Computational Number Theory

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