What is GKR? How can GKR improve Ethereum?

October 27th What is GKR? How can GKR improve Ethereum?

GKR (Goldwasser-Kalai-Rothblum) proofs are advanced cryptographic proof methods designed to make complex calculations faster and more efficient by verifying only the inputs and outputs of a process, rather than all intermediate steps. GKR uses recursive “sum-check” reduction to significantly reduce prover overhead compared to traditional proof systems such as STARK and FRI, providing concise and cost-effective verification without inherently providing any privacy. However, it can be combined with SNARK or STARK for zero-knowledge functionality. For Ethereum, GKR has great potential to improve scalability, especially for rollups and zkEVM, by reducing proof generation costs, accelerating verification, and enabling more frequent and smaller proof submissions. Its efficiency could improve user experience, reduce transaction fees, and expand Ethereum’s capacity for advanced crypto applications such as verifiable AI and private computing. However, the benefits of GKR depend on the quality of the implementation and the structure of the workload to which it is applied, so actual performance improvements require careful optimization. If the integration is successful, GKR could become the cornerstone of Ethereum’s drive to become a more scalable, secure, and cryptographically verifiable network.

What is GKR proof?

GKR (Goldwasser-Kalai-Rothblum) is a family of interactive proof techniques tailored for “many inputs flowing through many layers” computations, such as batched hash functions and neural network-style pipelines. Its core optimization is structural. Rather than committing all intermediate values ​​of the computational trace, the prover commits only the inputs and outputs, and uses a series of “sum-check” reductions to convince the verifier that each layer was applied correctly. Because expensive commitments for large traces are avoided, GKR-based provers can achieve much lower overhead than traditional STARK/FRI-style approaches for the same workload. Importantly, GKR provides simplicity and quick verification, not privacy. If confidentiality is required, GKR certificates are wrapped within a SNARK or STARK.

For Ethereum, this is most important in the context of rollups and zkEVM, where cost and latency proofs dominate pricing and user experience. GKR-oriented provers can speed up the most important parts of a validity proof, such as large batches of hashes, state transition layers, or Merkle/Kecak-like routines, by treating the trace as a layered, lower-order computation and applying sum checks rather than hashing the entire trace. Faster and cheaper proof generation lowers the marginal cost per transaction for rollups, enabling higher throughput and tighter pricing markets while keeping L1 validation lightweight. In practice, this means more frequent proof posting, faster verification times for L2 users, and a path to real-time proofing of selected workloads.

GKR’s design also fits well into Ethereum’s modular roadmap. Excellent when many similar operations are batched, rollups can reorganize transformations like pipelines, grouping hashes, signature checks, or matrices to maximize GKR efficiency while leaving other parts to traditional math or polynomial commitment schemes. This approach consists of an existing ecosystem. Proofs can still be verified on Ethereum in combination with EVM-compatible circuits and can be wrapped to provide zero-knowledge properties for privacy-preserving applications. The end effect is a toolkit that improves scalability without requiring protocol changes at L1, in line with Ethereum’s preference for innovation at the edge.

There are trade-offs. GKR doesn’t universally win at every circuit. It focuses on a “batch and layer” pattern and may be memory limited when implemented, so careful engineering is required to realize the theoretical benefits. Mitigation measures should be considered for security subtleties, such as making the Fiat-Shamir challenge unpredictable within shallow circuits. Still, by reducing prover overhead and keeping verification costs low for common workloads, GKR can reduce fees, reduce latency, and expand the feasible design space for zk rollup and EVM-compatible proof systems. Collectively, this advances Ethereum’s goals of increasing throughput and strengthening cryptographic guarantees while maintaining platform versatility and decentralized verification at L1.

Can GKR proofs revolutionize ZK cryptography?

GKR proofs represent a significant conceptual leap in the way we generate and verify cryptographic proofs of computations, and have the potential to meaningfully restructure zero-knowledge (ZK) cryptography. Unlike traditional approaches that require commitment to all intermediate computational steps, the GKR scheme focuses only on the inputs and outputs of the process and uses recursive sum checks to verify correctness layer by layer. This significantly reduces computational and storage overhead, making proof generation faster and cheaper. GKR alone is not zero-knowledge, but it guarantees simplicity rather than privacy, and serves as a very efficient foundation that can be wrapped into ZK-SNARK or ZK-STARK for full zero-knowledge properties. This modular design makes GKR a strong candidate to form the backbone of next-generation proof systems.

From a practical perspective, the increased efficiency of GKR could make ZK proofs much more accessible and scalable. Many of today’s bottlenecks in ZK systems, especially zk-EVM and rollups, stem from the significant cost of committing to huge computational traces. By eliminating the need to store or verify each intermediate step, GKR reduces the prover’s workload by an order of magnitude, making real-time or near real-time proof generation more feasible. This will enable the ZK system to move from experimental deployment to everyday large-scale use in applications ranging from blockchain scalability to verifiable machine learning (zk-ML), supporting more complex logic and higher throughput without compromising verification integrity.

The impact on Ethereum and other blockchain ecosystems is particularly strong. As proof generation becomes faster and cheaper, Layer 2 networks and distributed applications are likely to adopt GKR-based systems to verify transactions, state updates, and computations with minimal delay. This efficiency not only reduces fees but also enables new forms of on-chain verification, such as private computing, verifiable AI, and minimal trust financial systems. GKR is compatible with existing cryptographic primitives such as Merkle trees and polynomial commitments, making it a flexible framework that can integrate with your current infrastructure rather than completely replacing it.

But describing GKR as a total revolution overstates its scope. It does not solve all the challenges of ZK cryptography, especially those related to privacy, hardware constraints, and protocol-level decentralization. Its effectiveness depends on the structure of the computation, with layered parallel workloads offering the most benefit, but requiring significant engineering effort to implement them efficiently. Still, GKR represents a major step forward in the evolution of verifiable computation by providing a path to lighter, faster, and more general-purpose proofs. If carefully combined with other ZK advances, it could be the beginning of a new phase in which zero-knowledge systems become standard components of scalable, privacy-preserving digital infrastructure.

What impact could GKR have to improve Ethereum?

The introduction of GKR proofs could have a transformative impact on Ethereum by making cryptographic proof generation faster, cheaper, and more scalable. One of the main challenges of Ethereum is the high computational cost associated with verifying the large number of transactions and execution of smart contracts, especially in the era of rollups and zkEVM. GKR proofs address this problem by significantly reducing the workload required for the prover to prove the correctness of a computation. GKR proofs rely on validating only the inputs and outputs, rather than committing to all intermediate states, and use recursive sum-checking techniques to validate the steps in between. This efficiency allows Ethereum’s layer 2 ecosystem to post proofs to the main chain more frequently, reducing latency and increasing overall throughput without increasing on-chain verification costs.

From a scalability perspective, GKR’s architecture closely aligns with Ethereum’s long-term roadmap towards modularization. Rollups rely heavily on validity proofs to ensure the integrity of off-chain computations, but current proof systems can be expensive to run and slow to update. GKR’s streamlined design reduces prover overhead by orders of magnitude, reduces rollup operator costs, and potentially enables real-time or near real-time proof generation. This improvement results in faster verification times, smaller batches, and a smoother user experience. Additionally, GKR-based systems generate concise proofs that are efficient for on-chain verification, allowing Ethereum to maintain its commitment to decentralized security without overburdening the base layer with computational complexity.

Beyond scalability, GKR may also enhance Ethereum’s capabilities for advanced cryptographic applications such as privacy-preserving transactions, verifiable AI (zkML), and complex multi-party computations. When combined with SNARK or STARK, GKR’s simplicity provides a backbone for efficient zero-knowledge proofs, making it possible to perform private computations and secure data validation on Ethereum-compatible networks. This opens the door to a new generation of decentralized applications that can prove the authenticity of sensitive operations such as identity verification, compliance checks, and data analysis without revealing the underlying information. As Ethereum continues to expand beyond financial applications, the ability to incorporate high-performance, privacy-friendly computation could prove crucial in evolving Ethereum into a global verification layer.

However, the impact of GKR will vary depending on implementation and adoption. Although theoretically the performance gains are impressive, real-world benefits require careful optimization of memory processing, batching strategies, and circuit design. GKR works best with computations that can be expressed as layered or batched processes. This is suitable for many, but not all, blockchain workloads. Still, once the engineering challenges are overcome, GKR could significantly improve Ethereum’s efficiency, enabling higher transaction capacity, more cost-effective rollups, and broader use of verifiable computation. In essence, GKR provides a scalable path toward Ethereum’s vision of a secure, efficient, and cryptographically verifiable global computer, reducing the barriers that currently constrain proof-based scalability.