Number Theoretic Algorithms In Cryptography

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Number-Theoretic Algorithms in Cryptography

Oleg Nikolaevich Vasilenko
Number Theoretic Algorithms in Cryptography Book PDF

Author : Oleg Nikolaevich Vasilenko
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 54,9 Mb
Release : 2007
Category : Language Arts & Disciplines
ISBN : 0821840908

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Number-Theoretic Algorithms in Cryptography by Oleg Nikolaevich Vasilenko Pdf

Algorithmic number theory is a rapidly developing branch of number theory, which, in addition to its mathematical importance, has substantial applications in computer science and cryptography. Among the algorithms used in cryptography, the following are especially important: algorithms for primality testing; factorization algorithms for integers and for polynomials in one variable; applications of the theory of elliptic curves; algorithms for computation of discrete logarithms; algorithms for solving linear equations over finite fields; and, algorithms for performing arithmetic operations on large integers. The book describes the current state of these and some other algorithms. It also contains extensive bibliography. For this English translation, additional references were prepared and commented on by the author.

Cryptanalysis of Number Theoretic Ciphers

Samuel S. Wagstaff, Jr.
Cryptanalysis of Number Theoretic Ciphers Book PDF

Author : Samuel S. Wagstaff, Jr.
Publisher : CRC Press
Page : 336 pages
File Size : 46,6 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.

A Handbook of Algorithms in Number Theory

N.B. Singh
A Handbook of Algorithms in Number Theory Book PDF

Author : N.B. Singh
Publisher : N.B. Singh
Page : 44 pages
File Size : 53,8 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 8210379456XXX

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A Handbook of Algorithms in Number Theory by N.B. Singh Pdf

"A Handbook of Algorithms in Number Theory" is designed for absolute beginners, providing a comprehensive introduction to the fundamental concepts of number theory and their applications in computer science. This book explores a range of topics, from cryptographic hash functions and primality testing to random number generation and error detection. Through clear, step-by-step descriptions, readers will gain a solid understanding of how number theory underpins modern algorithms and cryptographic protocols, making complex ideas accessible and engaging for those new to the subject.

Computational Number Theory and Modern Cryptography

Song Y. Yan
Computational Number Theory and Modern Cryptography Book PDF

Author : Song Y. Yan
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 45,9 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.

Number Theoretic Algorithms

N.B. Singh
Number Theoretic Algorithms Book PDF

Author : N.B. Singh
Publisher : N.B. Singh
Page : 41 pages
File Size : 48,6 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 8210379456XXX

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Number Theoretic Algorithms by N.B. Singh Pdf

"Number Theoretic Algorithms" presents a comprehensive exploration of algorithms specifically designed for number theory applications. Through clear explanations and illustrative examples, this book delves into various algorithmic techniques used to solve fundamental number theoretic problems. From prime number generation to factorization methods, and from modular arithmetic to advanced cryptographic protocols, readers will gain a deep understanding of the algorithms that underpin many important mathematical and cryptographic systems. This invaluable resource equips readers with the tools and insights needed to tackle a wide range of number theoretic challenges.

A Course in Number Theory and Cryptography

Neal Koblitz
A Course in Number Theory and Cryptography Book PDF

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 52,6 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.

Algorithmic Number Theory

Duncan Buell
Algorithmic Number Theory Book PDF

Author : Duncan Buell
Publisher : Springer Science & Business Media
Page : 461 pages
File Size : 41,8 Mb
Release : 2004-06
Category : Computers
ISBN : 9783540221562

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Algorithmic Number Theory by Duncan Buell Pdf

This book constitutes the refereed proceedings of the 6th International Algorithmic Number Theory Symposium, ANTS 2004, held in Burlington, VT, USA, in June 2004. The 30 revised full papers presented together with 3 invited papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are zeta functions, elliptic curves, hyperelliptic curves, GCD algorithms, number field computations, complexity, primality testing, Weil and Tate pairings, cryptographic algorithms, function field sieve, algebraic function field mapping, quartic fields, cubic number fields, lattices, discrete logarithms, and public key cryptosystems.

The Mathematics of Ciphers

S.C. Coutinho
The Mathematics of Ciphers Book PDF

Author : S.C. Coutinho
Publisher : CRC Press
Page : 213 pages
File Size : 49,9 Mb
Release : 1999-01-15
Category : Mathematics
ISBN : 9781439863893

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The Mathematics of Ciphers by S.C. Coutinho Pdf

This book is an introduction to the algorithmic aspects of number theory and its applications to cryptography, with special emphasis on the RSA cryptosys-tem. It covers many of the familiar topics of elementary number theory, all with an algorithmic twist. The text also includes many interesting historical notes.

Cryptology and Computational Number Theory

Carl Pomerance,Shafi Goldwasser
Cryptology and Computational Number Theory Book PDF

Author : Carl Pomerance,Shafi Goldwasser
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 44,7 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.

Algorithmic Number Theory

J. P. Buhler,P. Stevenhagen
Algorithmic Number Theory Book PDF

Author : J. P. Buhler,P. Stevenhagen
Publisher : Cambridge University Press
Page : 653 pages
File Size : 45,5 Mb
Release : 2008-10-20
Category : Computers
ISBN : 9780521808545

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Algorithmic Number Theory by J. P. Buhler,P. Stevenhagen Pdf

An introduction to number theory for beginning graduate students with articles by the leading experts in the field.

Cryptography and Computational Number Theory

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

Author : Kwok Y. Lam,Igor Shparlinski,Huaxiong Wang,Chaoping Xing
Publisher : Birkhäuser
Page : 376 pages
File Size : 55,8 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.

Prime Numbers and Computer Methods for Factorization

Hans Riesel
Prime Numbers and Computer Methods for Factorization Book PDF

Author : Hans Riesel
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 47,6 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.

Algorithmic Number Theory

Alf J. van der Poorten,Andreas Stein
Algorithmic Number Theory Book PDF

Author : Alf J. van der Poorten,Andreas Stein
Publisher : Springer
Page : 463 pages
File Size : 41,8 Mb
Release : 2008-05-07
Category : Computers
ISBN : 9783540794561

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Algorithmic Number Theory by Alf J. van der Poorten,Andreas Stein Pdf

This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008. The 28 revised full papers presented together with 2 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on elliptic curves cryptology and generalizations, arithmetic of elliptic curves, integer factorization, K3 surfaces, number fields, point counting, arithmetic of function fields, modular forms, cryptography, and number theory.

Quantum Computational Number Theory

Song Y. Yan
Quantum Computational Number Theory Book PDF

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.

Number Theory and Cryptography

J. H. Loxton
Number Theory and Cryptography Book PDF

Author : J. H. Loxton
Publisher : Cambridge University Press
Page : 249 pages
File Size : 51,6 Mb
Release : 1990-04-19
Category : Mathematics
ISBN : 9780521398770

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Number Theory and Cryptography by J. H. Loxton Pdf

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