Polynomial Commitments

poly-commit is a Rust library that implements polynomial commitment schemes. This library was initially developed as part of the Marlin paper, and is released under the MIT License and the Apache v2 License (see License).

WARNING: This is an academic prototype, and in particular has not received careful code review. This implementation is NOT ready for production use.

Overview

A polynomial commitment scheme is a cryptographic primitive that enables a party to commit to a polynomial over a given finite field, and then, later on, to reveal desired evaluations of the polynomial along with cryptographic proofs attesting to their correctness.

This library provides various constructions of polynomial commitment schemes. These constructions support committing to multiple polynomials at a time with differing degree bounds, batching multiple evaluation proofs for the same evaluation point into a single one, and batch verification of proofs.

The key properties satisfied by the polynomial commitment schemes are succinctness, extractability, and hiding. See the Marlin paper for definitions of these properties.

Build guide

The library compiles on the stable toolchain of the Rust compiler. To install the latest version of Rust, first install rustup by following the instructions here, or via your platform's package manager. Once rustup is installed, install the Rust toolchain by invoking:

rustup install stable

After that, use cargo (the standard Rust build tool) to build the library:

git clone https://github.com/scipr-lab/poly-commit.git
cd poly-commit
cargo build --release

This library comes with some unit and integration tests. Run these tests with:

cargo test

A benchmarking module is also provided for the commit, open and verify methods, as well as for computing the commitment and proof size. You can add a new benchmark for your scheme following the examples in the pcs/benches directory, or run the existing benchmarks with:

cargo bench

Lastly, this library is instrumented with profiling infrastructure that prints detailed traces of execution time. To enable this, compile with cargo build --features print-trace.

Usage

PolynomialCommitment

This trait defines the interface for a polynomial commitment scheme. It is recommended to use the schemes from this crate that implement the PolynomialCommitment trait (e.g. the vanilla KZG scheme does not implement this trait, but the Marlin scheme which uses it under the hood, does).

// In this example, we will commit to a single polynomial, open it first at one point, and then batched at two points, and finally verify the proofs.
// We will use the KZG10 polynomial commitment scheme, following the approach from Marlin.

use ark_poly_commit::{Polynomial, marlin_pc::MarlinKZG10, LabeledPolynomial, PolynomialCommitment, QuerySet, Evaluations};
use ark_bls12_377::Bls12_377;
use ark_crypto_primitives::sponge::poseidon::{PoseidonSponge, PoseidonConfig};
use ark_crypto_primitives::sponge::CryptographicSponge;
use ark_ec::pairing::Pairing;
use ark_ff::UniformRand;
use ark_std::test_rng;
use ark_poly::{univariate::DensePolynomial, DenseUVPolynomial};
use rand_chacha::ChaCha20Rng;
use ark_ff::PrimeField;

type UniPoly_377 = DensePolynomial<<Bls12_377 as Pairing>::ScalarField>;
type Sponge_Bls12_377 = PoseidonSponge<<Bls12_377 as Pairing>::ScalarField>;
type PCS = MarlinKZG10<Bls12_377, UniPoly_377, Sponge_Bls12_377>;

let rng = &mut test_rng();

let max_degree = 16; // max degree supported by the scheme with the given public parameters generated by the setup here.

// 1. PolynomialCommitment::setup
// The setup procedure in this example is for demonstration purposes only - typically a setup ceremony would be run to generate the public parameters.
let pp = PCS::setup(max_degree, None, rng).unwrap();

let degree = 10; //degree of our polynomial
let secret_poly = UniPoly_377::rand(degree, rng);

let point_1 = <Bls12_377 as Pairing>::ScalarField::rand(rng);
let point_2 = <Bls12_377 as Pairing>::ScalarField::rand(rng);

let label = String::from("secret_poly");
let labeled_poly = LabeledPolynomial::new(
   label.clone(),
   secret_poly.clone(),
   Some(degree),
   Some(2), // we will open a univariate poly at two points
);

// TODO: replace by https://github.com/arkworks-rs/crypto-primitives/issues/112.
fn test_sponge<F: PrimeField>() -> PoseidonSponge<F> {
   let full_rounds = 8;
   let partial_rounds = 31;
   let alpha = 17;

   let mds = vec![
      vec![F::one(), F::zero(), F::one()],
      vec![F::one(), F::one(), F::zero()],
      vec![F::zero(), F::one(), F::one()],
   ];

   let mut v = Vec::new();
   let mut ark_rng = test_rng();

   for _ in 0..(full_rounds + partial_rounds) {
      let mut res = Vec::new();

      for _ in 0..3 {
         res.push(F::rand(&mut ark_rng));
      }
      v.push(res);
   }
   let config = PoseidonConfig::new(full_rounds, partial_rounds, alpha, mds, v, 2, 1);
   PoseidonSponge::new(&config)
}
let mut test_sponge = test_sponge::<<Bls12_377 as Pairing>::ScalarField>();

// 2. PolynomialCommitment::trim
// Since the setup produced pp with a max degree of 16, and our poly is of degree 10, we can trim the SRS to tailor it to this example.
let (ck, vk) = PCS::trim(&pp, degree, 2, Some(&[degree])).unwrap(); 

// 3. PolynomialCommitment::commit
// The prover commits to the polynomial using their committer key `ck`.
let (comms, states) = PCS::commit(&ck, [&labeled_poly], Some(rng)).unwrap(); 

// 4a. PolynomialCommitment::open
// Opening proof at a single point.
let proof_single = PCS::open(&ck, [&labeled_poly], &comms, &point_1, &mut (test_sponge.clone()), &states, None).unwrap(); 

// 5a. PolynomialCommitment::check
// Verifying the proof at a single point, given the commitment, the point, the claimed evaluation, and the proof.
assert!(PCS::check(&vk, &comms, &point_1, [secret_poly.evaluate(&point_1)], &proof_single, &mut (test_sponge.clone()), Some(rng)).unwrap()); 

let mut query_set = QuerySet::new();
let mut values = Evaluations::new();
for (i, point) in [point_1, point_2].iter().enumerate() {
   query_set.insert((label.clone(), (format!("{}", i), point.clone())));
   let value = secret_poly.evaluate(&point);
   values.insert((label.clone(), point.clone()), value);
}

// 4b. PolynomialCommitment::batch_open
// Some schemes support batch opening proofs. Generate a single proof for opening the polynomial at multiple points.
let proof_batched = PCS::batch_open(
   &ck,
   [&labeled_poly],
   &comms,
   &query_set,
   &mut (test_sponge.clone()),
   &states,
   Some(rng),
).unwrap();

// 5b. PolynomialCommitment::batch_check
assert!(PCS::batch_check(
   &vk,
   &comms,
   &query_set,
   &values,
   &proof_batched,
   &mut (test_sponge.clone()),
   rng,
).unwrap());

License

This library is licensed under either of the following licenses, at your discretion.

• Apache License Version 2.0
• MIT License

Unless you explicitly state otherwise, any contribution that you submit to this library shall be dual licensed as above (as defined in the Apache v2 License), without any additional terms or conditions.

Reference papers

Polynomial Commitments
Aniket Kate, Gregory M. Zaverucha, Ian Goldberg
ASIACRYPT 2010

Sonic: Zero-Knowledge SNARKs from Linear-Size Universal and Updateable Structured Reference Strings
Mary Maller, Sean Bowe, Markulf Kohlweiss, Sarah Meiklejohn
CCS 2019

AuroraLight: Improved Prover Efficiency and SRS Size in a Sonic-Like System
Ariel Gabizon
ePrint, 2019

Marlin: Preprocessing zkSNARKs with Universal and Updatable SRS
Alessandro Chiesa, Yuncong Hu, Mary Maller, Pratyush Mishra, Noah Vesely, Nicholas Ward
EUROCRYPT 2020

Proof-Carrying Data from Accumulation Schemes
Benedikt Bünz, Alessandro Chiesa, Pratyush Mishra, Nicholas Spooner
TCC 2020

Signatures of Correct Computation
Charalampos Papamanthou, Elaine Shi, Roberto Tamassia
TCC 2013

Acknowledgements

This work was supported by: an Engineering and Physical Sciences Research Council grant; a Google Faculty Award; the RISELab at UC Berkeley; and donations from the Ethereum Foundation and the Interchain Foundation.