I hope not to be asking much, but I have N parties, each one holding a polynomial in with 0-1 coefficients and fixed degree $n-1$. I was wandering if it is possible (I mean feasible) to compute the product of all of these polynomials with an MPC protocol.
Actually, for security I would need the result modulo $X^n+1$, so my actual request is the following : Given $N$ polynomials $P_1,P_2,\dots,P_N$ with $0-1$ coefficients and degree $n-1$, compute $(\prod P_i)\mod(X^n+1)$ with a multiparty computation protocol where each party holds a $P_i$.
My question regards the complexity of such a product ($O(n \log n\log N)$ integer multiplications if an FFT algorithm is used ?)
It is my first question here, so please attach a welcome message to you answer :-)