Nethermind Secures Multiple Grants in ZK Grants Round

We are proud to announce that Nethermind has secured grants for three submissions in Ethereum Foundation’s ZK Grant Round! The ZK (Zero-Knowledge) grant round, organized by the Ethereum Foundation in collaboration with Aztec, Polygon, Scroll, Taiko, and zkSync featured a shared pool of $900,000 amongst a total of 25 winners and is aimed at supporting innovative projects advancing the field of zero-knowledge proofs.

‍

The submission by Nethermind which have received grants are the following:

‍

‍

Lean Extraction of Circuit Constraints from Halo2

‍

Submitted by Julian Sutherland, the “Lean Extraction of Circuit Constraints from Halo2” project focuses on enhancing the security and formal verification of circuits within the widely used Halo2 library.

‍

‍The Halo2 library is a crucial ZK infrastructure tool that enables developers to create prover/verifier pairs using a high-level domain-specific language embedded in Rust. To formally verify circuits in this language, and thus ensure the highest level of security, this project aims to develop a formal verification harness to seamlessly extract the constraints from a Halo2 circuit and reason about them in the Lean 4 proof assistant.

‍

‍

LatticeFold Implementation and Folding Schemes for FRI-based SNARKs

‍

Submitted by Albert Garreta, our proposal aims to develop and implement a Proof of Concept (PoC) for the LatticeFold folding scheme [BC24], benchmarking it against existing schemes like HyperNova. Additionally, we aim to research methodologies to create a "STARK-friendly" folding scheme based on LatticeFold.

‍

This would allow to use folding techniques in the context of FRI-based SNARKs (e.g., ethSTARK, Plonky2/3, Risc Zero, Boojum, etc.) Prof. Dan Boneh and Prof. Binyi Chen, authors of the LatticeFold paper, have agreed to assist our team for the project's duration.

‍

‍

SNARKs for Non-Prime Arithmetics

‍

Submitted by Albert Garreta, this proposal seeks to develop a SNARK tailored for proving statements over rings of the form Z/nZ, for Z the ring of integers and n an arbitrary integer.

‍

This deviates from the usual setting where statements are expressed over a prime field F_p=Z/pZ for p a prime. We aim to focus on the cases where n is a power of 2 or a product of two large primes. This would enable to natively prove statements involving computations such as: RSA-based cryptography operations, CPU operations, floating point arithmetic (required for, e.g., machine learning), non-algebraic hash functions, etc. Here, by “natively,” we mean that each of these computations is arithmetized overZ/nZ, for n an appropriate integer, rather than over a finite field. It is known that the latter “non-native” arithmetization can create overheads of an order of magnitude in the circuit/R1CS/AIR size.

‍

‍

Summary

‍

Being recognized with this grant underscores the importance of our work in advancing the security and reliability of zero-knowledge proofs. We are honored to be among a distinguished group of researchers and developers to have our submissions recognized. This support only strengthens our commitment of continued contributions to the broader Ethereum ecosystem and advancement of ZK technology.

‍

These grant will enable us to accelerate our development efforts, bringing us closer to achieving our goals of making Halo2 circuits formal verification, implementations for LatticeFold’s folding scheme, and developments in SNARKs implementation a reality.

‍

We extend our sincere thanks to the Ethereum Foundation, Aztec, Polygon, Scroll, Taiko, and zkSync for their generous support and commitment to fostering innovation in this critical area. We look forward to the continued progress and collaboration within the ZK and Ethereum ecosystems.

‍

Stay connected for further updates as we advance our projects!