Diffie-Hellman in GF(2^n)?

[Wei Dai]

> I don't know enough about number theory to judge for myself;
> but you can read the (long) paper yourself at
> 
> 	ftp://netlib.att.com/netlib/att/math/odlyzko/discrete.logs.ps.Z

Thanks for the reference.  The paper gives a running time of exp(c(n 
log n)^(1/2)) for discrete log in GF(p) and exp(c*n^(1/3)*(log n)^(2/3)) 
for discrete log in GF(2^n).  However, this paper was published in 1985. 
There is now an algorithm to calculate discrete logs in GF(p) in
exp(c*n^(1/3)*(log n)^(2/3)) (see prime.discrete.logs.ps.Z in the same
directory), so perhaps GF(2^n) isn't so bad after all. 

Wei Dai