Polynomial factorisation on integers modulo n

Question

Is there a known (efficient) algorithm to compute the list of factors of a polynomial modulo $n$ (for any integer $n$)?

For example in $\mathbb Z_8$, $X^2+2X$ has a list of 4 factors (multiplicity 1 for all of them) : $X$, $X+2$, $X+4$ and $X+8$, because $$X^2+2X=X(X+2)=(X+4)(X+6)$$

Or in $\mathbb Z_9$, $X^3$ has a list of factors (with multiplicity) $X^3, (X+3)^3, (X+6)^3$ because $$X^3=(X+3)^3=(X+6)^3=X(X+3)(X+6)$$

PS : I already asked in this question for prime $n$ and got nice answers, so the question is more for $n=p^k$ with $p$ prime.

Answer 1

See Factoring Polynomials Modulo Composites.