Computational and Combinatorial Group Theory and Cryptography
About this Title
Benjamin Fine, Fairfield University, Fairfield, CT, Delaram Kahrobaei, CUNY Graduate Center, New York, NY and Gerhard Rosenberger, University of Hamburg, Hamburg, Germany, Editors
Publication: Contemporary Mathematics
Publication Year 2012: Volume 582
ISBNs: 978-0-8218-7563-6 (print); 978-0-8218-9404-0 (online)
This volume contains the proceedings of the AMS Special Session on Computational Algebra, Groups, and Applications, held April 30–May 1, 2011, at the University of Nevada, Las Vegas, Nevada, and the AMS Special Session on the Mathematical Aspects of Cryptography and Cyber Security, held September 10–11, 2011, at Cornell University, Ithaca, New York.
Over the past twenty years combinatorial and infinite group theory has been energized by three developments: the emergence of geometric and asymptotic group theory, the development of algebraic geometry over groups leading to the solution of the Tarski problems, and the development of group-based cryptography. These three areas in turn have had an impact on computational algebra and complexity theory.
The papers in this volume, both survey and research, exhibit the tremendous vitality that is at the heart of group theory in the beginning of the twenty-first century as well as the diversity of interests in the field.
Graduate students and research mathematicians interested in combinatorial and computational group theory and their applications to cryptography.
Table of Contents
- Rashid Ali and Martin Kreuzer – Weyl Gröbner Basis Cryptosystems
- Gilbert Baumslag, Roman Mikhailov and Kent E. Orr – A New Look at Finitely Generated Metabelian Groups
- Marianna Bonanome, Margaret H. Dean and Marcos Zyman – $IA$-Automorphisms of Groups with Almost Constant Upper Central Series
- Chi Sing Chum, Benjamin Fine, Gerhard Rosenberger and Xiaowen Zhang – A Proposed Alternative to the Shamir Secret Sharing Scheme
- Chi Sing Chum and Xiaowen Zhang – Improving Latin Square Based Secret Sharing Schemes
- Anthony E. Clement – A Hand-Computation Involving Surface Groups, the Reidemeister-Schreier Rewriting Process and Kurosh Subgroup Theorem
- Margaret H. Dean, Stephen Majewicz and Marcos Zyman – Adjunction of Roots in Exponential A-Groups
- Volker Diekert, Jonathan Kausch and Markus Lohrey – Logspace Computations in Coxeter Groups and Graph Groups
- Bettina Eick – Collection by Polynomials in Finite $p$-groups
- Benjamin Fine, Alexander Hulpke and Gerhard Rosenberger – All Finite Generalized Tetrahedon Groups II
- Benjamin Fine and Gerhard Rosenberger – The Classification of One Relator Limit Groups and the Surface Group Conjecture
- Anthony M. Gaglione, Seymour Lipschutz and Dennis Spellman – Discrimination and Separation in the Metabelian Variety
- Maggie Habeeb, Delaram Kahrobaei and Vladimir Shpilrain – A Secret Sharing Scheme Based on Group Presentations and the Word Problem
- Stanislaw Jarecki and Nitesh Saxena – Authenticated Key Agreement with Key Re-Use in the Short Authenticated Strings Model
- Delaram Kahrobaei and Elizabeth Vidaurre – Publicly Verifiable Secret Sharing Using Non-Abelian Groups
- Matthias Neumann-Brosig – A Note on the Hyperbolicity of Strict Pride Groups
- Ellen Ziliak – An Algorithm to Express Words as a Product of Conjugates of Relators