Finite field arithmetic

Summary

Finite field arithmetic is the way to add, multiply and divide elements of a finite field in practice. The usual model of $\F_{p^n}$ is the set of polynomials of degree less than $n$ over $\F_p$. One computes with them modulo a fixed irreducible polynomial of degree $n$. It is the basis of error-correcting codes and of much of modern cryptography.