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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