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

Name: Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography
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Author: Delaram Kahrobaei, Vladimir Shpilrain
ISBN: 9780821898598

av Delaram Kahrobaei, Vladimir Shpilrain

Häftad, Engelska, 2015-03-30

2013

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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.

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Algebra and Computer Science

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Applications of Group Theory in Cryptography

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Delaram Kahrobaei, City University of New York, NY, USA. Vladimir Shpilrain, City College of New York, NY, USA.

Secret sharing using non-commutative groups and the shortlex order by B. Cavallo and D. Kahrobaei An algorithm that decides conjugacy in a certain generalized free product by A. E. Clement Classification of automorphic conjugacy classes in the free group on two generators by B. Cooper and E. Rowland On elementary free groups by B. Fine, A. Gaglione, G. Rosenberger, and D. Spellman An application of a localized version of an axiom of Ian Chiswell by A. M. Gaglione, S. Lipschutz, and D. Spellman A note on Stallings' pregroups by A. M. Gaglione, S. Lipschutz, and D. Spellman A CCA secure cryptosystem using matrices over group rings by D. Kahrobaei, C. Koupparis, and V. Shpilrain The MOR cryptosystem and finite $p$-groups by A. Mahalanobis A group theoretical ElGamal cryptosystem based on a semidirect product of groups and a proposal for a signature protocol by A. I. S. Moldenhauer On some algorithmic properties of finite state automorphisms of rooted trees by B. Steinberg