Group Theoretic Cryptography

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Group Theoretic Cryptography

Author : Maria Isabel Gonzalez Vasco
Publisher : CRC Press
ISBN 13 : 1584888377
Total Pages : 244 pages
Book Rating : 4.5/5 (848 download)

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Book Synopsis Group Theoretic Cryptography by : Maria Isabel Gonzalez Vasco

Download or read book Group Theoretic Cryptography written by Maria Isabel Gonzalez Vasco and published by CRC Press. This book was released on 2015-04-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Group-based Cryptography

Author : Alexei Myasnikov
Publisher : Springer Science & Business Media
ISBN 13 : 3764388277
Total Pages : 183 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Group-based Cryptography by : Alexei Myasnikov

Download or read book Group-based Cryptography written by Alexei Myasnikov and published by Springer Science & Business Media. This book was released on 2008-11-04 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Group-based Cryptography

Author : Alexei Myasnikov
Publisher : Springer Science & Business Media
ISBN 13 : 3764388269
Total Pages : 192 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Group-based Cryptography by : Alexei Myasnikov

Download or read book Group-based Cryptography written by Alexei Myasnikov and published by Springer Science & Business Media. This book was released on 2008-07-17 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Group Theory, Statistics, and Cyptography

Author : Alexei G. Myasnikov
Publisher : American Mathematical Soc.
ISBN 13 : 0821834444
Total Pages : 177 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Group Theory, Statistics, and Cyptography by : Alexei G. Myasnikov

Download or read book Group Theory, Statistics, and Cyptography written by Alexei G. Myasnikov and published by American Mathematical Soc.. This book was released on 2004 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Interactions between Group Theory, Symmetry and Cryptology

Author : María Isabel González Vasco
Publisher : MDPI
ISBN 13 : 3039288024
Total Pages : 164 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Interactions between Group Theory, Symmetry and Cryptology by : María Isabel González Vasco

Download or read book Interactions between Group Theory, Symmetry and Cryptology written by María Isabel González Vasco and published by MDPI. This book was released on 2020-04-22 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Non-commutative Cryptography and Complexity of Group-theoretic Problems

Author : Alexei G. Myasnikov
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (732 download)

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Book Synopsis Non-commutative Cryptography and Complexity of Group-theoretic Problems by : Alexei G. Myasnikov

Download or read book Non-commutative Cryptography and Complexity of Group-theoretic Problems written by Alexei G. Myasnikov and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-commutative Cryptography and Complexity of Group-theoretic Problems

Author : Alexei G. Myasnikov
Publisher : American Mathematical Soc.
ISBN 13 : 0821853600
Total Pages : 402 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Non-commutative Cryptography and Complexity of Group-theoretic Problems by : Alexei G. Myasnikov

Download or read book Non-commutative Cryptography and Complexity of Group-theoretic Problems written by Alexei G. Myasnikov and published by American Mathematical Soc.. This book was released on 2011 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Cryptanalysis of Number Theoretic Ciphers

Author : Samuel S. Wagstaff, Jr.
Publisher : CRC Press
ISBN 13 : 1351991949
Total Pages : 340 pages
Book Rating : 4.3/5 (519 download)

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Book Synopsis Cryptanalysis of Number Theoretic Ciphers by : Samuel S. Wagstaff, Jr.

Download or read book Cryptanalysis of Number Theoretic Ciphers written by Samuel S. Wagstaff, Jr. and published by CRC Press. This book was released on 2019-08-22 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the heart of modern cryptographic algorithms lies computational number theory. Whether you're encrypting or decrypting ciphers, a solid background in number theory is essential for success. Written by a number theorist and practicing cryptographer, Cryptanalysis of Number Theoretic Ciphers takes you from basic number theory to the inner workings of ciphers and protocols. First, the book provides the mathematical background needed in cryptography as well as definitions and simple examples from cryptography. It includes summaries of elementary number theory and group theory, as well as common methods of finding or constructing large random primes, factoring large integers, and computing discrete logarithms. Next, it describes a selection of cryptographic algorithms, most of which use number theory. Finally, the book presents methods of attack on the cryptographic algorithms and assesses their effectiveness. For each attack method the author lists the systems it applies to and tells how they may be broken with it. Computational number theorists are some of the most successful cryptanalysts against public key systems. Cryptanalysis of Number Theoretic Ciphers builds a solid foundation in number theory and shows you how to apply it not only when breaking ciphers, but also when designing ones that are difficult to break.

Computational and Combinatorial Group Theory and Cryptography

Author : Benjamin Fine (mathématicien).)
Publisher :
ISBN 13 : 9780821875636
Total Pages : 199 pages
Book Rating : 4.8/5 (756 download)

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Book Synopsis Computational and Combinatorial Group Theory and Cryptography by : Benjamin Fine (mathématicien).)

Download or read book Computational and Combinatorial Group Theory and Cryptography written by Benjamin Fine (mathématicien).) and published by . This book was released on 2012 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elliptic Curves

Author : Lawrence C. Washington
Publisher : CRC Press
ISBN 13 : 1420071475
Total Pages : 533 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Elliptic Curves by : Lawrence C. Washington

Download or read book Elliptic Curves written by Lawrence C. Washington and published by CRC Press. This book was released on 2008-04-03 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application

Non-commutative Cryptography and Complexity of Group-theoretic Problems

Author : Sandy Weedman
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781974040322
Total Pages : 402 pages
Book Rating : 4.0/5 (43 download)

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Book Synopsis Non-commutative Cryptography and Complexity of Group-theoretic Problems by : Sandy Weedman

Download or read book Non-commutative Cryptography and Complexity of Group-theoretic Problems written by Sandy Weedman and published by Createspace Independent Publishing Platform. This book was released on 2014-10-30 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

International Symposium on Mathematics, Quantum Theory, and Cryptography

Author : Tsuyoshi Takagi
Publisher : Springer Nature
ISBN 13 : 981155191X
Total Pages : 275 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis International Symposium on Mathematics, Quantum Theory, and Cryptography by : Tsuyoshi Takagi

Download or read book International Symposium on Mathematics, Quantum Theory, and Cryptography written by Tsuyoshi Takagi and published by Springer Nature. This book was released on 2020-10-22 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography.

Computational and Combinatorial Group Theory and Cryptography

Author : Benjamin Fine
Publisher : American Mathematical Soc.
ISBN 13 : 0821875639
Total Pages : 210 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Computational and Combinatorial Group Theory and Cryptography by : Benjamin Fine

Download or read book Computational and Combinatorial Group Theory and Cryptography written by Benjamin Fine and published by American Mathematical Soc.. This book was released on 2012 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Foundations of Public Key Cryptography

Author : Xiaoyun Wang
Publisher : CRC Press
ISBN 13 : 1498702244
Total Pages : 236 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Mathematical Foundations of Public Key Cryptography by : Xiaoyun Wang

Download or read book Mathematical Foundations of Public Key Cryptography written by Xiaoyun Wang and published by CRC Press. This book was released on 2015-10-22 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Mathematical Foundations of Public Key Cryptography, the authors integrate the results of more than 20 years of research and teaching experience to help students bridge the gap between math theory and crypto practice. The book provides a theoretical structure of fundamental number theory and algebra knowledge supporting public-key cryptography.R

Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography

Author : Delaram Kahrobaei
Publisher : American Mathematical Soc.
ISBN 13 : 0821898590
Total Pages : 123 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography by : Delaram Kahrobaei

Download or read book Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography written by Delaram Kahrobaei and published by American Mathematical Soc.. This book was released on 2015-02-25 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics of Public Key Cryptography

Author : Steven D. Galbraith
Publisher : Cambridge University Press
ISBN 13 : 1107013925
Total Pages : 631 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Mathematics of Public Key Cryptography by : Steven D. Galbraith

Download or read book Mathematics of Public Key Cryptography written by Steven D. Galbraith and published by Cambridge University Press. This book was released on 2012-03-15 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.

Functional Encryption

Author : Khairol Amali Bin Ahmad
Publisher : Springer Nature
ISBN 13 : 3030608905
Total Pages : 311 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Functional Encryption by : Khairol Amali Bin Ahmad

Download or read book Functional Encryption written by Khairol Amali Bin Ahmad and published by Springer Nature. This book was released on 2021-06-12 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides awareness of methods used for functional encryption in the academic and professional communities. The book covers functional encryption algorithms and its modern applications in developing secure systems via entity authentication, message authentication, software security, cyber security, hardware security, Internet of Thing (IoT), cloud security, smart card technology, CAPTCHA, digital signature, and digital watermarking. This book is organized into fifteen chapters; topics include foundations of functional encryption, impact of group theory in cryptosystems, elliptic curve cryptography, XTR algorithm, pairing based cryptography, NTRU algorithms, ring units, cocks IBE schemes, Boneh-Franklin IBE, Sakai-Kasahara IBE, hierarchical identity based encryption, attribute based Encryption, extensions of IBE and related primitives, and digital signatures. Explains the latest functional encryption algorithms in a simple way with examples; Includes applications of functional encryption in information security, application security, and network security; Relevant to academics, research scholars, software developers, etc.