Bernstein's fast factorization

[Sidney Markowitz]

Someone on another mailing list pointed me to this posting by Dan
Bernstein on sci.crypt newsgroup:

http://groups.google.com/groups?hl=en&selm=2002Jan1608.53.39.5497%40cr.yp.to

[begin quote]

 From: D. J. Bernstein (djb at cr.yp.to)
 Subject: Re: Strength of PGP vs SSL
 Newsgroups: comp.security.pgp.discuss, sci.crypt, alt.security.pgp
 Date: 2002-01-16 01:00:11 PST

Protecting against the http://cr.yp.to/papers.html#nfscircuit speedup
means switching from n-bit keys to f(n)-bit keys. I'd like to emphasize
that, at this point, very little is known about the function f. It's
clear that f(n) is approximately (3.009...)n for _very large_ sizes n,
but I don't know whether f(n) is larger than n for _useful_ sizes n.

I'd also like to emphasize that special-purpose hardware is useful for
much more than factorization. In fact, it's much easier to reduce cost
this way for secret-key cryptanalysis or elliptic-curve discrete log
than for factorization.

[end quote]

 -- sidney



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