Computing isomorphisms and embeddings of finite fields

摘要

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_qX, with deg f dividing deg g. Define k = F_qX/f and K = F_qX/g, then there is an embedding φ : k ? K, unique up to F_q-automorphisms of k. Our goal is to describe algorithms to efficiently represent and evaluate one such embedding.