Suppose Alice is a traitor and suspects Bob might also be a traitor. If Bob is a traitor, she would like to conspire with him together, if not she doesn't want to reveal that she is a traitor. Is there a protocol Alice and Bob can engage in that would reveal that they are either:
- Both traitors
- Not both traitors
With a trusted third party, this would be be easy. Both Alice and Bob reveal their traitor/non-traitor status to the TTP and if both are traitors the TTP tells them so, if only one or none of them are traitors the TTP just says they are not both traitors.
But is there a way without a trusted third party?
I did some research and found this might be an example of a fair exchange and thus be technically impossible without a TTP. Most of the info I can find on fair exchange is over my head though and I thought this situation might be unique in that it involves agreement on potentially the same information, the protocol equivalent of an AND operation. And of course there is that feeling of "it's such a simple problem, how could it be impossible?" so I had to ask.