Thu, 21 Sep 2000 09:54:52 -0500
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Big Brother tells me that Simpson, Sam wrote:
> For a start: Elgamal keys are (currently thought to be...) stronger than
> RSA keys of the same size?
> (see for example: http://www.scramdisk.clara.net/pgpfaq.html#SubRSADH).
This document is a good example of what I was talking about.
Go to this link to verify the following:
% It is, in fact, slightly harder to compute discrete logs modulo an
% appropriate prime than to factor a "hard" integer of the same size -
% so RSA would appear slightly weaker than DHP [Odl95], [Sch97c]. From
% [Sch99a]: "RSA users have to choose a larger key size those using than
% DH over GF(p), for equivalent security.
% Another relevant quote [Wie98]: "The most important factor in choosing a
% public-key technology is security. Based on the best attacks known, RSA
% at 1024 bits, DSA and Diffie-Hellman at 1024 bits, and elliptic curves
% at about 170 bits give comparable levels of security.
"slightly weaker". "comparable levels of security".
I point out that this part of the article is talking about DH, not
ElGamal. They are NOT the same thing. DH is a methodology of key exchange
that depends on selection of a finite group. From earlier in the FAQ:
% ... ElGamal [ElG85], which is a public-key encryption variant of the
% Diffie-Hellman Problem (DHP)
% The security of the DH system is based upon the DH Problem (DHP). This
% problem is conjectured (but not proven) to be equivalent to the Discrete
% Logarithm Problem (DLP)
% DHP is equivalent to the DLP under the "Diffie-Hellman assumption"
Earlier in the article, it talks about the downsides of DH:
% b.Signature Strength. Current implementations of DH only offer DSS as
% the signature algorithm. This limits key length to 1,024-bits which may,
% on its own, be insufficient for long term security. RSA signatures utilise
% a key of up to 2048 or 4096 bits (depending on the implementation).
The only significant entries in the contrast (the downside of RSA) are:
% d. RSA offers less "security-per-bit" of key material than both DH/DSS.
% e. DH appears to be based upon more solid mathematical theory (see the
% section "Any recent developments?" for details).
For my opinion on these, see the earlier quotes. As for the other
downsides, a) is defunct as of Sep 6; b) does not apply if you don't
choose to shoot yourself in the foot as it describes (key signing and
trust prevent a man-in-the-middle exploit of this); c) does not apply
in a document signing situation (though ssh has been using it anyway);
and f) is an implementation issue. What if _I_ want to save the
transactions. With DH, I can encrypt the data on my end, but then
someone could _still_ coerce my encryption key...
I could go on for a while on this. I have not taken the time yet
to study ElGamal mathematically (I am a mathematician), so I have no
inherent opinion. The opinions I give above are just a demonstration
of how the FAQ is dancing around the security issue. Somewhere in
that FAQ (I need to look again) is a paragraph that really made me
wary of using GnuPG. If I find it, I'll post it.
"Of course its your fault. Everything that goes wrong Jack McKinney
here is your fault. It says so in your contract." firstname.lastname@example.org
-Quark to his brother Rom, DS9 http://www.lorentz.com
F4 A0 65 67 58 77 AF 9B FC B3 C5 6B 55 36 94 A6
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