FFT enables us to perform multiplication of polynomials in O(nlogn), where "multiplication" is the standard multiplication over the complex numbers. Is there a general procedure to extend this use of FFT for cases where the "multiplication" is any arbitrary commutative binary operator? for example, for the case where we define ab = a+b (mod n) for an arbitrary n (assuming, in this case, the coefficients of the polynomials are integers)?
Thanks.