Cost-Scalable Verification of Outsourced Structured Arithmetic Computation in Smart Contracts
TL;DR
This paper presents a cross-platform implementation of GKR-based transparent on-chain verification for outsourced structured arithmetic circuits on the Ethereum Virtual Machine and Starknet (Cairo) and shows that direct execution cost increases rapidly with input size, whereas GKR-based verification scales much more favorably.
Abstract
Protocol-level validity mechanisms, such as validity rollups and STARK-based proving systems, improve blockchain scalability, but do not remove the cost of executing computation-intensive application logic inside smart contracts. At the application layer, a meaningful class of structured arithmetic workloads—including polynomial evaluations, cryptographic primitive computations, and signal-processing operations over finite fields—arises naturally in contract logic, yet remains subject to the on-chain fee model regardless of protocol-level optimizations. This paper investigates whether outsourcing such workloads and replacing direct execution with transparent on-chain verification can provide a practical cost advantage under realistic smart-contract fee models. We present a cross-platform implementation of GKR-based transparent on-chain verification for outsourced structured arithmetic circuits on the Ethereum Virtual Machine (Solidity) and Starknet (Cairo). GKR requires no trusted setup, which makes it particularly suitable for deployment in permissionless public blockchain environments where trust assumptions must be minimized. The design targets layered circuits with regular structure and incorporates implementation techniques that reduce verifier-side overhead and eliminate the linear input-handling bottleneck in naive deployments. These workloads can be represented as layered arithmetic circuits with regular wiring and logarithmic depth. Our evaluation shows that direct execution cost increases rapidly with input size, whereas GKR-based verification scales much more favorably. At size 4096, verification reduces execution cost by approximately 84% on the EVM and 91% on Starknet. These results identify outsourced execution with on-chain GKR verification as a practical design point for application-layer verifiable computation, especially in public blockchain environments where transparency and the absence of trusted setup are important.