Adaptively-Sound Succinct Arguments for NP from Indistinguishability Obfuscation

A succinct non-interactive argument (SNARG) for NP allows a prover to convince a verifier that an NP statement x is true with a proof of size o(|x| + |w|), where w is the associated NP witness. A SNARG satisfies adaptive soundness if the malicious prover can choose the statement to prove after seeing the scheme parameters. In this work, we provide the first adaptively-sound SNARG for NP in the plain model assuming sub-exponentially-hard indistinguishability obfuscation, sub-exponentially-hard one-way functions, and either the (polynomial) hardness of the discrete log assumption or the (polynomial) hardness of factoring. This gives the first adaptively-sound SNARG for NP from falsifiable assumptions. All previous SNARGs for NP in the plain model either relied on non-falsifiable cryptographic assumptions or satisfied a weak notion of non-adaptive soundness (where the adversary has to choose the statement it proves before seeing the scheme parameters).