Computational And Combinatorial Group Theory And Cryptography
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Computational And Combinatorial Group Theory And Cryptography
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Author : Benjamin Fine
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Computational And Combinatorial Group Theory And Cryptography written by Benjamin Fine and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Computers categories.
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.
Group Based Cryptography
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Author : Alexei Myasnikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-04
Group Based Cryptography written by Alexei Myasnikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-04 with Mathematics categories.
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.
Public Key Cryptography And Computational Number Theory
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Author : Kazimierz Alster
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24
Public Key Cryptography And Computational Number Theory written by Kazimierz Alster and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.
The Proceedings contain twenty selected, refereed contributions arising from the International Conference on Public-Key Cryptography and Computational Number Theory held in Warsaw, Poland, on September 11-15, 2000. The conference, attended by eightyfive mathematicians from eleven countries, was organized by the Stefan Banach International Mathematical Center. This volume contains articles from leading experts in the world on cryptography and computational number theory, providing an account of the state of research in a wide variety of topics related to the conference theme. It is dedicated to the memory of the Polish mathematicians Marian Rejewski (1905-1980), Jerzy Róøycki (1909-1942) and Henryk Zygalski (1907-1978), who deciphered the military version of the famous Enigma in December 1932 January 1933. A noteworthy feature of the volume is a foreword written by Andrew Odlyzko on the progress in cryptography from Enigma time until now.
Group Theory Statistics And Cyptography
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Author : Alexei G. Myasnikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Group Theory Statistics And Cyptography written by Alexei G. Myasnikov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Cryptology And Computational Number Theory
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Author : Carl Pomerance
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Cryptology And Computational Number Theory written by Carl Pomerance and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Computers categories.
In the past dozen or so years, cryptology and computational number theory have become increasingly intertwined. Because the primary cryptologic application of number theory is the apparent intractability of certain computations, these two fields could part in the future and again go their separate ways. But for now, their union is continuing to bring ferment and rapid change in both subjects. This book contains the proceedings of an AMS Short Course in Cryptology and Computational Number Theory, held in August 1989 during the Joint Mathematics Meetings in Boulder, Colorado. These eight papers by six of the top experts in the field will provide readers with a thorough introduction to some of the principal advances in cryptology and computational number theory over the past fifteen years. In addition to an extensive introductory article, the book contains articles on primality testing, discrete logarithms, integer factoring, knapsack cryptosystems, pseudorandom number generators, the theoretical underpinnings of cryptology, and other number theory-based cryptosystems. Requiring only background in elementary number theory, this book is aimed at nonexperts, including graduate students and advanced undergraduates in mathematics and computer science.
Non Commutative Cryptography And Complexity Of Group Theoretic Problems
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Author : Alexei G. Myasnikov
language : en
Publisher:
Release Date : 2012
Non Commutative Cryptography And Complexity Of Group Theoretic Problems written by Alexei G. Myasnikov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Combinatorial group theory categories.
Algorithms And Classification In Combinatorial Group Theory
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Author : Gilbert Baumslag
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algorithms And Classification In Combinatorial Group Theory written by Gilbert Baumslag and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The papers in this volume are the result of a workshop held in January 1989 at the Mathematical Sciences Research Institute. Topics covered include decision problems, finitely presented simple groups, combinatorial geometry and homology, and automatic groups and related topics.
Interactions Between Group Theory Symmetry And Cryptology
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Author : María Isabel González Vasco
language : en
Publisher: MDPI
Release Date : 2020-04-22
Interactions Between Group Theory Symmetry And Cryptology written by María Isabel González Vasco and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-22 with Mathematics categories.
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.
Group Theoretic Cryptography
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Author : Maria Isabel Gonzalez Vasco
language : en
Publisher: CRC Press
Release Date : 2015-04-01
Group Theoretic Cryptography written by Maria Isabel Gonzalez Vasco and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-01 with Computers categories.
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.
Non Commutative Cryptography And Complexity Of Group Theoretic Problems
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Author : Sandy Weedman
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2014-10-30
Non Commutative Cryptography And Complexity Of Group Theoretic Problems written by Sandy Weedman and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-30 with categories.
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.