.NET Security and Cryptography

Modular Arithmetic

Before we look at the code in the RSA program example, let's first understand a bit more about modular arithmetic. Modular arithmetic is used in many cryptographic systems, including RSA, DSA, and SSL. The algebraic structure that is used is referred to as Z_n , which is the set of nonnegative integers modulo n. Z_n consists of the set {0, 1, 2, …, n – 1} along with operators defined for addition and multiplication. Note that Z_n is integer arithmetic on a finite circle, not an infinite number line. Z_n is sometimes referred to as clock arithmetic, since a twelve hour clock implies Z₁₂ arithmetic.

For example, Z₁₂ would be the set of numbers from 0 to 11, with addition defined much like regular addition, but any result over 11 ...