#### Paper 2020/1212

##### Abstract

Non-interactive zero knowledge (NIZK) enables proving the validity of NP statement without leaking anything else. We study multi-instance NIZKs in the common reference string (CRS) model, against an adversary that adaptively corrupts parties and chooses statements to be proven. We construct the first such $\textit{triply adaptive}$ NIZK that provides full adaptive soundness, as well as adaptive zero-knowledge, assuming either LWE or else LPN and DDH (previous constructions rely on non-falsifiable knowledge assumptions). In addition, our NIZKs are universally composable (UC). Along the way, we: - Formulate an ideal functionality, $\mathcal{F}_\textsf{NICOM}$, which essentially captures $\textit{non-interactive}$ commitments, and show that it is realizable by existing protocols using standard assumptions. - Define and realize, under standard assumptions, Sigma protocols which satisfy triply adaptive security with access to $\mathcal{F}_\textsf{NICOM}$. - Use the Fiat-Shamir transform, instantiated with correlation intractable hash functions, to compile a Sigma protocol with triply adaptive security with access to $\mathcal{F}_\textsf{NICOM}$ into a triply adaptive UC-NIZK argument in the CRS model with access to $\mathcal{F}_\textsf{NICOM}$, assuming LWE (or else LPN and DDH). - Use the UC theorem to obtain UC-NIZK in the CRS model.

Note: Minor changes in the abstract and F_NICOM functionality

Available format(s)
Category
Cryptographic protocols
Publication info
Keywords
Non-interactive Zero Knowledge Correlation Intractability Adaptive Security Zero Knowledge Universal Composability
Contact author(s)
canetti @ bu edu
pratik93 @ bu edu
wangxiao @ cs northwestern edu
History
2022-10-17: last of 5 revisions
See all versions
Short URL
https://ia.cr/2020/1212

CC BY

BibTeX

@misc{cryptoeprint:2020/1212,
author = {Ran Canetti and Pratik Sarkar and Xiao Wang},
title = {Triply Adaptive UC NIZK},
howpublished = {Cryptology ePrint Archive, Paper 2020/1212},
year = {2020},
note = {\url{https://eprint.iacr.org/2020/1212}},
url = {https://eprint.iacr.org/2020/1212}
}

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