An interesting aside is that the encryption system most of us rely on every day, AES, relies on a prime over a finite (Galois) field 2^8. The "subbytes" step is

An interesting aside is that the encryption system most of us rely on every day, AES, relies on a prime over a finite (Galois) field 2^8. The "subbytes" step is a one to one mapping of a byte to another byte, and it's defined in terms of a prime polynomial in the field GF(2^8). In practice though, the table is pre-computed and hardcoded into AES implementations.