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Title:
Improved (Almost) Tightly-Secure Simulation-Sound QA-NIZK with Applications
Authors: Masayuki Abe, Charanjit S. Jutla, Miyako Ohkubo, Arnab Roy
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. Specifically, our construction has O(\log Q) reduction to the SXDH, DLIN and matrix-DDH assumptions, where Q is the number of simulated proofs given out. 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, \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.
ePrint: https://eprint.iacr.org/2018/849
Slides: https://asiacrypt.iacr.org/2018/files/SLIDES/MONDAY/514/1610-1700/Tight-uss-qanizk-AC18.pdf
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