[math-fun] multiplication/division over GF(2^k)

In this day & age of fast CPU's & GPU's, is there any hardware support for multiplication/division over GF(2^k)? Alternatively, can the instructions for integer multiplication/division be "hacked" (in the HAKMEM sense of the word) to do multiplication/division over GF(2^k) relatively efficiently? I'd be happy with multiplying arbitrary polynomials with coefficients in GF(2)=Z/2Z, and long division of such polynomials to produce a quotient & a remainder polynomial.