On QA-NIZK in the BPK Model

Behzad Abdolmaleki; Helger Lipmaa; Janno Siim; Michał Zając

Paper 2018/877

On QA-NIZK in the BPK Model

Behzad Abdolmaleki, Helger Lipmaa, Janno Siim, and Michał Zając

Abstract

Recently, Bellare et al. defined subversion-resistance (security in the case the CRS creator may be malicious) for NIZK. In particular, a Sub-ZK NIZK is zero-knowledge, even in the case of subverted CRS. We study Sub-ZK QA-NIZKs, where the CRS can depend on the language parameter. First, we observe that subversion zero-knowledge (Sub-ZK) in the CRS model corresponds to no-auxiliary-string non-black-box NIZK in the Bare Public Key model, and hence, the use of non-black-box techniques is needed to obtain Sub-ZK. Second, we give a precise definition of Sub-ZK QA-NIZKs that are (knowledge-)sound if the language parameter but not the CRS is subverted and zero-knowledge even if both are subverted. Third, we prove that the most efficient known QA-NIZK for linear subspaces by Kiltz and Wee is Sub-ZK under a new knowledge assumption that by itself is secure in (a weaker version of) the algebraic group model. Depending on the parameter setting, it is (knowledge-)sound under different non-falsifiable assumptions, some of which do not belong to the family of knowledge assumptions.

Note: 14 Feb 2020: this eprint corresponds to the version accepted to PKC 2020. It is very different from the older eprint: we now achieve security also in the case the language parameter is subverted ("Sub-PAR soundness/knowledge-soundness"), we additionally prove knowledge-soundness in the case the language-parameter matrix is full-rank. We also use somewhat different assumptions: in particular, Sub-PAR (knowledge-)soundness relies on interactive non-falsifiable assumptions, that are markedly different from knowledge assumptions that are used in the case of SNARKs. 19 Feb 2019: This version is substantially updated: the main new protocol is better explained (and the case k = 2 is simplified), the security proof is different, etc.17 May 2019: This version has a bit more common terminology. Somewhat better comparison with the previous work.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published by the IACR in PKC 2020
Keywords: Bare public key model no-auxiliary-string zero knowledge non-black-box zero knowledge QA-NIZK subversion-security
Contact author(s): helger lipmaa @ gmail com
History: 2020-02-14: last of 3 revisions; 2018-09-23: received; See all versions
Short URL: https://ia.cr/2018/877
License: CC BY

BibTeX

@misc{cryptoeprint:2018/877,
      author = {Behzad Abdolmaleki and Helger Lipmaa and Janno Siim and Michał Zając},
      title = {On {QA}-{NIZK} in the {BPK} Model},
      howpublished = {Cryptology {ePrint} Archive, Paper 2018/877},
      year = {2018},
      url = {https://eprint.iacr.org/2018/877}
}