Computing isomorphisms and embeddings of finite fields

Abstract

Let q be a prime power and let F_q be a field with q elements. Let f and g be irreducible polynomials in F_q[X], with deg f dividing deg g. Define k = F_q[X]/f and K = F_q[X]/g, then there is an embedding φ : k [EQUATION] K, unique up to F_q-automorphisms of k. Our goal is to describe algorithms to efficiently represent and evaluate one such embedding.