On the randomness complexity of interactive proofs and statistical zero-knowledge proofs

Benny Applebaum*, Eyal Golombek*

*Corresponding author for this work

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

2 Scopus citations

Abstract

We study the randomness complexity of interactive proofs and zero-knowledge proofs. In particular, we ask whether it is possible to reduce the randomness complexity, R, of the verifier to be comparable with the number of bits, CV, that the verifier sends during the interaction. We show that such randomness sparsification is possible in several settings. Specifically, unconditional sparsification can be obtained in the non-uniform setting (where the verifier is modelled as a circuit), and in the uniform setting where the parties have access to a (reusable) common-random-string (CRS). We further show that constant-round uniform protocols can be sparsified without a CRS under a plausible worst-case complexity-theoretic assumption that was used previously in the context of derandomization. All the above sparsification results preserve statistical-zero knowledge provided that this property holds against a cheating verifier. We further show that randomness sparsification can be applied to honest-verifier statistical zero-knowledge (HVSZK) proofs at the expense of increasing the communication from the prover by R − F bits, or, in the case of honest-verifier perfect zero-knowledge (HVPZK) by slowing down the simulation by a factor of 2RF. Here F is a new measure of accessible bit complexity of an HVZK proof system that ranges from 0 to R, where a maximal grade of R is achieved when zero-knowledge holds against a “semi-malicious” verifier that maliciously selects its random tape and then plays honestly. Consequently, we show that some classical HVSZK proof systems, like the one for the complete Statistical-Distance problem (Sahai and Vadhan, JACM 2003) admit randomness sparsification with no penalty. Along the way we introduce new notions of pseudorandomness against interactive proof systems, and study their relations to existing notions of pseudorandomness.

Original languageEnglish
Title of host publication2nd Conference on Information-Theoretic Cryptography, ITC 2021
EditorsStefano Tessaro
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771979
DOIs
StatePublished - 1 Jul 2021
Event2nd Conference on Information-Theoretic Cryptography, ITC 2021 - Virtual, Bertinoro, Italy
Duration: 23 Jul 202126 Jul 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume199
ISSN (Print)1868-8969

Conference

Conference2nd Conference on Information-Theoretic Cryptography, ITC 2021
Country/TerritoryItaly
CityVirtual, Bertinoro
Period23/07/2126/07/21

Funding

FundersFunder number
Check Point Institute for Information Security
ERC-StG-2014-2020639813 ERC-CLC
European Union's Horizon 2020 Programme
European Union’s Horizon 2020 Programme
Horizon 2020 Framework Programme639813

    Keywords

    • Interactive proofs
    • Pseudorandomness
    • Zero-knowledge proofs

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