Diffie-Hellman for Matchmaking?

[Dimitris Tsapakidis <dimitrt@dcs.rhbnc.ac.uk>]

sci.crypters and cypherpunks:

This is a followup to my "Dating Problem" question I posted on
sci.crypt, some months ago. I am trying to find or design some
matchmaking protocols (and implement one of them, eventually)
that have all the nice properties, like privacy and fairness.

I came up with two or three candidate protocols, but they all
rely on the Diffie-Hellman "common key" for mutual authentication.
I haven't seen it used for such purposes in the literature, and I
am suspicious.

The setup is the same as in Diffie-Hellman key exchange.
Assume global: prime n and primitive element g mod n. All the
participants have a pair of (secret, public) keys, where
public=g^secret mod n. By common key I mean
g^(secret_a*secret_b)mod n.

Person A is interested to match person B, so he computes
g^(AB)mod n. B is interested in X, where X may or may not
be A, and calculates g^(BX)mod n. Now, they compare these
two "common keys" either using some Zero Knowledge scheme
that ensures fairness (at no point one party has significantly
more information than the other) or through a Trusted Third Party.
If they are the same, then this means X=A, so A and B
have a match (e.g. a date). The common keys must remain
secret (hence the ZK above): if g^(BX)mod n "escaped"
to the public, then the real X would find out that
B is interested in him.

Is anything wrong with this, specificaly with the use
of the "common key"?

  Dimitris

-- 
Dimitris Tsapakidis               PGP keyID: 735590D5
dimitrt@dcs.rhbnc.ac.uk           MSc in Information Security,
This space reserved               Royal Holloway, University of London
for future use.                   Origin: Thessaloniki, Macedonia, Hellas