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Re: Diffie-Hellman in GF(2^n)?
I wrote earlier:
> 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.
To clarify my earlier post, although both of the latter two algorithms
have a runtime of the form exp(c*n^(1/3)*(log n)^(2/3)), for GF(p)
c=1.922+o(1), for GF(2^n) c=1.405+o(1). This seems to imply that if
GF(2^n) is to be used, n needs to be 2.56*log p to achieve a comparable
level of security to using GF(p). (2.56=1.922^3/1.405^3)