Number Theoretic Algorithms In Cryptography
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Number Theoretic Algorithms In Cryptography
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Author : Oleg Nikolaevich Vasilenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Number Theoretic Algorithms In Cryptography written by Oleg Nikolaevich Vasilenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Language Arts & Disciplines categories.
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
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Author : Samuel S. Wagstaff, Jr.
language : en
Publisher: CRC Press
Release Date : 2019-08-22
Cryptanalysis Of Number Theoretic Ciphers written by Samuel S. Wagstaff, Jr. and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-22 with Mathematics categories.
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
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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :
A Handbook Of Algorithms In Number Theory written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
"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.
Number Theoretic Algorithms
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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :
Number Theoretic Algorithms written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
"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.
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.
Algorithmic Number Theory
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Author : Duncan Buell
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06
Algorithmic Number Theory written by Duncan Buell 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 2004-06 with Computers categories.
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
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Author : S.C. Coutinho
language : en
Publisher: CRC Press
Release Date : 1999-01-15
The Mathematics Of Ciphers written by S.C. Coutinho and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-15 with Mathematics categories.
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.
Cryptography And Computational Number Theory
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Author : Kwok Y. Lam
language : en
Publisher: Birkhäuser
Release Date : 2013-03-07
Cryptography And Computational Number Theory written by Kwok Y. Lam and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Computers categories.
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.
A Course In Number Theory And Cryptography
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Author : Neal Koblitz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Course In Number Theory And Cryptography written by Neal Koblitz 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 2012-12-06 with Mathematics categories.
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
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Author : J. P. Buhler
language : en
Publisher: Cambridge University Press
Release Date : 2008-10-20
Algorithmic Number Theory written by J. P. Buhler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-20 with Computers categories.
An introduction to number theory for beginning graduate students with articles by the leading experts in the field.