**Contemporary Mathematics**

Volume: 633;
2015;
123 pp;
Softcover

MSC: Primary 20; 68;

Print ISBN: 978-0-8218-9859-8

Product Code: CONM/633

List Price: $105.00

Individual Member Price: $84.00

**Electronic ISBN: 978-1-4704-2263-9
Product Code: CONM/633.E**

List Price: $105.00

Individual Member Price: $84.00

# Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography

Share this page *Edited by *
*Delaram Kahrobaei; Vladimir Shpilrain*

This volume contains the proceedings of the AMS Special Session on Algorithmic Problems of Group Theory and Their Complexity, held January 9–10, 2013 in San Diego, CA and the AMS Special Session on Algorithmic Problems of Group Theory and Applications to Information Security, held April 6–7, 2013 at Boston College, Chestnut Hill, MA.

Over the past few years the field of group-based cryptography has attracted attention from both group theorists and cryptographers. The new techniques inspired by algorithmic problems in non-commutative group theory and their complexity have offered promising ideas for developing new cryptographic protocols. The papers in this volume cover algorithmic group theory and applications to cryptography.

#### Table of Contents

# Table of Contents

## Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- Secret sharing using non-commutative groups and the shortlex order 110 free
- An algorithm that decides conjugacy in a certain generalized free product 918
- Classification of automorphic conjugacy classes in the free group on two generators 1322
- 1. Introduction 1322
- 2. The graph Γ(𝑊) 1726
- 3. Non-root classes 2231
- 4. Root classes 2736
- 5. Enumeration 3241
- Appendix A. Table of automorphic conjugacy classes 3544
- Appendix B. Number of automorphic conjugacy classes of each type 3847
- Appendix C. Number of paths of each size 3948
- Acknowledgement 3948
- References 3948

- On elementary free groups 4150
- 1. Introduction 4150
- 2. The Tarski Problems and Elementary Free Groups 4251
- 3. Surface Groups and Magnus’ Theorem 4554
- 4. Cyclic Centralizers and Commuting Elements 4655
- 5. Hyperbolicity and Stable Hyperbolicity 4958
- 6. The Retract Theorem and Turner Groups 4958
- 7. Conjugacy Separability of Elementary Free Groups 5059
- 8. Tame Automorphisms of Elementary Free Groups 5160
- 9. Faithful Representations in 𝑃𝑆𝐿(2,\C) 5261
- References 5564

- An application of a localized version of an axiom of Ian Chiswell 5968
- A note on Stallings’ pregroups 6574
- A CCA secure cryptosystem using matrices over group rings 7382
- The MOR cryptosystem and finite 𝑝-groups 8190
- 1. Introduction 8190
- 2. Definitions and notations 8291
- 3. The MOR cryptosystem 8392
- 4. MOR cryptosystems on finite 𝑝-groups using 𝑝′-automorphisms 8695
- 5. The MOR cryptosystem and elementary abelian 𝑝-group 8897
- 6. The extra-special 𝑝-groups and its automorphism group 9099
- 7. MOR cryptosystems on finite 𝑝-groups using 𝑝-automorphisms 93102
- 8. Conclusion 94103
- References 94103

- A group theoretical ElGamal cryptosystem based on a semidirect product of groups and a proposal for a signature protocol 97106
- On some algorithmic properties of finite state automorphisms of rooted trees 115124
- Back Cover Back Cover1136

#### Readership

Graduate students and research mathematicians interested in group theory and crytography.