The action of a few random permutations on r-tuples and an application to cryptography

Joel Friedman, Antoine Joux, Yuval Roichman, Jacques Stern, Jean Pierre Tillich

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

2 Scopus citations

Abstract

We prove that for every r and d≥2 there is a C such that for most choices of d permutations π 1, π2, ..., πd of Sn , a product of less than C log n of these permutations is needed to map any r-tuple of distinct integers to another r-tuple. We came across this problem while studying a seemingly unrelated cryptographic problem, and use this result in order to show that certain cryptographic devices using permutation automata are highly insecure. The proof techniques we develop here give more general results, and constitute a first step towards the study of expansion properties of random Cayley graphs over the symmetric group, whose relevance to theoretical computer science is well-known (see [B&al90]).

Original languageEnglish
Title of host publicationSTACS 1996 - 13th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings
EditorsClaude Puech, Rudiger Reischuk
PublisherSpringer Verlag
Pages375-386
Number of pages12
ISBN (Print)9783540609223
DOIs
StatePublished - 1996
Externally publishedYes
Event13th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1996 - Grenoble, France
Duration: 22 Feb 199624 Feb 1996

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1046
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1996
Country/TerritoryFrance
CityGrenoble
Period22/02/9624/02/96

Bibliographical note

Publisher Copyright:
© 1996, Springer Verlag. All rights reserved.

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