poseidon
// (grain LFRS-like structure)
export function grainGenConstants(opts: PoseidonGrainOpts, skipMDS: number = 0): PoseidonConstants {
  const { Fp, t, roundsFull, roundsPartial } = opts;
  const rounds = roundsFull + roundsPartial;
  const sample = poseidonGrain(opts);
  const roundConstants: bigint[][] = [];
  for (let r = 0; r < rounds; r++) roundConstants.push(sample(t, true));
  if (skipMDS > 0) for (let i = 0; i < skipMDS; i++) sample(2 * t, false);
  const xs = sample(t, false);
  const ys = sample(t, false);
  // Construct MDS Matrix M[i][j] = 1 / (xs[i] + ys[j])
  const mds: bigint[][] = [];
  for (let i = 0; i < t; i++) {
    const row: bigint[] = [];
    for (let j = 0; j < t; j++) {
      const xy = Fp.add(xs[i], ys[j]);
      if (Fp.is0(xy))
        throw new Error(`Error generating MDS matrix: xs[${i}] + ys[${j}] resulted in zero.`);
      row.push(xy);
    }
    mds.push(FpInvertBatch(Fp, row));
  }

  return { roundConstants, mds };
}

export type PoseidonOpts = PoseidonBasicOpts &
  PoseidonConstants & {
    sboxPower?: number;
    reversePartialPowIdx?: boolean; // Hack for stark
  };

export function validateOpts(opts: PoseidonOpts): Readonly<{
  rounds: number;
  sboxFn: (n: bigint) => bigint;
  roundConstants: bigint[][];
  mds: bigint[][];
  Fp: IField<bigint>;
  t: number;
  roundsFull: number;
  roundsPartial: number;
  sboxPower?: number;
  reversePartialPowIdx?: boolean; // Hack for stark
}> {
  assertValidPosOpts(opts);
  const { Fp, mds, reversePartialPowIdx: rev, roundConstants: rc } = opts;
  const { roundsFull, roundsPartial, sboxPower, t } = opts;

  // MDS is TxT matrix
  if (!Array.isArray(mds) || mds.length !== t) throw new Error('Poseidon: invalid MDS matrix');
  const _mds = mds.map((mdsRow) => {
    if (!Array.isArray(mdsRow) || mdsRow.length !== t)
      throw new Error('invalid MDS matrix row: ' + mdsRow);
    return mdsRow.map((i) => {
      if (typeof i !== 'bigint') throw new Error('invalid MDS matrix bigint: ' + i);
      return Fp.create(i);
    });
  });

  if (rev !== undefined && typeof rev !== 'boolean')
    throw new Error('invalid param reversePartialPowIdx=' + rev);

  if (roundsFull & 1) throw new Error('roundsFull is not even' + roundsFull);
  const rounds = roundsFull + roundsPartial;

  if (!Array.isArray(rc) || rc.length !== rounds)
    throw new Error('Poseidon: invalid round constants');
  const roundConstants = rc.map((rc) => {
    if (!Array.isArray(rc) || rc.length !== t) throw new Error('invalid round constants');
    return rc.map((i) => {
      if (typeof i !== 'bigint' || !Fp.isValid(i)) throw new Error('invalid round constant');
      return Fp.create(i);
    });
  });

  if (!sboxPower || ![3, 5, 7, 17].includes(sboxPower)) throw new Error('invalid sboxPower');
  const _sboxPower = BigInt(sboxPower);
  let sboxFn = (n: bigint) => FpPow(Fp, n, _sboxPower);
  // Unwrapped sbox power for common cases (195->142μs)
  if (sboxPower === 3) sboxFn = (n: bigint) => Fp.mul(Fp.sqrN(n), n);
  else if (sboxPower === 5) sboxFn = (n: bigint) => Fp.mul(Fp.sqrN(Fp.sqrN(n)), n);

  return Object.freeze({ ...opts, rounds, sboxFn, roundConstants, mds: _mds });
}

export function splitConstants(rc: bigint[], t: number): bigint[][] {
  if (typeof t !== 'number') throw new Error('poseidonSplitConstants: invalid t');
  if (!Array.isArray(rc) || rc.length % t) throw new Error('poseidonSplitConstants: invalid rc');
  const res = [];
  let tmp = [];
  for (let i = 0; i < rc.length; i++) {
    tmp.push(rc[i]);
    if (tmp.length === t) {
      res.push(tmp);
      tmp = [];
    }
  }
  return res;
}

export type PoseidonFn = {
  (values: bigint[]): bigint[];
  // For verification in tests
  roundConstants: bigint[][];
};
/** Poseidon NTT-friendly hash. */
export function poseidon(opts: PoseidonOpts): PoseidonFn {
  const _opts = validateOpts(opts);
  const { Fp, mds, roundConstants, rounds: totalRounds, roundsPartial, sboxFn, t } = _opts;
  const halfRoundsFull = _opts.roundsFull / 2;
  const partialIdx = _opts.reversePartialPowIdx ? t - 1 : 0;
  const poseidonRound = (values: bigint[], isFull: boolean, idx: number) => {
    values = values.map((i, j) => Fp.add(i, roundConstants[idx][j]));

    if (isFull) values = values.map((i) => sboxFn(i));
    else values[partialIdx] = sboxFn(values[partialIdx]);
    // Matrix multiplication
    values = mds.map((i) => i.reduce((acc, i, j) => Fp.add(acc, Fp.mulN(i, values[j])), Fp.ZERO));
    return values;
  };
  const poseidonHash = function poseidonHash(values: bigint[]) {
    if (!Array.isArray(values) || values.length !== t)
      throw new Error('invalid values, expected array of bigints with length ' + t);
    values = values.map((i) => {
      if (typeof i !== 'bigint') throw new Error('invalid bigint=' + i);
      return Fp.create(i);
    });
    let lastRound = 0;
    // Apply r_f/2 full rounds.
    for (let i = 0; i < halfRoundsFull; i++) values = poseidonRound(values, true, lastRound++);
    // Apply r_p partial rounds.
    for (let i = 0; i < roundsPartial; i++) values = poseidonRound(values, false, lastRound++);
    // Apply r_f/2 full rounds.
    for (let i = 0; i < halfRoundsFull; i++) values = poseidonRound(values, true, lastRound++);

    if (lastRound !== totalRounds) throw new Error('invalid number of rounds');
    return values;
  };
  // For verification in tests
  poseidonHash.roundConstants = roundConstants;
  return poseidonHash;
}

export class PoseidonSponge {
  private Fp: IField<bigint>;
  readonly rate: number;
  readonly capacity: number;
  readonly hash: PoseidonFn;
  private state: bigint[]; // [...capacity, ...rate]
  private pos = 0;
  private isAbsorbing = true;

  constructor(Fp: IField<bigint>, rate: number, capacity: number, hash: PoseidonFn) {
    this.Fp = Fp;
    this.hash = hash;
    this.rate = rate;
    this.capacity = capacity;
    this.state = new Array(rate + capacity);
    this.clean();
  }
  private process(): void {
    this.state = this.hash(this.state);
  }
  absorb(input: bigint[]): void {
    for (const i of input)
      if (typeof i !== 'bigint' || !this.Fp.isValid(i)) throw new Error('invalid input: ' + i);
    for (let i = 0; i < input.length; ) {
      if (!this.isAbsorbing || this.pos === this.rate) {
        this.process();
        this.pos = 0;
        this.isAbsorbing = true;
      }
      const chunk = Math.min(this.rate - this.pos, input.length - i);
      for (let j = 0; j < chunk; j++) {
        const idx = this.capacity + this.pos++;
        this.state[idx] = this.Fp.add(this.state[idx], input[i++]);
      }
    }
  }
  squeeze(count: number): bigint[] {
    const res: bigint[] = [];
    while (res.length < count) {
      if (this.isAbsorbing || this.pos === this.rate) {
        this.process();
        this.pos = 0;
        this.isAbsorbing = false;
      }
      const chunk = Math.min(this.rate - this.pos, count - res.length);
      for (let i = 0; i < chunk; i++) res.push(this.state[this.capacity + this.pos++]);
    }
    return res;
  }
  clean(): void {
    this.state.fill(this.Fp.ZERO);
    this.isAbsorbing = true;
    this.pos = 0;
  }
  clone(): PoseidonSponge {
    const c = new PoseidonSponge(this.Fp, this.rate, this.capacity, this.hash);
    c.pos = this.pos;
    c.state = [...this.state];
    return c;
  }
}

export type PoseidonSpongeOpts = Omit<PoseidonOpts, 't'> & {
  rate: number;
  capacity: number;
};

/**
 * The method is not defined in spec, but nevertheless used often.
 * Check carefully for compatibility: there are many edge cases, like absorbing an empty array.
 * We cross-test against:
 * - https://github.com/ProvableHQ/snarkVM/tree/staging/algorithms
 * - https://github.com/arkworks-rs/crypto-primitives/tree/main
 */
export function poseidonSponge(opts: PoseidonSpongeOpts): () => PoseidonSponge {
  for (const k of ['rate', 'capacity'] as const) asafenumber(opts[k], k);
  const { rate, capacity } = opts;
  const t = opts.rate + opts.capacity;
  // Re-use hash instance between multiple instances
  const hash = poseidon({ ...opts, t });
  const { Fp } = opts;
  return () => new PoseidonSponge(Fp, rate, capacity, hash);
}