### New Constructions of Statistical NIZKs: Dual-Mode DV-NIZKs and More

Benoît Libert, Alain Passelègue, Hoeteck Wee, and David J. Wu

##### Abstract

Non-interactive zero-knowledge proofs (NIZKs) are important primitives in cryptography. A major challenge since the early works on NIZKs has been to construct NIZKs with a statistical zero-knowledge guarantee against unbounded verifiers. In the common reference string (CRS) model, such "statistical NIZK arguments" are currently known from k-Lin in a pairing-group and from LWE. In the (reusable) designated-verifier model (DV-NIZK), where a trusted setup algorithm generates a reusable verification key for checking proofs, we also have a construction from DCR. If we relax our requirements to computational zero-knowledge, we additionally have NIZKs from factoring and CDH in a pairing group in the CRS model, and from nearly all assumptions that imply public-key encryption (e.g., CDH, LPN, LWE) in the designated-verifier model. Thus, there still remains a gap in our understanding of statistical NIZKs in both the CRS and the designated-verifier models. In this work, we develop new techniques for constructing statistical NIZK arguments. First, we construct statistical DV-NIZK arguments from the k-Lin assumption in pairing-free groups, the QR assumption, and the DCR assumption. These are the first constructions in pairing-free groups and from QR that satisfy statistical zero-knowledge. All of our constructions are secure even if the verification key is chosen maliciously (i.e., they are "malicious-designated-verifier" NIZKs), and moreover, they satisfy a "dual-mode" property where the CRS can be sampled from two computationally indistinguishable distributions: one distribution yields statistical DV-NIZK arguments while the other yields computational DV-NIZK proofs. We then show how to adapt our k-Lin construction in a pairing group to obtain new publicly-verifiable statistical NIZK arguments from pairings with a qualitatively weaker assumption than existing constructions of pairing-based statistical NIZKs. Our constructions follow the classic paradigm of Feige, Lapidot, and Shamir (FLS). While the FLS framework has traditionally been used to construct computational (DV)-NIZK proofs, we newly show that the same framework can be leveraged to construct dual-mode (DV)-NIZKs.

Available format(s)
Category
Foundations
Publication info
A major revision of an IACR publication in EUROCRYPT 2020
Keywords
zero knowledgeNIZKstatistical ZKdesignated-verifier NIZK
Contact author(s)
dwu4 @ virginia edu
History
Short URL
https://ia.cr/2020/265

CC BY

BibTeX

@misc{cryptoeprint:2020/265,
author = {Benoît Libert and Alain Passelègue and Hoeteck Wee and David J.  Wu},
title = {New Constructions of Statistical NIZKs: Dual-Mode DV-NIZKs and More},
howpublished = {Cryptology ePrint Archive, Paper 2020/265},
year = {2020},
note = {\url{https://eprint.iacr.org/2020/265}},
url = {https://eprint.iacr.org/2020/265}
}

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