Set (Non-)Membership NIZKs from Determinantal Accumulators

We construct a falsifiable set (non-)membership NIZK Pi* that is considerably more efficient than known falsifiable set (non-)membership NIZKs. 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. (CLPO, Asiacrypt 2021) that structure-preserving primitives have to the Groth-Sahai NIZK. We also extend CLPO by proposing efficient (non-succinct) set non-membership arguments for a large class of languages.