Paper 2021/808

SNARGs for $\mathcal{P}$ from LWE

Arka Rai Choudhuri and Abhishek Jain and Zhengzhong Jin

Abstract

We provide the first construction of a succinct non-interactive argument (SNARG) for *all* polynomial time deterministic computations based on standard assumptions. For $T$ steps of computation, the size of the proof and the common random string (CRS) as well as the verification time are poly-logarithmic in $T$. The security of our scheme relies on the hardness of the Learning with Errors (LWE) problem against polynomial-time adversaries. Previously, SNARGs based on standard assumptions could support bounded-depth computations and required sub-exponential hardness assumptions [Jawale-Kalai-Khurana-Zhang, STOC'21]. Along the way, we also provide the first construction of non-interactive batch arguments for $\mathsf{NP}$ based solely on the LWE assumption. The size of the proof and CRS for a batch of $k$ statements grows only with the size of a *single* witness.