Set (Non-)Membership NIZKs from Determinantal Accumulators

Helger Lipmaa; Roberto Parisella

Paper 2022/1570

Set (Non-)Membership NIZKs from Determinantal Accumulators

Helger Lipmaa

, Simula UiB, Norway

Roberto Parisella, Simula UiB, Norway

Abstract

We construct a falsifiable set (non-)membership NIZK $Π^{*}$ that is considerably more efficient than known falsifiable set (non-)membership NIZKs. It also has a universal CRS. $Π^{*}$ 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 Groth-Sahai NIZK. We also extend CLPØ by proposing efficient (non-succinct) set non-membership arguments for a large class of languages.

Note: The second eprint corresponds to the published version. The main difference: we explain that CLPØ allows for efficient batch verification (not noted in [CLPØ21]), and use this to speed up our verifiers.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published elsewhere. Major revision. Latincrypt 2023
Keywords: Commit-and-prove non-interactive zero-knowledge set (non-)membership argument universal accumulator
Contact author(s): helger lipmaa @ gmail com
robertoparisella @ hotmail it
History: 2023-08-10: revised; 2022-11-11: received; See all versions
Short URL: https://ia.cr/2022/1570
License: CC BY

BibTeX

@misc{cryptoeprint:2022/1570,
      author = {Helger Lipmaa and Roberto Parisella},
      title = {Set (Non-)Membership {NIZKs} from Determinantal Accumulators},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/1570},
      year = {2022},
      url = {https://eprint.iacr.org/2022/1570}
}