Number Theory for Computing - Hardcover

Yan, Song Y.

Hardcover

ISBN 10: 3540430725 ISBN 13: 9783540430728

Publisher: Springer, 2002

Synopsis

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.

About this title

From the Back Cover

There are many surprising connections between the theory of numbers, which is one of the oldest branches of mathematics, and computing and information theory. Number theory has important applications in computer organization and security, coding and cryptography, random number generation, hash functions, and graphics. Conversely, number theorists use computers in factoring large integers, determining primes, testing conjectures, and solving other problems. This book takes the reader from elementary number theory, via algorithmic number theory, to applied number theory in computer science. It introduces basic concepts, results, and methods, and discusses their applications in the design of hardware and software, cryptography, and security. It is aimed at undergraduates in computing and information technology, including electrical and electronic engineering, but will also be valuable to mathematics students interested in applications. It presupposes only high-shool math.
In this 2nd edition proofs of many theorems are added and some corrections are made.

Edition details

• Publisher: Springer
• Publication date: 2002
• Language: English
• ISBN 10: 3540430725
• ISBN 13: 9783540430728
• Binding: Hardcover
• Edition number: 2
• Number of pages: 457