Hyrax Polynomial Commitment Scheme (PCS)

Overview

This repository contains an implementation of the Hyrax polynomial commitment scheme. In particular, it allows one to generate a zero-knowledge commitment to an array of bytes' (&[u8]) worth of data which can be used in the verification of a zero-knowledge proof over computation involving such data.

Note that this repository contains only the code needed to generate a commitment, and does not provide the implementation necessary to generate a proof-of-evaluation against any such committed polynomial, nor the verification of such an evaluation proof.

Example Usage

Example library usage

To run the built-in example through our library, run cargo run --release --bin example_hyrax_commit. The main function computes the commitment to a mock iris image of size 2^17 (=128 x 1024). It also demonstrates binary serialization/deserialization, and writes/reads the byte stream to/from file.

Example binary usage

In ./examples, we've included a shell script run_hyrax_commit which will execute our binary using a dummy image found in ./examples/dummy-data/left_normalized_image.bin. You can generate the commitment and blinding factors for this commitment and write them to file by running ./run_hyrax_commit within the ./examples directory. The commitment will get written to ./examples/dummy-data/left_normalized_image_commitment.bin and the blinding factors will get written to dummy-data/left_normalized_image_blinding_factors.bin.

Production Usage

The primary user-friendly function can be found in ./src/iriscode_commit/mod.rs as the compute_commitments_binary_outputs function. The function takes in as input

• A data: &[u8] parameter, corresponding to the iris image (and/or mask!) to be committed to, and
• A blinding_factor_seed: [u8; 32] parameter, corresponding to 32 bytes' worth of entropy to be sampled externally and used as the seed for the CSPRNG generating the blinding factors for zero-knowledge.

The function outputs

pub struct HyraxCommitmentOutputSerialized {
    pub commitment_serialized: Vec<u8>,
    pub blinding_factors_serialized: Vec<u8>,
}

where

• commitment_serialized is a bytestring representation of the polynomial commitment, to be signed by the Orb and included as part of the payload to the backend servers/verifier, and
• blinding_factors_serialized is a bytestring representation of the blinding factors generated during the commitment process, to be sent from the Orb to the user's self-custody device (as part of the self-custody payload) through a secure channel and deleted immediately afterward.

Additional Notes

Blinding Factor Generation

We generate blinding factors by taking as input a random seed of 32 bytes (e.g., by using Rust's OsRng which derives entropy from /dev/urandom). We then use this to seed a CSPRNG, ChaCha20, which is then used to generate random scalar field elements which are our blinding factors.

Public Generator Setup

We sample the generators for the Pedersen commitment deterministically using the Shake256 hash function which uses a public string as an initializer. This can be found under the sample_generators function in ./src/pedersen/mod.rs. The public string (once used, this must be fixed) can be found as the constant PUBLIC_STRING within src/iriscode_commit/mod.rs.

Contributing

We plan to accept contributions at a later date, but do not have bandwidth to review PRs currently.

Likewise, we are providing this source code for the benefit of the community, but cannot commit to any SemVer or API stability guarantees. Be warned: we may change things in a backwards-incompatible way at any time!

License

Unless otherwise specified, all code in this repository is dual-licensed under either:

• MIT License (LICENSE-MIT)
• Apache License, Version 2.0, with LLVM Exceptions (LICENSE-APACHE)

at your option. This means you may select the license you prefer to use.

Any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.