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We design and implement a simple zero-knowledge argument protocol for NP whose communication complexity is proportional to the square-root of the verification circuit size. The protocol can be based on any collision-resistant hash function. Alternatively, it can be made non-interactive in the random oracle model, yielding concretely efficient zk-SNARKs that do not require a trusted setup or public-key cryptography.

Our protocol is attractive not only for very large verification circuits but also for moderately large circuits that arise in applications. For instance, for verifying a SHA-256 preimage in zero-knowledge with 2^-40 soundness error, the communication complexity is roughly 44KB (or less than 34KB under a plausible conjecture), the prover running time is 140 ms, and the verifier running time is 62 ms. This proof is roughly 4 times shorter than a similar proof of ZKB++ (Chase et al., CCS 2017), an optimized …