Number Theory for Computing / Edition 2

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Overview

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, but will also be valuable to mathematics students interested in applications. In this 2nd edition full proofs of many theorems are added and some corrections are made.

"...takes the reader from elementary number theory, via algorithmic number theory, to applications in computer science, such as security, coding, cryptography, random number generation, hash functions, and graphics.

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Editorial Reviews

From the Publisher
From the reviews of the second edition:

"This book gives a profound and detailed insight at an undergraduate level in abstract and computational number theory as well as in applications in computing and cryptography. … The author has done a lot of work in providing a plenty of examples, in adding many historical comments including sketchy biographies … and in presenting the whole topic in a very accessible style. So the book can be recommended warmly for the laymen as well as for the mathematician without experience in applied number theory." (G. Kowol, Monatshefte für Mathematik, Vol. 140 (4), 2003)

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Product Details

  • ISBN-13: 9783540430728
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 6/10/2002
  • Edition description: 2nd ed. 2002
  • Edition number: 2
  • Pages: 435
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.00 (d)

Table of Contents

1 Elementary Number Theory 1
Theory of Divisibility 21
Diophantine Equations 52
Arithmetic Functions 63
Distribution of Prime Numbers 85
Theory of Congruences 111
Arithmetic of Elliptic Curves 160
2 Computational/Algorithmic Number Theory 173
Algorithms for Primality Testing 202
Algorithms for Integer Factorization 228
Algorithms for Discrete Logarithms 254
Quantum Number-Theoretic Algorithms 273
Miscellaneous Algorithms in Number Theory 287
3 Applied Number Theory in Computing/Cryptography 303
Why Applied Number Theory? 303
Computer Systems Design 305
Cryptography and Information Security 332
Bibliography 415
Index 429
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