TensorSwitch: Nearly Optimal Polynomial Commitments from Tensor Codes.

A polynomial commitment scheme (PCS) enables a prover to succinctly commit to a large polynomial and later generate evaluation proofs that can be efficiently verified. In recent years, PCSs have emerged as a central focus of succinct non-interactive argument (SNARG) design. We present TensorSwitch, a hash-based PCS for multilinear polynomials that improves the state-of-the-art in two fundamental bottlenecks: prover time and proof size. We frame our results as an interactive oracle PCS, which can be compiled into a cryptographic PCS using standard techniques. The protocol uses any linear code with rate ρ , list-decoding and correlated agreement up to δ , and encoding time τ·ℓ , where ℓ is the block length. For a size n polynomial, security parameter λ , and sufficiently large field, it has the following efficiency measures, up to lower order terms: Moreover, the evaluation proof only contains O(loglog n) oracles of total size (λ n)^0.5 + o(1) . With a Reed-Solomon code of rate 1/2, the query complexity is 2.41 λ and commitment time is dominated by (6 log n+ 3) · n field multiplications. With an RAA code of rate 1/4 and distance 0.19, the query complexity is 19 λ and the commitment time is 42 n field additions and 3n field multiplications. For both instantiations, the opening time is dominated by 6 n field multiplications.