This post explores optimizations for the sumcheck protocol when proving values in a small field with randomness from a large field. By minimizing expensive large × large multiplications, using evaluation tables, precomputing accumulators, and applying Lagrange interpolation, the authors significantly reduce prover time. SageMath implementations are provided for each algorithm.
"In this episode Anna Rose and Nico Mohnblatt chat with Binyi Chen, researcher at Stanford University. They discuss his work on lattice-based folding schemes, revisit LatticeFold and LatticeFold+, and cover how lattices enable low-cost, post-quantum-secure folding by replacing Pedersen hashes with Ajtai commitments. They discuss the early folding work from 2023 and how it has evolved and explore the advantages of lattices over other approaches in the folding context while also highlighting their tradeoffs.
Binyi goes on to introduce Symphony, his new work that eliminates the need to implement Fiat-Shamir in the recursive verification circuit, and describes how that improves efficiency and removes the chances for a KRS-style attack."
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