Weak zero-knowledge beyond the black-box barrier

Nir Bitansky, Dakshita Khurana, Omer Paneth

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The round complexity of zero-knowledge protocols is a longstanding open question, yet to be settled under standard assumptions. So far, the question has appeared equally challenging for relaxations such as weak zero-knowledge and witness hiding. Protocols satisfying these relaxed notions under standard assumptions have at least four messages, just like full-fledged zero-knowledge. The difficulty in improving round complexity stems from a fundamental barrier: none of these notions can be achieved in three messages via reductions (or simulators) that treat the verifier as a black box. We introduce a new non-black-box technique and use it to obtain the first protocols that cross this barrier under standard assumptions. We obtain weak zero-knowledge for NP in two messages, assuming the existence of quasipolynomially-secure fully-homomorphic encryption and other standard primitives (known based on the quasipolynomial hardness of Learning with Errors), and subexponentially-secure one-way functions. We also obtain weak zero-knowledge for NP in three messages under standard polynomial assumptions (following for example from fully homomorphic encryption and factoring). We also give, under polynomial assumptions, a two-message witness-hiding protocol for any language L ∈ NP that has a witness encryption scheme. This protocol is publicly verifiable. Our technique is based on a new homomorphic trapdoor paradigm, which can be seen as a non-black-box analog of the classic Feige-Lapidot-Shamir trapdoor paradigm.

Original languageEnglish
Title of host publicationSTOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
EditorsMoses Charikar, Edith Cohen
PublisherAssociation for Computing Machinery
Pages1091-1102
Number of pages12
ISBN (Electronic)9781450367059
DOIs
StatePublished - 23 Jun 2019
Event51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, United States
Duration: 23 Jun 201926 Jun 2019

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019
Country/TerritoryUnited States
CityPhoenix
Period23/06/1926/06/19

Keywords

  • Homomorphic trapdoor
  • Non black-box simulation
  • Witness hiding
  • Zero-knowledge

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