Original Author: Weikeng Chen
Core Breakthrough: 5.7x Speedup in Keccak Proof
Binary GKR has achieved the fastest Keccak zero-knowledge proof performance to date, with approximately a 5.7x speedup compared to the best existing binary proof system, FRI-Binius. This breakthrough is significant not only in theory but also opens up new possibilities for practical applications.Application Prospects: A "Universal Acceleration Sidecar" for zkEVM
We believe that Binary GKR can serve as a "universal acceleration sidecar" in various zkEVM architectures, efficiently handling the numerous Keccak computations in Ethereum state trees, thereby significantly reducing proof costs and improving system throughput and response speed. Polyhedra will continue to promote the productization and open-source process of Binary GKR, empowering zk architecture upgrades in Ethereum and broader ecosystems.Keccak: The "Holy Grail" of Zero-Knowledge Ethereum
Ethereum is gradually evolving towards a zero-knowledge proof-native Layer-1. The Ethproofs project, involving 21 teams and covering 22 ZK(E)VM implementations, is taking a critical step by attempting to provide complete proofs for Ethereum historical blocks. On the Ethproofs website, you can track the real-time progress of multiple teams: Projects like ZkCloud, Succinct, Snarkify, and ZKM have begun continuously submitting ZK proofs for the latest blocks. The ultimate goal of this trend is to transform Ethereum into an execution layer driven by zero-knowledge proofs, with the consensus layer only performing lightweight tasks like transaction list proposals. [The rest of the translation follows the same professional and accurate approach, maintaining technical terminology and preserving the original structure.]This is precisely why Keccak is hailed as the "zero-knowledge holy grail". In comparison, early hash functions like SHA-256 and Blake 2/3, while also relying on bitwise operations such as XOR and AND, have their maximum performance bottleneck originating from integer addition. In proof systems, integer addition is usually optimized by breaking it down into multiple 4-bit chunks to significantly improve performance. However, Keccak does not involve any integer addition, rendering these optimization strategies ineffective.
The most cutting-edge solution currently is Binius. Its core idea is: since Keccak is entirely composed of bitwise operations, we can implement a proof system based on bits as the basic unit. This is Binius's breakthrough.
In Binius, Keccak is represented as operations on the finite field 𝐹₂ (binary field). Since XOR is essentially addition in 𝐹₂, its related overhead is almost completely eliminated. The entire process is constructed as a series of polynomial operations, and bit rotation operations can be easily implemented in a bit-processing model. The proof cost is mainly concentrated in the AND gates appearing in the χ step.
Binius's benchmarks show that when proving 8192 Keccak operations, it only requires about 12.35 seconds, far superior to Groth 16 (attempt one) and lookup table methods (attempt two).
Is Binius the end point? Actually not. We discovered that by removing certain redundant parts in Keccak proofs, we could potentially further improve performance by about five times, surpassing the current Binius implementation.
Polyhedra Launches Binary GKR: A Binary Proof System Optimized for Keccak
The Polyhedra team is constructing a brand new proof system - Binary GKR (see: ePrint 2025/717), a framework specifically designed for efficient proof of binary operations, particularly suitable for functions like Keccak that are core to bitwise operations. The key advantages of Binary GKR stem from three critical technical innovations:
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