Quasi-Optimal SNARGs via Linear Multi-Prover Interactive Proofs

Succinct non-interactive arguments (SNARGs) enable verifying \(\mathsf {NP} \) computations with significantly less complexity than that required for classical \(\mathsf {NP} \) verification. In this work, we focus on simultaneously minimizing the proof size and the prover complexity of SNARGs. Concretely, for a security parameter \(\lambda \), we measure the asymptotic cost of achieving soundness error \(2^{-\lambda }\) against provers of size \(2^\lambda \). We say a SNARG is quasi-optimally succinct if its proof length is \(\widetilde{O}(\lambda )\), and that it is quasi-optimal, if moreover, its prover complexity is only polylogarithmically greater than the running time of the classical \(\mathsf {NP} \) prover. We show that this definition is the best we could hope for assuming that \(\mathsf {NP} \) does not have succinct proofs. Our definition strictly strengthens the previous notion of quasi-optimality introduced in the work of Boneh et al. (Eurocrypt 2017).