Diffie-Hellman in GF(2^n)?

Most Diffie-Hellman implementations currently use the multiplicative group of prime fields. However, the multiplicative group of finite fields of characteristic 2 (GF(2^n)) can also be used and should be easier to implement. Is there any reason why they should not be used? Does anyone know the asymptotic running time of the best algorithm for calculating discrete logarithms in GF(2^n)? Wei Dai