List-decoding of linear functions and analysis of a two-round zero-knowledge argument

Cynthia Dwork, Ronen Shaltiel, Adam Smith, Luca Trevisan

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Abstract

Dwork and Stockmeyer showed 2-round zero-knowledge proof systems secure against provers which are resource-bounded during the interaction [6]. The resources considered are running time and advice (the amount of precomputed information). We re-cast this construction in the language of list-decoding. This perspective leads to the following improvements: 1. We give a new, simpler analysis of the protocol's unconditional security in the advice-bounded case. Like the original, the new analysis is asymptotically tight. 2. When the prover is bounded in both time and advice, we substantially improve the analysis of [6]: we prove security under a worst-case (instead of average-case) hardness assumption. Specifically, we assume that there exists g ∈ DTIME(2 3) such that g is hard in the worst case for MAM circuits of size O(2s(1/2+γ)) for some γ > 0. Here s is the input length and MAM corresponds the class of circuits which are verifiers in a 3-message interactive proof (with constant soundness error) in which the prover sends the first message. In contrast, Dwork and Stockmeyer require a function that is average-case hard for "proof auditors," a model of computation which generalizes randomized, non-deterministic circuits. 3. Our analyses rely on new results on list-decodability of codes whose codewords are linear functions from {0,1}l to {0,1}l. For (1), we show that the set of all linear transformations is a good list-decodable code. For (2), we give a new, non-deterministic list-decoding procedure which runs in time quasi-linear in l.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsMoni Naor
PublisherSpringer Verlag
Pages101-120
Number of pages20
ISBN (Print)3540210008, 9783540210009
DOIs
StatePublished - 2004

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2951
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Dwork, C., Shaltiel, R., Smith, A., & Trevisan, L. (2004). List-decoding of linear functions and analysis of a two-round zero-knowledge argument. In M. Naor (Ed.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 101-120). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2951). Springer Verlag. https://doi.org/10.1007/978-3-540-24638-1_6