Computational And Combinatorial Group Theory And Cryptography

Author : Benjamin Fine,Delaram Kahrobaei,Gerhard Rosenberger
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 53,6 Mb
Release : 2012
Category : Computers
ISBN : 9780821875636

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Computational and Combinatorial Group Theory and Cryptography by Benjamin Fine,Delaram Kahrobaei,Gerhard Rosenberger Pdf

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 : Alexei Myasnikov,Vladimir Shpilrain,Alexander Ushakov
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 54,7 Mb
Release : 2008-11-04
Category : Mathematics
ISBN : 9783764388270

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Group-based Cryptography by Alexei Myasnikov,Vladimir Shpilrain,Alexander Ushakov Pdf

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 : Carl Pomerance,Shafi Goldwasser
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 54,6 Mb
Release : 1990
Category : Computers
ISBN : 0821801554

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Cryptology and Computational Number Theory by Carl Pomerance,Shafi Goldwasser Pdf

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.

Author : Alexei G. Myasnikov,Vladimir Shpilrain
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 41,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821834442

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Group Theory, Statistics, and Cyptography by Alexei G. Myasnikov,Vladimir Shpilrain Pdf

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 : Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov
Publisher : Unknown
Page : 128 pages
File Size : 52,8 Mb
Release : 2012
Category : Combinatorial group theory
ISBN : OCLC:732847858

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Non-commutative Cryptography and Complexity of Group-theoretic Problems by Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov Pdf

Author : Kazimierz Alster,Jerzy Urbanowicz,Hugh C. Williams
Publisher : Walter de Gruyter
Page : 345 pages
File Size : 52,7 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110881035

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Public-Key Cryptography and Computational Number Theory by Kazimierz Alster,Jerzy Urbanowicz,Hugh C. Williams Pdf

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.

Author : Gilbert Baumslag,Charles F. III Miller
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461397304

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Algorithms and Classification in Combinatorial Group Theory by Gilbert Baumslag,Charles F. III Miller Pdf

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.

Author : María Isabel González Vasco
Publisher : MDPI
Page : 164 pages
File Size : 41,7 Mb
Release : 2020-04-22
Category : Mathematics
ISBN : 9783039288021

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Interactions between Group Theory, Symmetry and Cryptology by María Isabel González Vasco Pdf

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 : Sandy Weedman
Publisher : Createspace Independent Publishing Platform
Page : 402 pages
File Size : 44,7 Mb
Release : 2014-10-30
Category : Electronic
ISBN : 1974040321

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Non-commutative Cryptography and Complexity of Group-theoretic Problems by Sandy Weedman Pdf

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 : Maria Isabel Gonzalez Vasco,Rainer Steinwandt
Publisher : CRC Press
Page : 244 pages
File Size : 47,6 Mb
Release : 2015-04-01
Category : Computers
ISBN : 9781584888376

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Group Theoretic Cryptography by Maria Isabel Gonzalez Vasco,Rainer Steinwandt Pdf

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 : Luis M. Pardo,Jose Luis Montaña
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 42,9 Mb
Release : 2014-11-12
Category : Computers
ISBN : 9780821891506

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Recent Advances in Real Complexity and Computation by Luis M. Pardo,Jose Luis Montaña Pdf

This volume is composed of six contributions derived from the lectures given during the UIMP-RSME Lluis Santalo Summer School on ``Recent Advances in Real Complexity and Computation'', held July 16-20, 2012, in Santander, Spain. The goal of this Summer School was to present some of the recent advances on Smale's 17th Problem: ``Can a zero of $n$ complex polynomial equations in $n$ unknowns be found approximately, on the average, in polynomial time with a uniform algorithm?'' These papers cover several aspects of this problem: from numerical to symbolic methods in polynomial equation solving, computational complexity aspects (both worse and average cases and both upper and lower complexity bounds) as well as aspects of the underlying geometry of the problem. Some of the contributions also deal with either real or multiple solutions solving.

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783662036426

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Algebraic Aspects of Cryptography by Neal Koblitz Pdf

From the reviews: "This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. [...] Overall, this is an excellent expository text, and will be very useful to both the student and researcher." Mathematical Reviews

Author : Fine Benjamin,Gaglione Anthony,Baginski Paul
Publisher : World Scientific
Page : 260 pages
File Size : 52,7 Mb
Release : 2017-12-26
Category : Mathematics
ISBN : 9789813204065

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Infinite Group Theory: From The Past To The Future by Fine Benjamin,Gaglione Anthony,Baginski Paul Pdf

The development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest. Contents: Groups with the Weak Minimal Condition on Non-Permutable Subgroups (Laxmi K Chatuat and Martyn R Dixon)A Survey: Shamir Threshold Scheme and Its Enhancements (Chi Sing Chum, Benjamin Fine, and Xiaowen Zhang)The Zappa-Szep Product of Left-Orderable Groups (Fabienne Chouraqui)Totally Disconnected Groups From Baumslag-Solitar Groups (Murray Elder and George Willis)Elementary and Universal Theories of Nonabelian Commutative Transitive and CSA Groups (B Fine, A M Gaglione, and D Spellman)Commutative Transitivity and the CSA Property (Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger, and Dennis Spellman)The Universal Theory of Free Burnside Groups of Large Prime Exponent (Anthony M Gaglione, Seymour Lipschutz, and Dennis Spellman)Primitive Curve Lengths on Pairs of Pants (Jane Gilman)Drawing Inferences Under Maximum Entropy From Relational Probabilistic Knowledge Using Group Theory (Gabriele Kern-Isberner, Marco Wilhelm, and Christoph Beierle)On Some Infinite-Dimensional Linear Groups and the Structure of Related Modules (L A Kurdachenko and I Ya Subbotin)On New Analogs of Some Classical Group Theoretical Results in Lie Rings (L A Kurdachenko, A A Pypka and I Ya Subbotin)Log-Space Complexity of the Conjugacy Problem in Wreath Products (Alexei Myasnikov, Svetla Vassileva, and Armin Weiss)Group Presentations, Cayley Graphs and Markov Processes (Peter Olszewski) Readership: Graduate students and researchers in group theory. Keywords: Infinite Group Theory;Combinatorial Group Theory;Geometric Group TheoryReview: Key Features: This book is centered on infinite group theory from a combinatorial and geometric point of view. It also contains material on non-commutative algebraic group-based cryptography

Author : Delaram Kahrobaei,Bren Cavallo,David Garber
Publisher : American Mathematical Soc.
Page : 229 pages
File Size : 54,8 Mb
Release : 2016-11-28
Category : Algebra
ISBN : 9781470423032

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Algebra and Computer Science by Delaram Kahrobaei,Bren Cavallo,David Garber Pdf

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.

Author : Arkady. Berenstein,Vladimir. Retakh
Publisher : American Mathematical Soc.
Page : 265 pages
File Size : 51,8 Mb
Release : 2013-05-01
Category : Mathematics
ISBN : 9780821889800

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Noncommutative Birational Geometry, Representations and Combinatorics by Arkady. Berenstein,Vladimir. Retakh Pdf

"This volume contains the proceedings of the AMS Special Session on Noncommutative Birational Geometry, Representations and Cluster Algebras, held from January 6-7, 2012, in Boston, MA. The papers deal with various aspects of noncommutative birational geometry and related topics, focusing mainly on structure and representations of quantum groups and algebras, braided algebras, rational series in free groups, Poisson brackets on free algebras, and related problems in combinatorics. This volume is useful for researchers and graduate students in mathematics and mathematical physics who want to be introduced to different areas of current research in the new area of noncommutative algebra and geometry."--Publisher's website.