Number Theory for Computing / Edition 2

Number Theory for Computing / Edition 2

by M.E. Hellmann, Song Y. Yan
     
 

ISBN-10: 3540430725

ISBN-13: 9783540430728

Pub. Date: 06/10/2002

Publisher: Springer Berlin Heidelberg

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…  See more details below

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.

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Product Details

ISBN-13:
9783540430728
Publisher:
Springer Berlin Heidelberg
Publication date:
06/10/2002
Edition description:
2nd ed. 2002
Pages:
435
Product dimensions:
6.10(w) x 9.13(h) x 0.04(d)

Table of Contents

1Elementary Number Theory1
Theory of Divisibility21
Diophantine Equations52
Arithmetic Functions63
Distribution of Prime Numbers85
Theory of Congruences111
Arithmetic of Elliptic Curves160
2Computational/Algorithmic Number Theory173
Algorithms for Primality Testing202
Algorithms for Integer Factorization228
Algorithms for Discrete Logarithms254
Quantum Number-Theoretic Algorithms273
Miscellaneous Algorithms in Number Theory287
3Applied Number Theory in Computing/Cryptography303
Why Applied Number Theory?303
Computer Systems Design305
Cryptography and Information Security332
Bibliography415
Index429

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