[Resource Topic] 2022/1570: Set (Non-)Membership NIZKs from Determinantal Accumulators

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Set (Non-)Membership NIZKs from Determinantal Accumulators

Authors: Helger Lipmaa, Roberto Parisella


We construct the most efficient (in the argument size and the verifier’s computation) known falsifiable set (non-)membership NIZK \Pi^*, where the membership (resp., non-membership) argument consists of only 9 (resp., 15) group elements. It also has a universal CRS. \Pi^* is based on the novel concept of determinantal accumulators. Determinantal primitives have a similar relation to recent pairing-based (non-succinct) NIZKs of Couteau and Hartmann (Crypto 2020) and Couteau et al. (CLPØ, Asiacrypt 2021) that structure-preserving primitives have to the NIZKs of Groth and Sahai. \Pi^* is considerably more efficient than known falsifiable based set (non-)membership NIZKs. We also extend CLPØ by proposing efficient (non-succinct) set non-membership arguments for a large class of languages.

ePrint: https://eprint.iacr.org/2022/1570

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