Let R be a finite commutative ring, and let f : R ~ R. We call f a polynomial of degree n if there are a O, a t. a 2 ..... a~ ~ R, an ~ 0, such that for all t ~ R, we have f(t) = a 0 +air+ a2 t2 +...+ a~tt n. Such polynomials play an important role in coding theory, the logic of switching circuits (in case R is a Boolean ring), and classical number theory. We consider computational aspects of the following and related problems