[Back] A finite field is just a set with a finite number of elements. In cryptography we often define a finite field of integers modulo \(p\) (where modulo is the remainder of an integer division and \(p\) is a prime number). This is defined as GF\((p\)) - Galois field of \(p\) - or with \(\mathbb{F}_p\). The following are some examples:

- \(\mathbb{F}_{2}\) or GF(2) is [0,1]
- \(\mathbb{F}_{11}\) or GF(11) is [0,1,2,3,4,5,6,7,8,9,10]
- \(\mathbb{F}_{23}\) or GF(23) is [0,1,2,3,4,5,6,7,8,9,10,11,12...22]

In the following we will performance some arithmetic operations with a modulo operation of a prime number.