Preprocessing succinct non-interactive arguments for rank-1 constraint satisfiability from holographic proofs

We design a new preprocessing succinct non-interactive argument (SNARG) for rank-1 con-straint satisfiability (R1CS) from holographic Interactive Oracle Proofs (IOPs). The protocol is secure in the random oracle model (ROM). We achieve polylogarithm time verifier and polylogarithm proof size. Our construction consists of two parts: (1) a holographic IOP for R1CS with linear size proof and logarithmic query complexity. (2) A cryptography complier converts holographic IOPs to SNARGs. In the first part, univariate sumcheck and low degree testing play an important role in the holographic IOP. In the second part, we use Merkle tree scheme and Fiat-Shamir heuristic to achieve succinctness and non-interactivity.(c) 2022 Elsevier B.V. All rights reserved.