Algorithm for GCD of univariate polynomials, with integer coefficients

Question

I need a fast algorithm for finding the GCD of several univariate polynomials, all with integer coefficients. Those polynomials vary according to input data in a program of mine. But generally their degree can be pretty big (>15 or much more, depending on input values to my program). There seems to be a mess over the web as to which algorithms are the fastest, and furthermore, my problem has the strong condition of integer coefficients, so maybe this makes things easier for algorithms. Unfortunately I cannot find such an algorithm (that takes into account the integer-ness of coefficients). So, I need your help! Thanks in advance!