Re: ECDL on Oakley Grp 3&4

[Lewis McCarthy <lmccarth@cs.umass.edu>]

Niels Provos writes:
> FYI M. Wiener and R. Zuccherato will be presenting a paper with the
> title 'Faster attacks on Elliptic Curve Cryptosystems' at the SAC'98.
> The paper describes a speedup of the Pollard-\rho attack when an
> elliptic curve over GF(2**n), with n = ed, is defined over GF(2**e).
> The speedup is by a factor of \sqrt{2d}.
> 
> Since both Oakley Group 3 and 4 are defined over GF(2**31) and GF(2**37)
> respectivly, the speedup of a parallel collison-search in both cases is by a
> factor of about \sqrt(2*5) ~ 3.

See http://grouper.ieee.org/groups/1363/contrib.html (about 2/3 down the 
page) for a version of this paper.

-Lewis

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References:

• ECDL on Oakley Grp 3&4
• From: Niels Provos <provos@wserver.physnet.uni-hamburg.de>

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