Cryptology 2
Spring 2003
Modular Arithmetic Background

[ Home ] [ Up ]

Let a natural number R be given. Then the list of possible remainders upon division by R is

0, 1, ..., R-1.

We shall use the symbol N_R to denote this list of remainders upon division by R. The elements of N_R are called "residues modulo R", or "remainders modulo R". Frequently we abbreviate "modulo" by "mod". The objective of this chapter is to introduce a system of arithmetic for N_R. The term "Modular Arithmetic" refers to the arithmetic for N_R.

1. Addition and Subtraction mod R
2. Multiplication and division mod R
3. Exponentiation and logarithms mod R
4. Solving linear equations mod R
5. Solving quadratic equations mod a prime number