Public Key Cryptography And Computational Number Theory

Author : Kazimierz Alster,Jerzy Urbanowicz,Hugh C. Williams
Publisher : Walter de Gruyter
Page : 345 pages
File Size : 45,8 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 : Carl Pomerance,Shafi Goldwasser
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 43,8 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 : Song Y. Yan
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 46,9 Mb
Release : 2013-01-29
Category : Computers
ISBN : 9781118188583

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Computational Number Theory and Modern Cryptography by Song Y. Yan Pdf

The only book to provide a unified view of the interplay between computational number theory and cryptography Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yang combines knowledge of these two critical fields, providing a unified view of the relationships between computational number theory and cryptography. The author takes an innovative approach, presenting mathematical ideas first, thereupon treating cryptography as an immediate application of the mathematical concepts. The book also presents topics from number theory, which are relevant for applications in public-key cryptography, as well as modern topics, such as coding and lattice based cryptography for post-quantum cryptography. The author further covers the current research and applications for common cryptographic algorithms, describing the mathematical problems behind these applications in a manner accessible to computer scientists and engineers. Makes mathematical problems accessible to computer scientists and engineers by showing their immediate application Presents topics from number theory relevant for public-key cryptography applications Covers modern topics such as coding and lattice based cryptography for post-quantum cryptography Starts with the basics, then goes into applications and areas of 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 Companion Website Computational Number Theory and Modern Cryptography is ideal for graduate and advanced undergraduate students in computer science, communications engineering, cryptography and mathematics. Computer scientists, practicing cryptographers, and other professionals involved in various security schemes will also find this book to be a helpful reference.

Author : Kwok Y. Lam,Igor Shparlinski,Huaxiong Wang,Chaoping Xing
Publisher : Birkhäuser
Page : 376 pages
File Size : 52,5 Mb
Release : 2013-03-07
Category : Computers
ISBN : 9783034882958

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Cryptography and Computational Number Theory by Kwok Y. Lam,Igor Shparlinski,Huaxiong Wang,Chaoping Xing Pdf

This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT'99, which has been held in Singapore during the week of November 22-26, 1999. The workshop was organized by the Centre for Systems Security of the Na tional University of Singapore. We gratefully acknowledge the financial support from the Singapore National Science and Technology Board under the grant num ber RP960668/M. The idea for this workshop grew out of the recognition of the recent, rapid development in various areas of cryptography and computational number the ory. The event followed the concept of the research programs at such well-known research institutions as the Newton Institute (UK), Oberwolfach and Dagstuhl (Germany), and Luminy (France). Accordingly, there were only invited lectures at the workshop with plenty of time for informal discussions. It was hoped and successfully achieved that the meeting would encourage and stimulate further research in information and computer security as well as in the design and implementation of number theoretic cryptosystems and other related areas. Another goal of the meeting was to stimulate collaboration and more active interaction between mathematicians, computer scientists, practical cryptographers and engineers in academia, industry and government.

Author : Song Y. Yan
Publisher : Springer
Page : 252 pages
File Size : 46,7 Mb
Release : 2015-12-26
Category : Computers
ISBN : 9783319258232

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Quantum Computational Number Theory by Song Y. Yan Pdf

This book provides a comprehensive introduction to advanced topics in the computational and algorithmic aspects of number theory, focusing on applications in cryptography. Readers will learn to develop fast algorithms, including quantum algorithms, to solve various classic and modern number theoretic problems. Key problems include prime number generation, primality testing, integer factorization, discrete logarithms, elliptic curve arithmetic, conjecture and numerical verification. The author discusses quantum algorithms for solving the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP), and the Elliptic Curve Discrete Logarithm Problem (ECDLP) and for attacking IFP, DLP and ECDLP based cryptographic systems. Chapters also cover various other quantum algorithms for Pell's equation, principal ideal, unit group, class group, Gauss sums, prime counting function, Riemann's hypothesis and the BSD conjecture. Quantum Computational Number Theory is self-contained and intended to be used either as a graduate text in computing, communications and mathematics, or as a basic reference in the related fields. Number theorists, cryptographers and professionals working in quantum computing, cryptography and network security will find this book a valuable asset.

Author : Abhijit Das
Publisher : CRC Press
Page : 614 pages
File Size : 52,7 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781482205824

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Computational Number Theory by Abhijit Das Pdf

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 pract

Author : Song Y. Yan
Publisher : Springer Science & Business Media
Page : 249 pages
File Size : 46,8 Mb
Release : 2013-06-29
Category : Computers
ISBN : 9781475738162

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Primality Testing and Integer Factorization in Public-Key Cryptography by Song Y. Yan Pdf

Primality Testing and Integer Factorization in Public-Key Cryptography introduces various algorithms for primality testing and integer factorization, with their applications in public-key cryptography and information security. More specifically, this book explores basic concepts and results in number theory in Chapter 1. Chapter 2 discusses various algorithms for primality testing and prime number generation, with an emphasis on the Miller-Rabin probabilistic test, the Goldwasser-Kilian and Atkin-Morain elliptic curve tests, and the Agrawal-Kayal-Saxena deterministic test for primality. Chapter 3 introduces various algorithms, particularly the Elliptic Curve Method (ECM), the Quadratic Sieve (QS) and the Number Field Sieve (NFS) for integer factorization. This chapter also discusses some other computational problems that are related to factoring, such as the square root problem, the discrete logarithm problem and the quadratic residuosity problem.

Author : Steven D. Galbraith
Publisher : Cambridge University Press
Page : 631 pages
File Size : 55,7 Mb
Release : 2012-03-15
Category : Computers
ISBN : 9781107013926

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Mathematics of Public Key Cryptography by Steven D. Galbraith Pdf

This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.

Author : Xiaoyun Wang,Guangwu Xu,Mingqiang Wang,Xianmeng Meng
Publisher : CRC Press
Page : 236 pages
File Size : 53,5 Mb
Release : 2015-10-22
Category : Computers
ISBN : 9781498702249

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Mathematical Foundations of Public Key Cryptography by Xiaoyun Wang,Guangwu Xu,Mingqiang Wang,Xianmeng Meng Pdf

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

Author : Joppe Bos,Martijn Stam
Publisher : Unknown
Page : 402 pages
File Size : 43,9 Mb
Release : 2021-12-09
Category : Language Arts & Disciplines
ISBN : 9781108848428

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Computational Cryptography by Joppe Bos,Martijn Stam Pdf

The area of computational cryptography is dedicated to the development of effective methods in algorithmic number theory that improve implementation of cryptosystems or further their cryptanalysis. This book is a tribute to Arjen K. Lenstra, one of the key contributors to the field, on the occasion of his 65th birthday, covering his best-known scientific achievements in the field. Students and security engineers will appreciate this no-nonsense introduction to the hard mathematical problems used in cryptography and on which cybersecurity is built, as well as the overview of recent advances on how to solve these problems from both theoretical and practical applied perspectives. Beginning with polynomials, the book moves on to the celebrated Lenstra-Lenstra-Lovász lattice reduction algorithm, and then progresses to integer factorization and the impact of these methods to the selection of strong cryptographic keys for usage in widely used standards.

Author : Samuel S. Wagstaff, Jr.
Publisher : CRC Press
Page : 336 pages
File Size : 42,9 Mb
Release : 2019-08-22
Category : Mathematics
ISBN : 9781420057690

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Cryptanalysis of Number Theoretic Ciphers by Samuel S. Wagstaff, Jr. Pdf

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.

Author : Hans Riesel
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461202516

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Prime Numbers and Computer Methods for Factorization by Hans Riesel Pdf

In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem. A major component of this system is the factorization of large numbers into their primes. Thus an ancient number-theory concept now plays a crucial role in communication among millions of people who may have little or no knowledge of even elementary mathematics. The independent structure of each chapter of the book makes it highly readable for a wide variety of mathematicians, students of applied number theory, and others interested in both study and research in number theory and cryptography.

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 42,9 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 : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468403107

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A Course in Number Theory and Cryptography by Neal Koblitz Pdf

The purpose of this book is to introduce the reader to arithmetic topics, both ancient and modern, that have been at the center of interest in applications of number theory, particularly in cryptography. Because number theory and cryptography are fast-moving fields, this new edition contains substantial revisions and updated references.

Author : Anonim
Publisher : Springer-Verlag
Page : 250 pages
File Size : 50,7 Mb
Release : 2013-08-13
Category : Technology & Engineering
ISBN : 9783322966476

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Primality and Cryptography by Anonim Pdf