https://github.com/protolambda/go-kzg

FFT, data-recovery and KZG commitments, a.k.a. Kate commitments, in Go - *super experimental*
https://github.com/protolambda/go-kzg

bls12-381 data-availability-sampling data-recovery eth2 fft kate kate-commitment kate-proofs kzg kzg-commitment kzg-proofs ntt polynomial-commitments

Last synced: about 6 hours ago
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FFT, data-recovery and KZG commitments, a.k.a. Kate commitments, in Go - *super experimental*

• Host: GitHub
• URL: https://github.com/protolambda/go-kzg
• Owner: protolambda
• License: mit
• Created: 2020-10-22T18:07:39.000Z (almost 4 years ago)
• Default Branch: master
• Last Pushed: 2023-11-29T21:02:34.000Z (10 months ago)
• Last Synced: 2024-06-18T15:38:45.809Z (4 months ago)
• Topics: bls12-381, data-availability-sampling, data-recovery, eth2, fft, kate, kate-commitment, kate-proofs, kzg, kzg-commitment, kzg-proofs, ntt, polynomial-commitments
• Language: Go
• Homepage:
• Size: 1.32 MB
• Stars: 86
• Watchers: 6
• Forks: 26
• Open Issues: 5
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# KZG and FFT utils

This repo is *super experimental*.

This is an implementation in Go, initially aimed at chunkification and extension of data, 

and building/verifying KZG proofs for the output data.

The KZG proofs, or Kate proofs, are built on top of BLS12-381.

Part of a low-latency data-availability sampling network prototype for Eth2 Phase 1.

See https://github.com/protolambda/eth2-das

Code is based on:

- [KZG Data availability code by Dankrad](https://github.com/ethereum/research/tree/master/kzg_data_availability)

- [Verkle and FFT code by Dankrad and Vitalik](https://github.com/ethereum/research/tree/master/verkle)

- [Reed solomon erasure code recovery with FFTs by Vitalik](https://ethresear.ch/t/reed-solomon-erasure-code-recovery-in-n-log-2-n-time-with-ffts/3039)

- [FFT explainer by Vitalik](https://vitalik.ca/general/2019/05/12/fft.html)

- [Kate explainer by Dankrad](https://dankradfeist.de/ethereum/2020/06/16/kate-polynomial-commitments.html)

- [Kate amortized paper by Dankrad and Dmitry](https://github.com/khovratovich/Kate/blob/master/Kate_amortized.pdf)

Features:

- (I)FFT on `F_r`

- (I)FFT on `G1`

- Specialized FFT for extension of `F_r` data

- KZG

  - commitments

  - generate/verify proof for single point

  - generate/verify proofs for multiple points

  - generate/verify proofs for all points, using FK20

  - generate/verify proofs for ranges (cosets) of points, using FK20

- Data recovery: given an arbitrary subset of data (at least half), recover the rest

- Optimized for Data-availability usage

- Change Bignum / BLS with build tags.

## BLS

Currently supported BLS implementations: Herumi BLS and Kilic BLS (default).

## Field elements (Fr)

The BLS curve order is used for the modulo math, different libraries could be used to provide this functionality.

Note: some of these libraries do not have full BLS functionality, only Bignum / uint256. The KZG code will be excluded when compiling with a non-BLS build tag.

Build tag options:

- (no build tags, default): Use Kilic BLS library. Previously used by `bignum_kilic` build tag. [`kilic/bls12-381`](https://github.com/kilic/bls12-381)

- `-tags bignum_hbls`: use Herumi BLS library. [`herumi/bls-eth-go-binary`](https://github.com/herumi/bls-eth-go-binary/)

- `-tags bignum_hol256`: Use the uint256 code that Geth uses, [`holiman/uint256`](https://github.com/holiman/uint256)

- `-tags bignum_pure`: Use the native Go Bignum implementation.

## Benchmarks

See [`BENCH.md`](./BENCH.md) for benchmarks of FFT, FFT in G1, FFT-extension, zero polynomials, and sample recovery.

## License

MIT, see [`LICENSE`](./LICENSE) file.