Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography
Author | : Delaram Kahrobaei |
Publisher | : |
Total Pages | : 123 |
Release | : 2015 |
Genre | : Algebra |
ISBN | : 9781470422639 |
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Author | : Delaram Kahrobaei |
Publisher | : |
Total Pages | : 123 |
Release | : 2015 |
Genre | : Algebra |
ISBN | : 9781470422639 |
Author | : Delaram Kahrobaei |
Publisher | : American Mathematical Soc. |
Total Pages | : 136 |
Release | : 2015-02-25 |
Genre | : Business & Economics |
ISBN | : 0821898590 |
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.
Author | : Alexei Myasnikov |
Publisher | : Springer Science & Business Media |
Total Pages | : 192 |
Release | : 2008-07-17 |
Genre | : Language Arts & Disciplines |
ISBN | : 3764388269 |
This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. It is also shown that there is a 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. Then, complexity theory, notably generic-case complexity of algorithms, is employed for cryptanalysis of various cryptographic protocols based on infinite groups, and the ideas and machinery from the theory of generic-case complexity are used to study asymptotically dominant properties of some infinite groups that have been applied in public key cryptography so far. Its elementary exposition makes the book accessible to graduate as well as undergraduate students in mathematics or computer science.
Author | : Alexei G. Myasnikov |
Publisher | : American Mathematical Soc. |
Total Pages | : 402 |
Release | : 2011 |
Genre | : Computers |
ISBN | : 0821853600 |
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 |
Publisher | : |
Total Pages | : 0 |
Release | : 2024 |
Genre | : Business & Economics |
ISBN | : 9781470474690 |
Author | : Frédérique Bassino |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 386 |
Release | : 2020-06-08 |
Genre | : Mathematics |
ISBN | : 3110667029 |
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 | : Maria Isabel Gonzalez Vasco |
Publisher | : CRC Press |
Total Pages | : 244 |
Release | : 2015-04-01 |
Genre | : Computers |
ISBN | : 1584888377 |
Group theory appears to be a promising source of hard computational problems for deploying new cryptographic constructions. This reference focuses on the specifics of using groups, including in particular non-Abelian groups, in the field of cryptography. It provides an introduction to cryptography with emphasis on the group theoretic perspective, making it one of the first books to use this approach. The authors provide the needed cryptographic and group theoretic concepts, full proofs of essential theorems, and formal security evaluations of the cryptographic schemes presented. They also provide references for further reading and exercises at the end of each chapter.
Author | : María Isabel González Vasco |
Publisher | : MDPI |
Total Pages | : 164 |
Release | : 2020-04-22 |
Genre | : Mathematics |
ISBN | : 3039288024 |
Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: post-quantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in non-abelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, post-quantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.
Author | : Alexei G. Myasnikov |
Publisher | : American Mathematical Soc. |
Total Pages | : 186 |
Release | : 2004 |
Genre | : Language Arts & Disciplines |
ISBN | : 0821834444 |
This volume consists of contributions by speakers at the AMS Special Session on Combinatorial and Statistical Group Theory held at New York University. Readers will find a variety of contributions, including survey papers on applications of group theory in cryptography, research papers on various aspects of statistical group theory, and papers on more traditional combinatorial group theory. The book is suitable for graduate students and research mathematicians interested in group theory and its applications to cryptography.
Author | : Alexandre Borovik |
Publisher | : American Mathematical Soc. |
Total Pages | : 236 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9780821856840 |
Since its origin in the early 20th century, combinatorial group theory has been primarily concerned with algorithms for solving particular problems on groups given by generators and relations: word problems, conjugacy problems, isomorphism problems, etc. Recent years have seen the focus of algorithmic group theory shift from the decidability/undecidability type of result to the complexity of algorithms. Papers in this volume reflect that paradigm shift. Articles are based on the AMS/ASL Joint Special Session, Interactions Between Logic, Group Theory and Computer Science. The volume is suitable for graduate students and research mathematicians interested in computational problems of group theory.