Cryptanalysis of Number Theoretic Ciphers

Author: Samuel S. Wagstaff, Jr.

Publisher: CRC Press

ISBN: 9781584881537

Category: Mathematics

Page: 336

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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.

Elliptic Curves

Number Theory and Cryptography

Author: Lawrence C. Washington

Publisher: CRC Press

ISBN: 9780203484029

Category: Mathematics

Page: 440

View: 3475

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Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to senior undergraduate or beginning graduate students. Assuming only a modest background in elementary number theory, groups, and fields, Elliptic Curves: Number Theory and Cryptography introduces both the cryptographic and number theoretic sides of elliptic curves, interweaving the theory of elliptic curves with their applications. The author introduces elliptic curves over finite fields early in the treatment, leading readers directly to the intriguing cryptographic applications, but the book is structured so that readers can explore the number theoretic aspects independently if desired. By side-stepping algebraic geometry in favor an approach based on basic formulas, this book clearly demonstrates how elliptic curves are used and opens the doors to higher-level studies. Elliptic Curves offers a solid introduction to the mathematics and applications of elliptic curves that well prepares its readers to tackle more advanced problems in cryptography and number theory.

Computational Number Theory and Modern Cryptography

Author: Song Y. Yan

Publisher: John Wiley & Sons

ISBN: 1118188616

Category: Computers

Page: 432

View: 8228

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The only book to provide a unified view of the interplay betweencomputational number theory and cryptography Computational number theory and modern cryptography are two ofthe most important and fundamental research fields in informationsecurity. In this book, Song Y. Yang combines knowledge of thesetwo critical fields, providing a unified view of the relationshipsbetween computational number theory and cryptography. The authortakes an innovative approach, presenting mathematical ideas first,thereupon treating cryptography as an immediate application of themathematical concepts. The book also presents topics from numbertheory, which are relevant for applications in public-keycryptography, as well as modern topics, such as coding and latticebased cryptography for post-quantum cryptography. The authorfurther covers the current research and applications for commoncryptographic algorithms, describing the mathematical problemsbehind these applications in a manner accessible to computerscientists and engineers. Makes mathematical problems accessible to computer scientistsand engineers by showing their immediate application Presents topics from number theory relevant for public-keycryptography applications Covers modern topics such as coding and lattice basedcryptography for post-quantum cryptography Starts with the basics, then goes into applications and areasof active research Geared at a global audience; classroom tested in North America,Europe, and Asia Incudes exercises in every chapter Instructor resources available on the book’s CompanionWebsite Computational Number Theory and Modern Cryptography isideal for graduate and advanced undergraduate students incomputer science, communications engineering, cryptography andmathematics. Computer scientists, practicing cryptographers, andother professionals involved in various security schemes will alsofind this book to be a helpful reference.

Computational Number Theory

Author: Abhijit Das

Publisher: CRC Press

ISBN: 1482205823

Category: Computers

Page: 614

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Developed from the author’s popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and practitioners of cryptography in industry. Requiring no prior experience with number theory or sophisticated algebraic tools, the book covers many computational aspects of number theory and highlights important and interesting engineering applications. It first builds the foundation of computational number theory by covering the arithmetic of integers and polynomials at a very basic level. It then discusses elliptic curves, primality testing, algorithms for integer factorization, computing discrete logarithms, and methods for sparse linear systems. The text also shows how number-theoretic tools are used in cryptography and cryptanalysis. A dedicated chapter on the application of number theory in public-key cryptography incorporates recent developments in pairing-based cryptography. With an emphasis on implementation issues, the book uses the freely available number-theory calculator GP/PARI to demonstrate complex arithmetic computations. The text includes numerous examples and exercises throughout and omits lengthy proofs, making the material accessible to students and practitioners.

Public-Key Cryptography and Computational Number Theory

Proceedings of the International Conference organized by the Stefan Banach International Mathematical Center Warsaw, Poland, September 11-15, 2000

Author: Kazimierz Alster,Jerzy Urbanowicz,Hugh C. Williams

Publisher: Walter de Gruyter

ISBN: 3110881039

Category: Mathematics

Page: 343

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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.

Modern Cryptanalysis

Techniques for Advanced Code Breaking

Author: Christopher Swenson

Publisher: John Wiley & Sons

ISBN: 1118428625

Category: Computers

Page: 264

View: 6684

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As an instructor at the University of Tulsa, Christopher Swenson could find no relevant text for teaching modern cryptanalysis?so he wrote his own. This is the first book that brings the study of cryptanalysis into the 21st century. Swenson provides a foundation in traditional cryptanalysis, examines ciphers based on number theory, explores block ciphers, and teaches the basis of all modern cryptanalysis: linear and differential cryptanalysis. This time-honored weapon of warfare has become a key piece of artillery in the battle for information security.

Algorithmic Number Theory

4th International Symposium, ANTS-IV Leiden, The Netherlands, July 2-7, 2000 Proceedings

Author: Wieb Bosma

Publisher: Springer Science & Business Media

ISBN: 3540676953

Category: Computers

Page: 613

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This book constitutes the refereed proceedings of the 4th International Algorithmic Number Theory Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000. The book presents 36 contributed papers which have gone through a thorough round of reviewing, selection and revision. Also included are 4 invited survey papers. Among the topics addressed are gcd algorithms, primality, factoring, sieve methods, cryptography, linear algebra, lattices, algebraic number fields, class groups and fields, elliptic curves, polynomials, function fields, and power sums.

Cryptanalytic Attacks on RSA

Author: Song Y. Yan

Publisher: Springer Science & Business Media

ISBN: 0387487425

Category: Computers

Page: 255

View: 1596

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RSA is a public-key cryptographic system, and is the most famous and widely-used cryptographic system in today's digital world. Cryptanalytic Attacks on RSA, a professional book, covers almost all known cryptanalytic attacks and defenses of the RSA cryptographic system and its variants. Since RSA depends heavily on computational complexity theory and number theory, background information on complexity theory and number theory is presented first, followed by an account of the RSA cryptographic system and its variants. This book is also suitable as a secondary text for advanced-level students in computer science and mathematics.

Number Theory and Cryptography

Author: J. H. Loxton

Publisher: Cambridge University Press

ISBN: 0521398770

Category: Mathematics

Page: 235

View: 2217

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Papers presented by prominent contributors at a workshop on Number Theory and Cryptography, and the annual meeting of the Australian Mathematical Society.