Cryptology And Computational Number Theory
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Cryptography And Computational Number Theory
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Author : Kwok Yan Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Cryptography And Computational Number Theory written by Kwok Yan Lam 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 2001 with Computers categories.
The fields of cryptography and computational number theory have recently witnessed a rapid development, which was the subject of the CCNT workshop in Singapore in November 1999. Its aim was to stimulate further research in information and computer security as well as the design and implementation of number theoretic cryptosystems and other related areas. Another achievement of the meeting was the collaboration of mathematicians, computer scientists, practical cryptographers and engineers in academia, industry and government. The present volume comprises a selection of refereed papers originating from this event, presenting either a survey of some area or original and new results. They concern many different aspects of the field such as theory, techniques, applications and practical experience. It provides a state-of-the-art report on some number theoretical issues of significance to cryptography.
Computational Number Theory
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Author : Abhijit Das
language : en
Publisher: CRC Press
Release Date : 2013-03-18
Computational Number Theory written by Abhijit Das and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-18 with Computers categories.
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.
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.
Cryptology And Computational Number Theory
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Author : Carl Pomerance
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Cryptology And Computational Number Theory written by Carl Pomerance 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 1990 with Computers categories.
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.
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.
Number Theoretic Methods In Cryptology
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Author : Jerzy Kaczorowski
language : en
Publisher: Springer
Release Date : 2018-03-09
Number Theoretic Methods In Cryptology written by Jerzy Kaczorowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-09 with Computers categories.
This book constitutes the refereed post-conference proceedings of the First International Conference on Number-Theoretic Methods in Cryptology, NuTMiC 2017, held in Warsaw, Poland, in September 2017.The 15 revised full papers presented in this book together with 3 invited talks were carefully reviewed and selected from 32 initial submissions. The papers are organized in topical sections on elliptic curves in cryptography; public-key cryptography; lattices in cryptography; number theory; pseudorandomness; and algebraic structures and analysis.
Number Theory And Cryptography
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Author : J. H. Loxton
language : en
Publisher: Cambridge University Press
Release Date : 1990-04-19
Number Theory And Cryptography written by J. H. Loxton 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 1990-04-19 with Language Arts & Disciplines categories.
Papers presented by prominent contributors at a workshop on Number Theory and Cryptography, and the annual meeting of the Australian Mathematical Society.
Elliptic Curves
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Author : Lawrence C. Washington
language : en
Publisher: CRC Press
Release Date : 2008-04-03
Elliptic Curves written by Lawrence C. Washington and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-03 with Computers categories.
Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application
A Course In Computational Algebraic Number Theory
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Author : Henri Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
A Course In Computational Algebraic Number Theory written by Henri Cohen 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 2013-04-17 with Mathematics categories.
With the advent of powerful computing tools and numerous advances in math ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc ... Several books exist which treat parts of this subject. (It is essentially impossible for an author to keep up with the rapid pace of progress in all areas of this subject.) Each book emphasizes a different area, corresponding to the author's tastes and interests. The most famous, but unfortunately the oldest, is Knuth's Art of Computer Programming, especially Chapter 4. The present book has two goals. First, to give a reasonably comprehensive introductory course in computational number theory. In particular, although we study some subjects in great detail, others are only mentioned, but with suitable pointers to the literature. Hence, we hope that this book can serve as a first course on the subject. A natural sequel would be to study more specialized subjects in the existing literature.
Computational Cryptography
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Author : Joppe Bos
language : en
Publisher:
Release Date : 2021-12-09
Computational Cryptography written by Joppe Bos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-09 with Language Arts & Disciplines categories.
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.