Finite field

The simplest finite fields and those of most interest for elliptic curve cryptography are of prime order, and isomorphic to the integers modulo some prime number.

Other Galois fields also exist of order

$q=p^{k}$

for any prime number p and power k > 1.

“When n>1, GF(pⁿ) can be represented as the field of equivalence classes of polynomials whose coefficients belong to GF(p). Any irreducible polynomial of degree n yields the same field up to an isomorphism” .