عنوان

Number theory for computing

3662040530

9783662040539

b553369

Number theory for computing

[Book]

Song Y. Yan.

Berlin ; New York

Springer

©2000.

(xviii, 381 pages) : illustrations

Preface --;Notations --;Elementary Number Theory: Introduction. Theory of Divisibility. Diophantine Equations. Arithmetical Functions. Theory of Congruences. Arithmetic of Elliptic Curves. Bibliographic Notes and Further Reading --;Algorithmic Number Theory: Introduction. Algorithms for Primality Testing. Algorithms for Integer Factorization. Algorithms for Discrete Logarithms. Quantum Algorithmic Number Theory. Bibliographic Notes and Further Reading --;Applied Number Theory: Why Applied Number Theory. Computer Systems Design. Cryptology and Information Security --;Bibliographic Notes and Further Reading --;Bibliography --;Index.

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 interest mathematics students interested in applications. It presupposes only high-school math.

Computer science -- Mathematics.

Getaltheorie.

Number theory.

Song Y. Yan.

Song Y Yan

[Book]

Y