The knowledge tightness of parallel zero-knowledge

Kai Min Chung*, Rafael Pass, Wei Lung Dustin Tseng

*Corresponding author for this work

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


We investigate the concrete security of black-box zero- knowledge protocols when composed in parallel. As our main result, we give essentially tight upper and lower bounds (up to logarithmic factors in the security parameter) on the following measure of security (closely related to knowledge tightness): the number of queries made by black-box simulators when zero-knowledge protocols are composed in parallel. As a function of the number of parallel sessions, k, and the round complexity of the protocol, m, the bound is roughly k 1/m. We also construct a modular procedure to amplify simulator-query lower bounds (as above), to generic lower bounds in the black-box concurrent zero-knowledge setting. As a demonstration of our techniques, we give a self-contained proof of the o(logn /loglogn) lower bound for the round complexity of black-box concurrent zero-knowledge protocols, first shown by Canetti, Kilian, Petrank and Rosen (STOC 2002). Additionally, we give a new lower bound regarding constant-round black-box concurrent zero-knowledge protocols: the running time of the black-box simulator must be at least n Ω(logn).

Original languageEnglish
Title of host publicationTheory of Cryptography - 9th Theory of Cryptography Conference, TCC 2012, Proceedings
Number of pages18
StatePublished - 2012
Externally publishedYes
Event9th Theory of Cryptography Conference, TCC 2012 - Taormina, Sicily, Italy
Duration: 19 Mar 201221 Mar 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7194 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th Theory of Cryptography Conference, TCC 2012
CityTaormina, Sicily


  • Concrete Security
  • Concurrent Zero-Knowledge Lower Bounds
  • Knowledge Tightness
  • Zero-Knowledge


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