## Group Theory, Statistics, and Cryptography: AMS Special Session Combinatorial and Statistical Group Theory, April 12-13, 2003, New York UniversityThis volume consists of contributions by speakers at the AMS Special Session on Combinatorial and Statistical Group Theory held at New York University. Readers will find a variety of contributions, including survey papers on applications of group theory in cryptography, research papers on various aspects of statistical group theory, and papers on more traditional combinatorial group theory. The book is suitable for graduate students and research mathematicians interested in group theory and its applications to cryptography. |

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### Contents

1 | |

5 | |

Axiomatics | 35 |

The density of small words in a free group is 0 | 47 |

Braid groups and AutF2 are not rigid | 51 |

On varieties of groups in which all periodic groups are abelian | 55 |

algorithmic problems | 63 |

Weak hyperbolicity and free constructions | 103 |

Some properties of the conjugacy class growth function | 113 |

Boundary test elements | 119 |

Geodesics in the braid group on three strands | 133 |

Remarks on the growth of inverse semigroups | 151 |

Assessing security of some group based cryptosystems | 167 |

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abelian group Algebra algorithm assume attacks boundary test elements braid groups braid word Cayley graph class of squarelike complexity compute conjugacy classes Conjugacy Problem conjugate braids Conjugator Search Problem Corollary coset cryptography cryptosystem cyclically reduced defined definition denote discriminating groups eacists edge equivalent exists a path finitely generated fully finitely generated subgroups finitely presented follows Fººl fully residually free g e G geodesic geodesic growth series group G group theory hash function Hence HNN-extension hyperbolic groups infinite word initial segment integer inverse semigroup Ja(H Lemma length Let G Let H linear Math Mathematics Subject Classification monomorphism Myasnikov normal form o e Z[t oſp path q Proof Proposition proved quasi-isometry rank reduced word representation residually free group result scheme squarelike groups subset subwords Suppose syllable test word Theorem tſp u-components ultraproducts vertex weakly hyperbolic relative X)-graph