Factoring Modular Polynomials

This paper gives an algorithm to factor a polynomialf(in one variable) over rings like /r forr or [y]/r [y] forr [y]. The Chinese Remainder Theorem reduces our problem to the case whereris a prime power. Then factorization is not unique, but ifrdoes not divide the discriminant off, our (probabilistic) algorithm produces a description of all (possibly exponentially many) factorizations into irreducible factors in polynomial time. Ifrdivides the discriminant, we only know how to factor by exhaustive search, in exponential time.