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Author : Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov
Publisher : Unknown
Page : 128 pages
File Size : 52,5 Mb
Release : 2012
Category : Combinatorial group theory
ISBN : OCLC:732847858
Author : Sandy Weedman
Publisher : Createspace Independent Publishing Platform
Page : 402 pages
File Size : 55,6 Mb
Release : 2014-10-30
Category : Electronic
ISBN : 1974040321
This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public-key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research avenues within group theory. In particular, a lot of emphasis in the book is put on studying search problems, as compared to decision problems traditionally studied in combinatorial group theory.
Author : Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 52,9 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 9780821887004
Author : Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 53,9 Mb
Release : 2011
Category : Computers
ISBN : 9780821853603
Examines the relationship between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups can be used in public key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory.
Author : Delaram Kahrobaei,Vladimir Shpilrain
Publisher : Unknown
Page : 123 pages
File Size : 45,8 Mb
Release : 2015
Category : Algebra
ISBN : 1470422638
Author : Dmitry S. Kaliuzhnyi-Verbovetskyi,Victor Vinnikov
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 48,5 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9781470416973
In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is "dimensionless" matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, and quantum control.
Author : Frédérique Bassino,Ilya Kapovich,Markus Lohrey,Alexei Miasnikov,Cyril Nicaud,Andrey Nikolaev,Igor Rivin,Vladimir Shpilrain,Alexander Ushakov,Pascal Weil
Publisher : Walter de Gruyter GmbH & Co KG
Page : 386 pages
File Size : 45,6 Mb
Release : 2020-06-08
Category : Mathematics
ISBN : 9783110667028
This book shows new directions in group theory motivated by computer science. It reflects the transition from geometric group theory to group theory of the 21st century that has strong connections to computer science. Now that geometric group theory is drifting further and further away from group theory to geometry, it is natural to look for new tools and new directions in group theory which are present.
Author : Alexei Myasnikov,Vladimir Shpilrain,Alexander Ushakov
Publisher : Springer Science & Business Media
Page : 183 pages
File Size : 47,6 Mb
Release : 2008-11-04
Category : Mathematics
ISBN : 9783764388270
Covering relations between three different areas of mathematics and theoretical computer science, this book explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography.
Author : Benjamin Fine,Delaram Kahrobaei,Gerhard Rosenberger
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 54,5 Mb
Release : 2012
Category : Computers
ISBN : 9780821875636
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.
Author : Markus Lohrey
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 42,6 Mb
Release : 2014-04-04
Category : Mathematics
ISBN : 9781493907489
The Compressed Word Problem for Groups provides a detailed exposition of known results on the compressed word problem, emphasizing efficient algorithms for the compressed word problem in various groups. The author presents the necessary background along with the most recent results on the compressed word problem to create a cohesive self-contained book accessible to computer scientists as well as mathematicians. Readers will quickly reach the frontier of current research which makes the book especially appealing for students looking for a currently active research topic at the intersection of group theory and computer science. The word problem introduced in 1910 by Max Dehn is one of the most important decision problems in group theory. For many groups, highly efficient algorithms for the word problem exist. In recent years, a new technique based on data compression for providing more efficient algorithms for word problems, has been developed, by representing long words over group generators in a compressed form using a straight-line program. Algorithmic techniques used for manipulating compressed words has shown that the compressed word problem can be solved in polynomial time for a large class of groups such as free groups, graph groups and nilpotent groups. These results have important implications for algorithmic questions related to automorphism groups.
Author : Dmitri Koroliouk,Sergiy Lyashko,Nikolaos Limnios
Publisher : John Wiley & Sons
Page : 452 pages
File Size : 41,5 Mb
Release : 2024-04-16
Category : Science
ISBN : 9781394284337
Mathematical methods in engineering are characterized by a wide range of techniques for approaching various problems. Moreover, completely different analysis techniques can be applied to the same problem, which is justified by the difference in specific applications. Therefore, the study of the analyses and solutions of specific problems leads the researcher to generate their own techniques for the analysis of similar problems continuously arising in the process of technical development. Computational Methods and Mathematical Modeling in Cyberphysics and Engineering Applications contains solutions to specific problems in current areas of computational engineering and cyberphysics.
Author : Kohei Arai
Publisher : Springer Nature
Page : 721 pages
File Size : 43,5 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9783031540530
Author : Huanguo Zhang,Bo Zhao,Fei Yan
Publisher : Springer
Page : 410 pages
File Size : 48,6 Mb
Release : 2019-01-08
Category : Computers
ISBN : 9789811359132
This book constitutes the refereed proceedings of the Chinese Conference on Trusted Computing and Information Security, CTCIS 2018, held in Wuhan, China, in October 2018. The 24 revised full papers presented were carefully reviewed and selected from 73 submissions. The papers are centered around cryptography, systems security, trusted computing, information security, and network security.
Author : Mariana Durcheva
Publisher : Cambridge Scholars Publishing
Page : 132 pages
File Size : 53,8 Mb
Release : 2019-11-12
Category : Mathematics
ISBN : 9781527543317
Semirings as an algebraic structure have been known since 1934, but remained unapplied for mathematical purposes for a long time. It has only been in the past decade that they have been used in cryptography. The advantage of (additively) idempotent semirings is that the additive operation does not have an inverse, which can help in preventing the breakage of a cryptosystem. This book describes a number of cryptographic protocols, as well as the hard mathematical problems on which their security is based. It will appeal to cryptographers and specialists in applied algebra.
Author : Ngoc Thanh Nguyen,Tien Khoa Tran,Ualsher Tukayev,Tzung-Pei Hong,Bogdan Trawiński,Edward Szczerbicki
Publisher : Springer Nature
Page : 766 pages
File Size : 55,9 Mb
Release : 2022-12-08
Category : Computers
ISBN : 9783031219672
This book constitutes the refereed proceedings of the 14th Asian Conference on Intelligent Information and Database Systems, ACIIDS 2022, held Ho Chi Minh City, Vietnam in November 2022. The 113 full papers accepted for publication in these proceedings were carefully reviewed and selected from 406 submissions. The papers of the 2 volume-set are organized in the following topical sections: data mining and machine learning methods, advanced data mining techniques and applications, intelligent and contextual systems, natural language processing, network systems and applications, computational imaging and vision, decision support and control systems, and data modeling and processing for industry 4.0. The accepted and presented papers focus on new trends and challenges facing the intelligent information and database systems community.
