Efficient inner product arguments with sublogarithmic proof and sub-square-root verifier

Inner product arguments are core building blocks of numerous cryptographic primitives and therefore minimizing their complexity is a central goal in this research area. In this paper, we follow the work of Kim et al. (ASIACRYPT’22) and propose the first inner product argument having sublogarithmic communication complexity and sub-square-root verifier complexity simultaneously. We first devise a new subvector combination method for recursion and utilize an aggregated multi-exponentiation argument to prove some committed group elements are valid. We then modify the commitment keys in inner product arguments to be structured and reduce the verifier complexity by delegating the costly computations to the prover. Compared with the state-of-the-art inner product arguments, our protocol is highly competitive in terms of asymptotic complexity.