We are pleased to announce the publication of our research on using the Goldwasser-Kalai-Rothblum (GKR) protocol to prove Keccak hashes in zero-knowledge. This work was made possible through support from the Golem Foundation.
At vlayer, we're committed to contributing to the public goods upon which we build. This research is made freely available to the cryptographic community, and we're grateful to work with the Golem Foundation, who shares this commitment to advancing open-source research.
The Keccak-256 hash function is fundamental to Ethereum. It powers contract storage addressing, state management, and is implemented as the SHA3 opcode throughout the ecosystem. But there's a problem: Keccak wasn't designed with zero-knowledge systems in mind. Unlike ZK-friendly hash functions like Poseidon or BLAKE3, Keccak is computationally expensive to represent in ZK circuits.
This creates a real challenge. While developers can use ZK-friendly alternatives for many applications, when you need to reason directly about Ethereum's state, Keccak is unavoidable. As Ethereum moves toward its rollup-centric roadmap where ZK verification becomes increasingly important, we need better ways to handle these native operations. Read more about those challenges and potential solutions in our previous whitepaper on historical and multichain storage proofs.
We set out to answer a specific question: can the GKR protocol be used to prove Keccak operations more efficiently than other methods?
Our research provides a complete set of arithmetic representations for implementing Keccak within GKR. This includes polynomials for all basic building blocks – bitwise operations like XOR, AND, and OR, as well as more complex constructs needed for the Keccak permutation like binary addition and lane rotation.
We also analyzed the performance characteristics. Our modeling suggests that GKR becomes more efficient than direct implementation in systems like PLONK at around 15 Keccak operations, with the advantage growing as you scale up.
The research demonstrates that using GKR for Keccak is feasible and can offer real efficiency improvements when you need to prove multiple hash operations. We presented mathematical foundations and provided a systematic framework for implementation.
This research contributes to the ecosystem by providing new tools for a challenging problem. It could enable more efficient approaches to proving Ethereum state properties, cross-chain verification, and applications requiring multiple hash operations.
The work also addresses practical considerations. GKR proofs are too large for direct on-chain verification, but they can be embedded within more succinct proof systems. We outline how this recursive approach maintains efficiency gains while achieving small proof sizes needed for blockchain applications.
We extend our gratitude to the Golem Foundation for supporting this research and to the team at Reilabs for their collaboration in developing these ideas. This work builds on important contributions from a broader cryptographic research community.
Click on the button below to download the full whitepaper:
We welcome feedback and discussion - feel free to reach out to Maciej and Marek with your thoughts or questions about the paper.
At vlayer, we're working on making historical and cross-chain data accessible to smart contracts with Time Travel and Teleport. These require proving numerous Keccak computations in the Merkle proofs. Explore these in depth in our previous research on historical and multichain storage proofs.
We're excited to share new research on using the GKR protocol to prove Keccak-256 hashes in zero-knowledge, supported by the Golem Foundation. This work offers an efficient, scalable approach for ZK systems dealing with Ethereum-native operations—critical for historical proofs, cross-chain verification, and more. Full whitepaper now available.
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