New Constructions of Reusable Designated-Verifier NIZKs

Alex Lombardi, Willy Quach, Ron D. Rothblum, Daniel Wichs, David J. Wu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Scopus citations

Abstract

Non-interactive zero-knowledge arguments (NIZKs) for (Formula Presented) are an important cryptographic primitive, but we currently only have instantiations under a few specific assumptions. Notably, we are missing constructions from the learning with errors (LWE) assumption, the Diffie-Hellman (CDH/DDH) assumption, and the learning parity with noise (LPN) assumption. In this paper, we study a relaxation of NIZKs to the designated-verifier setting (DV-NIZK), where a trusted setup generates a common reference string together with a secret key for the verifier. We want reusable schemes, which allow the verifier to reuse the secret key to verify many different proofs, and soundness should hold even if the malicious prover learns whether various proofs are accepted or rejected. Such reusable DV-NIZKs were recently constructed under the CDH assumption, but it was open whether they can also be constructed under LWE or LPN. We also consider an extension of reusable DV-NIZKs to the malicious designated-verifier setting (MDV-NIZK). In this setting, the only trusted setup consists of a common random string. However, there is also an additional untrusted setup in which the verifier chooses a public/secret key needed to generate/verify proofs, respectively. We require that zero-knowledge holds even if the public key is chosen maliciously by the verifier. Such reusable MDV-NIZKs were recently constructed under the “one-more CDH” assumption, but constructions under CDH/LWE/LPN remained open. In this work, we give new constructions of (reusable) DV-NIZKs and MDV-NIZKs using generic primitives that can be instantiated under CDH, LWE, or LPN.

Original languageEnglish (US)
Title of host publicationAdvances in Cryptology – CRYPTO 2019 - 39th Annual International Cryptology Conference, Proceedings
EditorsDaniele Micciancio, Alexandra Boldyreva
PublisherSpringer Verlag
Pages670-700
Number of pages31
ISBN (Print)9783030269531
DOIs
StatePublished - 2019
Externally publishedYes
Event39th Annual International Cryptology Conference, CRYPTO 2019 - Santa Barbara, United States
Duration: Aug 18 2019Aug 22 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11694 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference39th Annual International Cryptology Conference, CRYPTO 2019
Country/TerritoryUnited States
CitySanta Barbara
Period8/18/198/22/19

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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