[Cryptography] Secret Handshake problem.

[Benjamin Kreuter]

On Sun, 2017-03-05 at 11:00 +1000, James A. Donald wrote:
> A is an identity that is a member of a club.
> 
> C and D are identities that are not members of this club.
> 
> C wants to reveal to D that C and A are the same, that C is secretly
> a member of the club, if and only if D is secretly a member of the
> club under a different identity.
> 
> I seem to recollect that this is a solved problem, but do not
> remember the solution.

Well, one theoretical solution would be to take whatever algorithm
verifies membership in the club (i.e. whatever information you could
reveal to prove your membership without privacy), express it as a
boolean circuit, and then use a garbled circuit protocol to evaluate it
for both parties' inputs.  Then you just need an AND gate for the
output, so that you only reveal membership when both are members, and
otherwise you reveal nothing.  A similar approach can be used for N
parties.

-- Ben
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