Algorithmic Problems Of Group Theory Their Complexity And Applications To Cryptography

Author : Delaram Kahrobaei, Vladimir Shpilrain
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 50,8 Mb
Release : 2015-02-25
Category : Business & Economics
ISBN : 9780821898598

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Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography by Delaram Kahrobaei, Vladimir Shpilrain Pdf

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,Vladimir Shpilrain,Alexander Ushakov
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 41,8 Mb
Release : 2008-07-17
Category : Language Arts & Disciplines
ISBN : 9783764388263

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

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,Vladimir Shpilrain,Alexander Ushakov
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 44,9 Mb
Release : 2011
Category : Computers
ISBN : 9780821853603

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

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 : Alexei G. Myasnikov,Vladimir Shpilrain
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 54,9 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 : Delaram Kahrobaei,Ramón Flores,Marialaura Noce,Maggie E. Habeeb,Christopher Battarbee
Publisher : Unknown
Page : 0 pages
File Size : 43,9 Mb
Release : 2024
Category : Business & Economics
ISBN : 1470474697

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Applications of Group Theory in Cryptography by Delaram Kahrobaei,Ramón Flores,Marialaura Noce,Maggie E. Habeeb,Christopher Battarbee Pdf

Author : Paul M. N. Feehan,Jian Song, Ben Weinkove,Richard A. Wentworth
Publisher : American Mathematical Soc.
Page : 359 pages
File Size : 51,9 Mb
Release : 2015-07-21
Category : Geometry, Differential
ISBN : 9781470414641

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Analysis, Complex Geometry, and Mathematical Physics by Paul M. N. Feehan,Jian Song, Ben Weinkove,Richard A. Wentworth Pdf

This volume contains the proceedings of the Conference on Analysis, Complex Geometry and Mathematical Physics: In Honor of Duong H. Phong, which was held from May 7-11, 2013, at Columbia University, New York. The conference featured thirty speakers who spoke on a range of topics reflecting the breadth and depth of the research interests of Duong H. Phong on the occasion of his sixtieth birthday. A common thread, familiar from Phong's own work, was the focus on the interplay between the deep tools of analysis and the rich structures of geometry and physics. Papers included in this volume cover topics such as the complex Monge-Ampère equation, pluripotential theory, geometric partial differential equations, theories of integral operators, integrable systems and perturbative superstring theory.

Author : Paul Baginski,Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger,Vladimir Shpilrain
Publisher : Walter de Gruyter GmbH & Co KG
Page : 272 pages
File Size : 43,6 Mb
Release : 2020-02-10
Category : Mathematics
ISBN : 9783110638387

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Elementary Theory of Groups and Group Rings, and Related Topics by Paul Baginski,Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger,Vladimir Shpilrain Pdf

This proceedings volume documents the contributions presented at the conference held at Fairfield University and at the Graduate Center, CUNY in 2018 celebrating the New York Group Theory Seminar, in memoriam Gilbert Baumslag, and to honor Benjamin Fine and Anthony Gaglione. It includes several expert contributions by leading figures in the group theory community and provides a valuable source of information on recent research developments.

Author : Stéphane Ballet,Marc Perret,Alexey Zaytsev
Publisher : American Mathematical Soc.
Page : 306 pages
File Size : 46,6 Mb
Release : 2015-04-20
Category : Coding theory
ISBN : 9781470414610

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Algorithmic Arithmetic, Geometry, and Coding Theory by Stéphane Ballet,Marc Perret,Alexey Zaytsev Pdf

This volume contains the proceedings of the 14th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held June 3-7, 2013, at CIRM, Marseille, France. These international conferences, held every two years, have been a major event in the area of algorithmic and applied arithmetic geometry for more than 20 years. This volume contains 13 original research articles covering geometric error correcting codes, and algorithmic and explicit arithmetic geometry of curves and higher dimensional varieties. Tools used in these articles include classical algebraic geometry of curves, varieties and Jacobians, Suslin homology, Monsky-Washnitzer cohomology, and -functions of modular forms.

Author : María Isabel González Vasco
Publisher : MDPI
Page : 164 pages
File Size : 40,6 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 : 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 : 45,8 Mb
Release : 2020-06-08
Category : Mathematics
ISBN : 9783110667028

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Complexity and Randomness in Group Theory by Frédérique Bassino,Ilya Kapovich,Markus Lohrey,Alexei Miasnikov,Cyril Nicaud,Andrey Nikolaev,Igor Rivin,Vladimir Shpilrain,Alexander Ushakov,Pascal Weil Pdf

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 : Jens G. Christensen,Susanna Dann,Azita Mayeli,Gestur Ólafsson
Publisher : American Mathematical Soc.
Page : 209 pages
File Size : 45,6 Mb
Release : 2015-10-27
Category : Harmonic analysis
ISBN : 9781470418793

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Trends in Harmonic Analysis and Its Applications by Jens G. Christensen,Susanna Dann,Azita Mayeli,Gestur Ólafsson Pdf

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Its Applications held March 29-30, 2014, at the University of Maryland, Baltimore County, Baltimore, MD. It provides an in depth look at the many directions taken by experts in Harmonic Analysis and related areas. The papers cover topics such as frame theory, Gabor analysis, interpolation and Besov spaces on compact manifolds, Cuntz-Krieger algebras, reproducing kernel spaces, solenoids, hypergeometric shift operators and analysis on infinite dimensional groups. Expositions are by leading researchers in the field, both young and established. The papers consist of new results or new approaches to solutions, and at the same time provide an introduction into the respective subjects.

Author : Joseph Auslander,Aimee Johnson,Cesar E. Silva
Publisher : American Mathematical Soc.
Page : 316 pages
File Size : 41,8 Mb
Release : 2016-11-29
Category : Dynamical systems and ergodic theory -- Arithmetic and non-Archimedean dynamical systems -- Non-Archimedean Fatou and Julia sets
ISBN : 9781470422998

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Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby by Joseph Auslander,Aimee Johnson,Cesar E. Silva Pdf

This volume contains the proceedings of three conferences in Ergodic Theory and Symbolic Dynamics: the Oxtoby Centennial Conference, held from October 30–31, 2010, at Bryn Mawr College; the Williams Ergodic Theory Conference, held from July 27–29, 2012, at Williams College; and the AMS Special Session on Ergodic Theory and Symbolic Dynamics, held from January 17–18, 2014, in Baltimore, MD. This volume contains articles covering a variety of topics in measurable, symbolic and complex dynamics. It also includes a survey article on the life and work of John Oxtoby, providing a source of information about the many ways Oxtoby's work influenced mathematical thought in this and other fields.

Author : Fernando Chamizo,Jordi Guàrdia, Antonio Rojas-León,José María Tornero
Publisher : American Mathematical Soc.
Page : 244 pages
File Size : 52,9 Mb
Release : 2015-09-28
Category : Number theory
ISBN : 9780821898581

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Trends in Number Theory by Fernando Chamizo,Jordi Guàrdia, Antonio Rojas-León,José María Tornero Pdf

This volume contains the proceedings of the Fifth Spanish Meeting on Number Theory, held from July 8-12, 2013, at the Universidad de Sevilla, Sevilla, Spain. The articles contained in this book give a panoramic vision of the current research in number theory, both in Spain and abroad. Some of the topics covered in this volume are classical algebraic number theory, arithmetic geometry, and analytic number theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).

Author : Noé Bárcenas,Fernando Galaz-García,Mónica Moreno Rocha
Publisher : American Mathematical Soc.
Page : 237 pages
File Size : 43,8 Mb
Release : 2016-02-01
Category : Mathematicians
ISBN : 9781470421922

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Mexican Mathematicians Abroad by Noé Bárcenas,Fernando Galaz-García,Mónica Moreno Rocha Pdf

This volume contains the proceedings of the First Workshop “Matemáticos Mexicanos Jóvenes en el Mundo”, held from August 22–24, 2012, at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. - See more at: http://bookstore.ams.org/conm-657/#sthash.cUjwTcvX.dpuf This volume contains the proceedings of the First Workshop "Matemáticos Mexicanos Jóvenes en el Mundo", held from August 22-24, 2012, at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. One of the main goals of this meeting was to present different research directions being pursued by young Mexican mathematicians based in other countries, such as Brazil, Canada, Colombia, Estonia, Germany, Spain and the United States, showcasing research lines currently underrepresented in Mexico. Featured are survey and research articles in six areas: algebra, analysis, applied mathematics, geometry, probability and topology. Their topics range from current developments related to well-known open problems to novel interactions between pure mathematics and computer science. Most of the articles provide a panoramic view of the fields and problems the authors work on, making the book accessible to advanced graduate students and researchers in mathematics from different fields. This book is published in cooperation with Sociedad Matemática Mexicana.

Author : James V Ralston
Publisher : American Mathematical Soc.
Page : 197 pages
File Size : 42,8 Mb
Release : 2015
Category : Differential equations, Partial
ISBN : 9781470409890

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Spectral Theory and Partial Differential Equations by James V Ralston Pdf

This volume contains the proceedings of the Conference on Spectral Theory and Partial Differential Equations, held from June 17-21, 2013, at the University of California, Los Angeles, California, in honor of James Ralston's 70th Birthday. Papers in this volume cover important topics in spectral theory and partial differential equations such as inverse problems, both analytical and algebraic; minimal partitions and Pleijel's Theorem; spectral theory for a model in Quantum Field Theory; and beams on Zoll manifolds.