Primality Testing And Integer Factorization In Public Key Cryptography

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Primality Testing And Integer Factorization In Public Key Cryptography

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Author : Song Y. Yan
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03

Primality Testing And Integer Factorization In Public Key Cryptography written by Song Y. Yan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Computers categories.

Intended for advanced level students in computer science and mathematics, this key text, now in a brand new edition, provides a survey of recent progress in primality testing and integer factorization, with implications for factoring based public key cryptography. For this updated and revised edition, notable new features include a comparison of the Rabin-Miller probabilistic test in RP, the Atkin-Morain elliptic curve test in ZPP and the AKS deterministic test.

Primality Testing And Integer Factorization In Public Key Cryptography

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Author : Song Y. Yan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Primality Testing And Integer Factorization In Public Key Cryptography written by Song Y. Yan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Computers categories.

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.

Computational Number Theory And Modern Cryptography

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Author : Song Y. Yan
language : en
Publisher: John Wiley & Sons
Release Date : 2013-01-29

Computational Number Theory And Modern Cryptography written by Song Y. Yan and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-29 with Computers categories.

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.

Euro Par 99 Parallel Processing

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Author : Patrick Amestoy
language : en
Publisher: Springer
Release Date : 2003-05-21

Euro Par 99 Parallel Processing written by Patrick Amestoy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-21 with Computers categories.

Euro-Parisaninternationalconferencededicatedtothepromotionandadvan- ment of all aspects of parallel computing. The major themes can be divided into the broad categories of hardware, software, algorithms and applications for p- allel computing. The objective of Euro-Par is to provide a forum within which to promote the development of parallel computing both as an industrial te- nique and an academic discipline, extending the frontier of both the state of the art and the state of the practice. This is particularly important at a time when parallel computing is undergoing strong and sustained development and experiencing real industrial take-up. The main audience for and participants in Euro-Parareseenasresearchersinacademicdepartments,governmentlabora- ries and industrial organisations. Euro-Par’s objective is to become the primary choice of such professionals for the presentation of new results in their specic areas. Euro-Par is also interested in applications which demonstrate the e - tiveness of the main Euro-Par themes. There is now a permanent Web site for the series http://brahms. fmi. uni-passau. de/cl/europar where the history of the conference is described. Euro-Par is now sponsored by the Association of Computer Machinery and the International Federation of Information Processing. Euro-Par’99 The format of Euro-Par’99follows that of the past four conferences and consists of a number of topics eachindividually monitored by a committee of four. There were originally 23 topics for this year’s conference. The call for papers attracted 343 submissions of which 188 were accepted. Of the papers accepted, 4 were judged as distinguished, 111 as regular and 73 as short papers.

Number Theory For Computing

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Author : Song Y. Yan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Number Theory For Computing written by Song Y. Yan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Computers categories.

Modern cryptography depends heavily on number theory, with primality test ing, factoring, discrete logarithms (indices), and elliptic curves being perhaps the most prominent subject areas. Since my own graduate study had empha sized probability theory, statistics, and real analysis, when I started work ing in cryptography around 1970, I found myself swimming in an unknown, murky sea. I thus know from personal experience how inaccessible number theory can be to the uninitiated. Thank you for your efforts to case the transition for a new generation of cryptographers. Thank you also for helping Ralph Merkle receive the credit he deserves. Diffie, Rivest, Shamir, Adleman and I had the good luck to get expedited review of our papers, so that they appeared before Merkle's seminal contribu tion. Your noting his early submission date and referring to what has come to be called "Diffie-Hellman key exchange" as it should, "Diffie-Hellman-Merkle key exchange", is greatly appreciated. It has been gratifying to see how cryptography and number theory have helped each other over the last twenty-five years. :'-Jumber theory has been the source of numerous clever ideas for implementing cryptographic systems and protocols while cryptography has been helpful in getting funding for this area which has sometimes been called "the queen of mathematics" because of its seeming lack of real world applications. Little did they know! Stanford, 30 July 2001 Martin E. Hellman Preface to the Second Edition Number theory is an experimental science.

Mathematics In Computing

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Author : Gerard O’Regan
language : en
Publisher: Springer Nature
Release Date : 2020-01-10

Mathematics In Computing written by Gerard O’Regan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-10 with Computers categories.

This illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The text spans a broad selection of key topics, ranging from the use of finite field theory to correct code and the role of number theory in cryptography, to the value of graph theory when modelling networks and the importance of formal methods for safety critical systems. This fully updated new edition has been expanded with a more comprehensive treatment of algorithms, logic, automata theory, model checking, software reliability and dependability, algebra, sequences and series, and mathematical induction. Topics and features: includes numerous pedagogical features, such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary; describes the historical contributions of such prominent figures as Leibniz, Babbage, Boole, and von Neumann; introduces the fundamental mathematical concepts of sets, relations and functions, along with the basics of number theory, algebra, algorithms, and matrices; explores arithmetic and geometric sequences and series, mathematical induction and recursion, graph theory, computability and decidability, and automata theory; reviews the core issues of coding theory, language theory, software engineering, and software reliability, as well as formal methods and model checking; covers key topics on logic, from ancient Greek contributions to modern applications in AI, and discusses the nature of mathematical proof and theorem proving; presents a short introduction to probability and statistics, complex numbers and quaternions, and calculus. This engaging and easy-to-understand book will appeal to students of computer science wishing for an overview of the mathematics used in computing, and to mathematicians curious about how their subject is applied in the field of computer science. The book will also capture the interest of the motivated general reader.

Cryptanalytic Attacks On Rsa

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Author : Song Y. Yan
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-15

Cryptanalytic Attacks On Rsa written by Song Y. Yan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-15 with Computers categories.

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.

Cryptography And Network Security

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Author : GUPTA, PRAKASH C.
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2014-11-01

Cryptography And Network Security written by GUPTA, PRAKASH C. and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-01 with Computers categories.

The book is intended for the undergraduate and postgraduate students of computer science and engineering and information technology, and the students of master of computer applications. The purpose of this book is to introduce this subject as a comprehensive text which is self contained and covers all the aspects of network security. Each chapter is divided into sections and subsections to facilitate design of the curriculum as per the academic needs. The text contains numerous examples and illustrations that enhance conceptual clarity. Each chapter has set of problems at the end of chapter that inspire the reader to test his understanding of the subject. Answers to most of the problems are given at the end of the book. Key Features • The subject matter is illustrated with about 200 figures and numerous examples at every stage of learning. • The list of recommended books, technical articles, and standards is included chapter-wise at the end of the book. • An exhaustive glossary and a list of frequently used acronyms are also given. • The book is based on the latest versions of the protocols (TLS, IKE, IPsec, S/MIME, Kerberos, X.509 etc.).

The Enchantment Of Numbers

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Author : Eric L. F. Roettger
language : en
Publisher: Springer Nature
Release Date : 2025-07-01

The Enchantment Of Numbers written by Eric L. F. Roettger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-01 with Mathematics categories.

Inspired by the classic Recreations in the Theory of Numbers—The Queen of Mathematics Entertains by Albert H. Beiler, this book brings the excitement of recreational number theory into the 21st century through the lens of computational techniques. While Beiler’s work, originally published in 1964, captivated readers with its breadth and charm, some sections have become dated. Here, we re-examine most of the key topics Beiler covered, while introducing fresh updates and insights rooted in computational number theory. The authors aim to present efficient computer algorithms to tackle various problems that arise in the theory of numbers, providing a deeper and more modern perspective on these timeless puzzles. Though we cannot rival Beiler’s exuberant prose, we hope our enduring fascination with these topics — cultivated over decades of study and teaching — will shine through and resonate with readers. The book is structured into 21 chapters, each focusing on different facets of number theory with which the authors have extensive expertise. From ancient problems to contemporary computational challenges, this volume will reignite the joy and wonder found in numbers while incorporating the power of modern computation. Whether you're a seasoned mathematician or a curious learner, this book promises a journey through the rich and playful landscape of number theory, making both historical and new discoveries accessible to all.

Handbook Of Applied Cryptography

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Author : Alfred J. Menezes
language : en
Publisher: CRC Press
Release Date : 2018-12-07

Handbook Of Applied Cryptography written by Alfred J. Menezes and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-07 with Mathematics categories.

Cryptography, in particular public-key cryptography, has emerged in the last 20 years as an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications. Standards are emerging to meet the demands for cryptographic protection in most areas of data communications. Public-key cryptographic techniques are now in widespread use, especially in the financial services industry, in the public sector, and by individuals for their personal privacy, such as in electronic mail. This Handbook will serve as a valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography. It is a necessary and timely guide for professionals who practice the art of cryptography. The Handbook of Applied Cryptography provides a treatment that is multifunctional: It serves as an introduction to the more practical aspects of both conventional and public-key cryptography It is a valuable source of the latest techniques and algorithms for the serious practitioner It provides an integrated treatment of the field, while still presenting each major topic as a self-contained unit It provides a mathematical treatment to accompany practical discussions It contains enough abstraction to be a valuable reference for theoreticians while containing enough detail to actually allow implementation of the algorithms discussed Now in its third printing, this is the definitive cryptography reference that the novice as well as experienced developers, designers, researchers, engineers, computer scientists, and mathematicians alike will use.