This article introduces Cantor's Additive FFT algorithm for polynomial evaluation and interpolation in characteristic 2 fields, addressing the limitations of traditional FFT in finite fields and enabling efficient Reed-Solomon encoding and polynomial commitments.
The GKR protocol is an interactive proof system based on Sumcheck, verifying the correctness of computations in layered arithmetic circuits by recursively applying Sumcheck from the output layer back to the input layer.
ZisK is an open-source zero-knowledge proving toolstack featuring a zkVM that enables verifiable execution of programs written in high-level languages like Rust
This article integrates and expands upon the research findings from two previous preprints (2024/1046 and 2024/1210), focusing on optimizations of the Sumcheck protocol in several common application scenarios. Specifically, the article proposes two optimization strategies: (1) for scenarios where polynomial evaluation results are consistently small in magnitude, and (2) for scenarios involving Zerocheck operations. Experimental results demonstrate that these optimizations can achieve a 2 to 3 times speedup in practical applications while significantly reducing memory overhead.
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