### Efficient Tightly-Secure Structure-Preserving Signatures and Unbounded Simulation-Sound QA-NIZK Proofs

Mojtaba Khalili and Daniel Slamanig

##### Abstract

We show how to construct structure-preserving signatures (SPS) and unbounded quasi-adaptive non-interactive zero-knowledge (USS QA-NIZK) proofs with a tight security reduction to simple assumptions, being the first with a security loss of $\mathcal{O}(1)$. Specifically, we present a SPS scheme which is more efficient than existing tightly secure SPS schemes and from an efficiency point of view is even comparable with other non-tight SPS schemes. In contrast to existing work, however, we only have a lower security loss of $\mathcal{O}(1)$, resolving an open problem posed by Abe et al. (CRYPTO 2017). In particular, our tightly secure SPS scheme under the SXDH assumption requires 11 group elements. Moreover, we present the first tightly secure USS QA-NIZK proofs with a security loss of $\mathcal{O}(1)$ which also simultaneously have a compact common reference string and constant size proofs (5 elements under the SXDH assumption, which is only one element more than the best non-tight USS QA-NIZK). From a technical perspective, we present a novel randomization technique, inspired by Naor-Yung paradigm and adaptive partitioning, to obtain a randomized pseudorandom function (PRF). In particular, our PRF uses two copies under different keys but with shared randomness. Then we adopt ideas of Kiltz, Pan and Wee (CRYPTO 2015), who base their SPS on a randomized PRF, but in contrast to their non-tight reduction our approach allows us to achieve tight security. Similarly, we construct the first compact USS QA-NIZK proofs adopting techniques from Kiltz and Wee (EUROCRYPT 2015). We believe that the techniques introduced in this paper to obtain tight security with a loss of $\mathcal{O}(1)$ will have value beyond our proposed constructions.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Structure-preserving signaturesQA-NIZKsimulation-soundnesstight securitystandard assumptions
Contact author(s)
m khalili @ ec iut ac ir
daniel slamanig @ ait ac at
History
2020-01-11: revised
See all versions
Short URL
https://ia.cr/2019/1026

CC BY

BibTeX

@misc{cryptoeprint:2019/1026,
author = {Mojtaba Khalili and Daniel Slamanig},
title = {Efficient Tightly-Secure Structure-Preserving Signatures and Unbounded Simulation-Sound QA-NIZK Proofs},
howpublished = {Cryptology ePrint Archive, Paper 2019/1026},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/1026}},
url = {https://eprint.iacr.org/2019/1026}
}

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