Standard Article

Computational Number Theory

  1. Wayne Patterson

Published Online: 14 DEC 2007

DOI: 10.1002/9780470050118.ecse534

Wiley Encyclopedia of Computer Science and Engineering

Wiley Encyclopedia of Computer Science and Engineering

How to Cite

Patterson, W. 2007. Computational Number Theory. Wiley Encyclopedia of Computer Science and Engineering. .

Author Information

  1. Howard University, Washington, D.C.

Publication History

  1. Published Online: 14 DEC 2007

Abstract

This article provides an introduction to number theory from a computational perspective, including topics such as divisibility, multiplicative functions, congruence, residues, prime numbers, diophantine equations, and elliptic curves. Additionally, applications of this very pure branch of mathematics to contemporary computer security problems are presented in some detail, including discussion of the Data Encryption Standard, public key cryptosystems and the Rivest–Shamir–Adelman cryptosystem, digital signatures, Elliptic Curve public key cryptosystems, and the Advanced Encryption Standard (Rijndael).

Keywords:

  • computational number theory;
  • congruence;
  • residues;
  • prime numbers;
  • computer security;
  • data encryption standard;
  • public key cryptosystems;
  • Rivest-Shamir-Adelman cryptosystem;
  • digital signatures;
  • elliptic curve public key cryptosystems;
  • advanced encryption standard;
  • Rijndael