Paper 2023/1938

Batch Arguments to NIZKs from One-Way Functions

Abstract

Succinctness and zero-knowledge are two fundamental properties in the study of cryptographic proof systems. Several recent works have formalized the connections between these two notions by showing how to realize non-interactive zero-knowledge (NIZK) arguments from succinct non-interactive arguments. Specifically, Champion and Wu (CRYPTO 2023) as well as Bitansky, Kamath, Paneth, Rothblum, and Vasudevan (ePrint 2023) recently showed how to construct a NIZK argument for NP from a (somewhere-sound) non-interactive batch argument (BARG) and a dual-mode commitment scheme (and in the case of the Champion-Wu construction, a local pseudorandom generator). The main open question is whether a BARG suffices for a NIZK (just assuming one-way functions). In this work, we first show that an adaptively-sound BARG for NP together with an one-way function imply a computational NIZK argument for NP. We then show that the weaker notion of somewhere soundness achieved by existing BARGs from standard algebraic assumptions are also adaptively sound if we assume sub-exponential security. This transformation may also be of independent interest. Taken together, we obtain a NIZK argument for NP from one-way functions and a sub-exponentially-secure somewhere-sound BARG for NP. If we instead assume plain public-key encryption, we show that a standard polynomially-secure somewhere-sound batch argument for NP suffices for the same implication. As a corollary, this means a somewhere-sound BARG can be used to generically upgrade any semantically-secure public-key encryption scheme into one secure against chosen-ciphertext attacks. More broadly, our results demonstrate that constructing non-interactive batch arguments for NP is essentially no easier than constructing NIZK arguments for NP.