SNARGs for P from LWE

We provide the €rst construction of a succinct non-interactive argument (SNARG) for all polynomial time deterministic computations based on standard assumptions. For ) steps of computation, the size of the proof and the common random string (CRS) as well as the veri€cation time are poly-logarithmic in ) . ‘e 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 €rst construction of non-interactive batch arguments for NP based solely on the LWE assumption.

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