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2018 | OriginalPaper | Buchkapitel

Improved (Almost) Tightly-Secure Simulation-Sound QA-NIZK with Applications

verfasst von : Masayuki Abe, Charanjit S. Jutla, Miyako Ohkubo, Arnab Roy

Erschienen in: Advances in Cryptology – ASIACRYPT 2018

Verlag: Springer International Publishing

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Abstract

We construct the first (almost) tightly-secure unbounded-simulation-sound quasi-adaptive non-interactive zero-knowledge arguments (USS-QA-NIZK) for linear-subspace languages with compact (number of group elements independent of the security parameter) common reference string (CRS) and compact proofs under standard assumptions in bilinear-pairings groups. In particular, under the SXDH assumption, the USS-QA-NIZK proof size is only seventeen group elements with a factor \(O(\log {Q})\) loss in security reduction to SXDH. The USS-QA-NIZK primitive has many applications, including structure-preserving signatures (SPS), CCA2-secure publicly-verifiable public-key encryption (PKE), which in turn have applications to CCA-anonymous group signatures, blind signatures and unbounded simulation-sound Groth-Sahai NIZK proofs. We show that the almost tight security of our USS-QA-NIZK translates into constructions of all of the above applications with (almost) tight-security to standard assumptions such as SXDH and, more generally, \(\mathcal{D}_k\)-MDDH. Thus, we get the first publicly-verifiable (almost) tightly-secure multi-user/multi-challenge CCA2-secure PKE with practical efficiency under standard bilinear assumptions. Our (almost) tight SPS construction is also improved in the signature size over previously known constructions.

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Vorheriges Kapitel Arya: Nearly Linear-Time Zero-Knowledge Proofs for Correct Program Execution

This requires adapting our USS-QA-NIZK to the multi-language USS-QA-NIZK described in [LPJY15], but our scheme readily adapts to that.

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Titel: Improved (Almost) Tightly-Secure Simulation-Sound QA-NIZK with Applications
verfasst von: Masayuki Abe
Charanjit S. Jutla
Miyako Ohkubo
Arnab Roy
Verlag: Springer International Publishing
Buch: Advances in Cryptology – ASIACRYPT 2018
Print ISBN: 978-3-030-03325-5

Electronic ISBN: 978-3-030-03326-2

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-030-03326-2_21

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