  Let p be prime and Zpn the degree n unramified extension of the ring of
p-adic integers Zp. In this paper we give an overview of some very fast
algorithms for common operations in Zpn modulo p^N. Combining existing methods
with recent work of Kedlaya and Umans about modular composition of polynomials,
we achieve quasi-linear time algorithms in the parameters n and N, and
quasi-linear or quasi-quadratic time in log p, for most basic operations on
these fields, including Galois conjugation, Teichmuller lifting and computing
minimal polynomials.
