## Cryptology ePrint Archive: Report 2020/1426

Linear-Time Arguments with Sublinear Verification from Tensor Codes

Jonathan Bootle and Alessandro Chiesa and Jens Groth

Abstract: Minimizing the computational cost of the prover is a central goal in the area of succinct arguments. In particular, it remains a challenging open problem to construct a succinct argument where the prover runs in linear time and the verifier runs in polylogarithmic time.

We make progress towards this goal by presenting a new linear-time probabilistic proof. For any fixed $\epsilon > 0$, we construct an interactive oracle proof (IOP) that, when used for the satisfiability of an $N$-gate arithmetic circuit, has a prover that uses $O(N)$ field operations and a verifier that uses $O(N^{\epsilon})$ field operations. The sublinear verifier time is achieved in the holographic setting for every circuit (the verifier has oracle access to a linear-size encoding of the circuit that is computable in linear time).

When combined with a linear-time collision-resistant hash function, our IOP immediately leads to an argument system where the prover performs $O(N)$ field operations and hash computations, and the verifier performs $O(N^{\epsilon})$ field operations and hash computations (given a short digest of the $N$-gate circuit).

Category / Keywords: foundations / interactive oracle proofs; tensor codes; succinct arguments

Original Publication (with major differences): IACR-TCC-2020