## Abstract

We prove that for every r and d≥2 there is a C such that for most choices of d permutations π _{1}, π_{2}, ..., π_{d} of S_{n} , 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 language | English |
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Title of host publication | STACS 1996 - 13th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings |

Editors | Claude Puech, Rudiger Reischuk |

Publisher | Springer Verlag |

Pages | 375-386 |

Number of pages | 12 |

ISBN (Print) | 9783540609223 |

DOIs | |

State | Published - 1996 |

Externally published | Yes |

Event | 13th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1996 - Grenoble, France Duration: 22 Feb 1996 → 24 Feb 1996 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1046 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 13th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1996 |
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Country/Territory | France |

City | Grenoble |

Period | 22/02/96 → 24/02/96 |

### Bibliographical note

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