**Contemporary Mathematics**

Volume: 360;
2004;
177 pp;
Softcover

MSC: Primary 20; 57; 68; 94;

Print ISBN: 978-0-8218-3444-2

Product Code: CONM/360

List Price: $69.00

Individual Member Price: $55.20

**Electronic ISBN: 978-0-8218-7950-4
Product Code: CONM/360.E**

List Price: $69.00

Individual Member Price: $55.20

# Group Theory, Statistics, and Cryptography

Share this page *Edited by *
*Alexei G. Myasnikov; Vladimir Shpilrain*

This 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.

#### Table of Contents

# Table of Contents

## Group Theory, Statistics, and Cryptography

- Contents iii4 free
- Preface v6 free
- On power- and commutation transitive, power commutative, and restricted Gromov groups 18 free
- Braid-based cryptography 512
- Discriminating and squarelike groups I: Axiomatics 3542
- The density of small words in a free group is 0 4754
- Braid groups and Aut(F2) are not rigid 5158
- On varieties of groups in which all periodic groups are abelian 5562
- Subgroups of fully residually free groups: algorithmic problems 6370
- 1. Introduction 6370
- 2. Preliminaries 6572
- 3. Intersection of two finitely generated subgroups of FZ[t] 7279
- 4. Properties of intersections of finitely generated subgroups of FZ[t] 7885
- 5. Centralizers in finitely generated fully residually free groups 98105
- 6. Conjugacy problem in finitely generated subgroups of FZ[t] 100107
- References 101108

- Weak hyperbolicity and free constructions 103110
- Some properties of the conjugacy class growth function 113120
- Boundary test elements 119126
- Geodesics in the braid group on three strands 133140
- Remarks on the growth of inverse semigroups 151158
- Assessing security of some group based cryptosystems 167174

#### Readership

Graduate students and research mathematicians interested in group theory and its applications to cryptography.