Number Theory For Computing

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Number Theory For Computing

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Author : Song Y. Yan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

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 2013-03-09 with Computers categories.

Mathematicians do not study objects, but relations among objectsj they are indifferent to the replacement of objects by others as long as relations do not change. Matter is not important, only form interests them. HENRI POINCARE (1854-1912) Computer scientists working on algorithms for factorization would be well advised to brush up on their number theory. IAN STEWART [219] The theory of numbers, in mathematics, is primarily the theory of the prop erties of integers (i.e., the whole numbers), particularly the positive integers. For example, Euclid proved 2000 years aga in his Elements that there exist infinitely many prime numbers. The subject has long been considered as the purest branch of mathematics, with very few applications to other areas. How ever, recent years have seen considerable increase in interest in several central topics of number theory, precisely because of their importance and applica tions in other areas, particularly in computing and information technology.

Number Theory For Computing

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Author : Song Y. Yan
language : en
Publisher:
Release Date : 2014-01-15

Number Theory For Computing written by Song Y. Yan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Number Theory With Computer Applications

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Author : Ramanujachary Kumanduri
language : en
Publisher: Pearson
Release Date : 1998

Number Theory With Computer Applications written by Ramanujachary Kumanduri and has been published by Pearson this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

Appropriate for most courses in Number Theory. This book effectively integrates computing algorithms into the number theory curriculum using a heuristic approach and strong emphasis on proofs. Its in-depth coverage of modern applications considers the latest trends and topics, such as elliptic curves--a subject that has seen a rise in popularity due to its use in the proof of Fermat's Last Theorem.

Number Theory For Computing

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Author : Song Y. Yan
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-04-24

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 2002-04-24 with Computers categories.

This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.

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.

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.

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.

Number Theory In Science And Communication

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Author : Manfred Schroeder
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-06

Number Theory In Science And Communication written by Manfred Schroeder 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 2008-11-06 with Science categories.

"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudo primes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography. From reviews of earlier editions – "I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvelous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American) "A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin Gardner

Introduction To Number Theory With Computing

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Author : R. B. J. T. Allenby
language : en
Publisher: Hodder Arnold
Release Date : 1989-01-01

Introduction To Number Theory With Computing written by R. B. J. T. Allenby and has been published by Hodder Arnold this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.

This introduction to number theory has been written specifically for mathematics and computing undergraduates. Computer programs in BASIC are accompanied by basic text which explains the subject and demonstrates how computers have opened up new horizons for number theorists.

Algorithmic Number Theory Efficient Algorithms

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Author : Eric Bach
language : en
Publisher: MIT Press
Release Date : 1996

Algorithmic Number Theory Efficient Algorithms written by Eric Bach and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Computers categories.

Volume 1.