Finite field

Finite field arithmetic is different than standard arithmetic.

The notation to describe finite fields is GF(pn), where p is a prime number and n is a positive integer.

GF(p) is a ring of integers, modulo p.

GF(pn is represented as polynomials of degree less than n / GF(p). Operations are performed modoulo polynomino R, where R is a polynominal of degree n over GF(p) (when using polynominal long division.)  Addition and subtraction are unaffected.  Multiplication is computerd by W=P * Q, and y computing the remainder modulo R.