Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography
About this Title
Delaram Kahrobaei, City University of New York, New York, NY and Vladimir Shpilrain, City College of New York, New York, NY, Editors
Publication: Contemporary Mathematics
Publication Year 2015: Volume 633
ISBNs: 978-0-8218-9859-8 (print); 978-1-4704-2263-9 (online)
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.
Graduate students and research mathematicians interested in group theory and crytography.
Table of Contents
- Bren Cavallo and Delaram Kahrobaei – Secret sharing using non-commutative groups and the shortlex order
- Anthony E. Clement – An algorithm that decides conjugacy in a certain generalized free product
- Bobbe Cooper and Eric Rowland – Classification of automorphic conjugacy classes in the free group on two generators
- Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger and Dennis Spellman – On elementary free groups
- Anthony M. Gaglione, Seymour Lipschutz and Dennis Spellman – An application of a localized version of an axiom of Ian Chiswell
- Anthony M. Gaglione, Seymour Lipschutz and Dennis Spellman – A note on Stallings’ pregroups
- Delaram Kahrobaei, Charalambos Koupparis and Vladimir Shpilrain – A CCA secure cryptosystem using matrices over group rings
- Ayan Mahalanobis – The MOR cryptosystem and finite $p$-groups
- Anja I. S. Moldenhauer – A group theoretical ElGamal cryptosystem based on a semidirect product of groups and a proposal for a signature protocol
- Benjamin Steinberg – On some algorithmic properties of finite state automorphisms of rooted trees