International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Statistical ZAPR Arguments from Bilinear Maps

Alex Lombardi , MIT
Vinod Vaikuntanathan , MIT
Daniel Wichs , Northeastern and NTT Research
DOI: 10.1007/978-3-030-45727-3_21 (login may be required)
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Conference: EUROCRYPT 2020
Abstract: Dwork and Naor (FOCS '00) defined ZAPs as 2-message witness-indistinguishable proofs that are public-coin. We relax this to \emph{ZAPs with private Randomness} (ZAPRs), where the verifier can use private coins to sample the first message (independently of the statement being proved), but the proof must remain publicly verifiable given only the protocol transcript. In particular, ZAPRs are \emph{reusable}, meaning that the first message can be reused for multiple proofs without compromising security. Known constructions of ZAPs from trapdoor permutations or bilinear maps are only computationally WI (and statistically sound). Two recent results of Badrinarayanan-Fernando-Jain-Khurana-Sahai and Goyal-Jain-Jin-Malavolta [EUROCRYPT '20] construct the first \emph{statistical ZAP arguments}, which are statistically WI (and computationally sound), from the quasi-polynomial LWE assumption. Here, we construct \emph{statistical ZAPR arguments} from the quasi-polynomial decision-linear (DLIN) assumption on groups with a bilinear map. Our construction relies on a combination of several tools including Groth-Ostrovsky-Sahai NIZK and NIWI [EUROCRYPT '06, CRYPTO '06, JACM '12], ``sometimes-binding statistically hiding commitments'' [Kalai-Khurana-Sahai, EUROCRYPT '18] and the ``MPC-in-the-head'' technique [Ishai-Kushilevitz-Ostrovsky-Sahai, STOC '07].
Video from EUROCRYPT 2020
  title={Statistical ZAPR Arguments from Bilinear Maps},
  booktitle={39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10–14, 2020, Proceedings},
  series={Lecture Notes in Computer Science},
  keywords={ZAPs;Statistical Witness Indistinguishability},
  author={Alex Lombardi and Vinod Vaikuntanathan and Daniel Wichs},