New 64 bit versions, Fermat 5.0, have been posted that implement a fast multivariate polynomial multiplication algorithm.
Though this way of multiplying polynomials actually has a long history, I am indebted to Michael Monagan of Simon Fraser University for bringing it to my attention at the 2013 ECCAD conference in Maryland. He has described the idea in a preprint http://www.cecm.sfu.ca/~monaganm/papers/ASCM13.pdf
Basically, the idea is to store each term, or monomial, of a multivariate polynomial in a single node instead of storing the polynomial as a recursive structure of nodes at one level pointing to nodes at lower levels. Remarkable speedups are possible, 30% - 84% in real problems involving 6 - 18 polynomial variables.