Polaris: Transparent Succinct Zero-Knowledge Arguments for R1CS with Efficient Verifier

Authors: Shihui Fu (University of Waterloo), Guang Gong (University of Waterloo)

Volume: 2022
Issue: 1
Pages: 544–564
DOI: https://doi.org/10.2478/popets-2022-0027

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Abstract: We present a new zero-knowledge succinct argument of knowledge (zkSNARK) scheme for Rank-1 Constraint Satisfaction (RICS), a widely deployed NPcomplete language that generalizes arithmetic circuit satisfiability. By instantiating with different commitment schemes, we obtain several zkSNARKs where the verifier’s costs and the proof size range from O(log2 N ) √ to O( N ) depending on the underlying polynomial commitment schemes when applied to an N -gate arithmetic circuit. All these schemes do not require a trusted setup. It is plausibly post-quantum secure when instantiated with a secure collision-resistant hash function. We report on experiments for evaluating the performance of our proposed system. For instance, for verifying a SHA-256 preimage (less than 23k AND gates) in zeroknowledge with 128 bits security, the proof size is less than 150kB and the verification time is less than 11ms, both competitive to existing systems.

Keywords: zkSNARK, verifiable computation, zeroknowledge proof, polynomial commitment

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