"you can only read this if we both are interested". Hmmm, cryptographic challenge...
This boils down to computing the logical and of two bits held by different parties without either of them having to reveal their bit. Incidentally, a flatmate of mine has put some time into this, and referred me to Yao, Andrew C. "Protocols for secure computations." 23rd annual symposium on foundations of computer science (sfcs 1982). IEEE, 1982.. That reference tackles a more general problem, but can be a good starting point.
For this specific problem, there exists a write-up in German by some researchers I do not know, but also a sheet of handwritten notes in English one room away from my desk. So if anyone wants to seriously delve into this, I could make introductions.