Paper 2024/1595

DeepFold: Efficient Multilinear Polynomial Commitment from Reed-Solomon Code and Its Application to Zero-knowledge Proofs

Abstract

This work presents Deepfold, a novel multilinear polynomial commitment scheme (PCS) based on Reed-Solomon code that offers optimal prover time and a more concise proof size. For the first time, Deepfold adapts the FRI-based multilinear PCS to the list decoding radius setting, requiring significantly fewer query repetitions and thereby achieving a 3$$ reduction in proof size compared to Basefold (Crypto'24), while preserving its advantages in prover time. Compared with PolyFRIM (USENIX Security'24), Deepfold achieves a 2$$ improvement in prover time, verifier time, and proof size. Another contribution of this work is a batch evaluation scheme, which enables the FRI-based multilinear PCS to handle polynomials whose size is not a power of two more efficiently. Our scheme has broad applications in zk-SNARKs, since PCS is a key component in modern zk-SNARK constructions. For example, when replacing the PCS component of Virgo (S&P'20) with Deepfold, our scheme achieves a 2.5$$ faster prover time when proving the knowledge of a Merkle tree with 256 leaves, while maintaining the similar proof size. When replacing the PCS component of HyperPlonk (Eurocrypt'23) with Deepfold, our scheme has about 3.6$$ faster prover time. Additionally, when applying our arbitrary length input commitment to verifiable matrix multiplications for matrices of size 1200$$768 and 768$$2304, which are actual use cases in GPT-2 model, the performance showcases a 2.4$$ reduction in prover time compared to previous approaches.