Ethereum co-founder Vitalik Buterin has published an article outlining the implementation of Goldwasser-Kalai-Rothblum (GKR) protocols in Ethereum, aiming to significantly improve the efficiency of zero-knowledge proof (ZKP) generation.
What Are GKR Protocols?
GKR, introduced by Shafi Goldwasser, Yael Tauman Kalai, and Guy Rothblum in 2008, is an interactive proof system that allows a server to perform complex computations without requiring full recomputation by the verifier, while still ensuring a high level of confidence in the results.
The method decomposes computations into multiple layers, each represented by polynomials. A verifier can confirm the correctness of the computation by checking only a few points, as the outcome is derived from the initial data and the interconnection of all layers.
Applying GKR to Zero-Knowledge Proofs
Buterin proposes using GKR to enhance the efficiency of zk-SNARKs and zk-STARKs, which require proofs at each intermediate step. By breaking computations into layers, verifiers can validate integrity with short, concise mathematical proofs, drastically reducing network load and speeding up proof generation.
At the core of GKR systems is the sumcheck protocol, which proves that the sum of a polynomial’s values equals a specific number without calculating each value individually. Buterin cites applications like Poseidon2 hashing functions and neural network computations as examples of how GKR can optimize ZKP processes.
Potential Benefits and Implications
According to Buterin, implementing GKR protocols could:
- Accelerate proof generation for thousands of transactions simultaneously.
- Reduce gas costs for Ethereum users.
- Enable complex ZKP applications, spanning from DeFi platforms to AI computation verification.
While sumcheck verification is more computationally intensive than simple hashing, the approach could make ZKP generation up to 15 times more efficient, representing a significant step toward scalable Ethereum solutions.
Previously, Buterin also introduced leanVM, a virtual machine optimized for ZK-proof computations, positioning it as the next evolution in Ethereum scaling. The integration of GKR protocols builds upon this foundation, offering a roadmap for more robust and efficient ZKP implementation across the network.
