Fast and Designated-verifier Friendly zkSNARKs in the BPK Model

Xudong Zhu; Xuyang Song; Yi Deng

Paper 2023/1806

Fast and Designated-verifier Friendly zkSNARKs in the BPK Model

Xudong Zhu, Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, CAS, Beijing, China, School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

Xuyang Song, Anoma

Yi Deng, Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, CAS, Beijing, China, School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

Abstract

After the pioneering results proposed by Bellare et al in ASIACRYPT 2016, there have been lots of efforts to construct zero-knowledge succinct non-interactive arguments of knowledge protocols (zk-SNARKs) that satisfy subversion zero knowledge (S-ZK) and standard soundness from the zk-SNARK in the common reference string (CRS) model. The various constructions could be regarded secure in the bare public key (BPK) model because of the equivalence between S-ZK in the CRS model, and uniform non-black-box zero knowledge in the BPK model has been proved by Abdolmaleki et al. in PKC 2020. In this study, by leveraging the power of random oracle (RO) model, we proposed the first publicly verifiable non-uniform ZK zk-SNARK scheme in the BPK model maintaining comparable efficiency with its conventional counterpart, which can also be compatible with the well-known transformation proposed by Bitansky et al. in TCC 2013 to obtain an efficient designated-verifier zk-SNARK. We achieve this goal by only adding a constant number of elements into the CRS, and using an unconventional but natural method to transform Groth’s zk-SNARK in EUROCRYPT 2016. In addition, we propose a new speed-up technique that provides a trade-off. Specifically, if a logarithmic number of elements are added into the CRS, according to different circuits, the CRS verification time in our construction could be approximately $9\%-23\%$ shorter than that in the conventional counterpart.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
Keywords: Subversion zero knowledge SNARK Common reference string Bare public key Random Oracle Generic group model
Contact author(s): zhuxudong @ iie ac cn
xuyangsong1012 @ gmail com
deng @ iie ac cn
History: 2024-01-23: last of 5 revisions; 2023-11-23: received; See all versions
Short URL: https://ia.cr/2023/1806
License: CC BY

BibTeX

@misc{cryptoeprint:2023/1806,
      author = {Xudong Zhu and Xuyang Song and Yi Deng},
      title = {Fast and Designated-verifier Friendly {zkSNARKs} in the {BPK} Model},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/1806},
      year = {2023},
      url = {https://eprint.iacr.org/2023/1806}
}