[Cryptography] ZK meeting scheduling protocol?

[Henry Baker]

As most of you already know, Microsoft Outlook provides some protocols for helping to schedule meetings via email.

Has anyone developed a zero knowledge protocol for such scheduling?

Basically, an invite goes out to N different peoples' computers to initiate a protocol to find the earliest common date in all of their calendars which is free.  The computers then communicate amongst themselves to try to find such a date.  Everyone is aware of the other N-1 people invited to the meeting, and is able to communicate with them directly.

At the end of the protocol, either no such common date is available -- ever -- or a common date is secured.  Everyone then knows the date.  However, no one ever learns (at least from the protocol itself) which non-selected dates matched on any subset of the peoples' calendars.  Thus, for example, no one can figure out who is the busiest (or least busy) person by studying all the messages from the protocol.

I guess the initial warmup problem would be to try to do this for exactly 2 people.

Any ideas?

(This is not a homework problem, at least not for any course I'm taking!)