Abstract : Some implementations of stage 2 of the P-1 method of factorization use convolutions. We describe a space-efficient implementation, allowing convolution lengths around 2^23 and stage 2 limit around 10^16 while attempting to factor 230-digit numbers on modern PC's. We use the discrete cosine transform to multiply reciprocal polynomials. We present adjustments for the P+1 algorithm. We list some new findings.