Algebra and Computer Science
About this Title
Delaram Kahrobaei, CUNY Graduate Center, City University of New York, New York, NY, Bren Cavallo, CUNY Graduate Center, City University of New York, New York, NY and David Garber, Holon Institute of Technology, Holon, Israel, Editors
Publication: Contemporary Mathematics
Publication Year: 2016; Volume 677
ISBNs: 978-1-4704-2303-2 (print); 978-1-4704-3587-5 (online)
This volume contains the proceedings of three special sessions: Algebra and Computer Science, held during the Joint AMS-EMS-SPM meeting in Porto, Portugal, June 10–13, 2015; Groups, Algorithms, and Cryptography, held during the Joint Mathematics Meeting in San Antonio, TX, January 10–13, 2015; and Applications of Algebra to Cryptography, held during the Joint AMS-Israel Mathematical Union meeting in Tel-Aviv, Israel, June 16–19, 2014.
Papers contained in this volume address a wide range of topics, from theoretical aspects of algebra, namely group theory, universal algebra and related areas, to applications in several different areas of computer science.
From the computational side, the book aims to reflect the rapidly emerging area of algorithmic problems in algebra, their computational complexity and applications, including information security, constraint satisfaction problems, and decision theory.
The book gives special attention to recent advances in quantum computing that highlight the need for a variety of new intractability assumptions and have resulted in a new area called group-based cryptography.
Graduate students and research mathematicians interested in cryptography, algebra, group theory, semigroup theory, information security, and theoretical computer science.
Table of Contents
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- Frédérique Bassino, Cyril Nicaud and Pascal Weil – Generic properties of subgroups of free groups and finite presentations
- Chi Sing Chum and Xiaowen Zhang – A new multi-server scheme for private information retrieval
- Chi Sing Chum, Benjamin Fine, Anja I. S. Moldenhauer, Gerhard Rosenberger and Xiaowen Zhang – On secret sharing protocols
- Maggie E. Habeeb – A verifiable secret sharing scheme using non-abelian groups
- Arkadius Kalka – Non-associative public-key cryptography
- Arkadius Kalka and Mina Teicher – Non-associative key establishment protocols and their implementation
- Daniel König, Markus Lohrey and Georg Zetzsche – Knapsack and subset sum problems in nilpotent, polycyclic, and co-context-free groups
- Anja I. S. Moldenhauer, Gerhard Rosenberger and Kristina Rosenthal – On the Tits alternative for a class of finitely presented groups with a special focus on symbolic computations
- Andrew Sale – Geometry of the conjugacy problem in lamplighter groups
- Armin Weiß – A logspace solution to the word and conjugacy problem of generalized Baumslag-Solitar groups
- Serena Yuan – Cryptographic hash functions from sequences of lifted Paley graphs