Fun with Protocols

Alright, since it seems this thread is now dead, I'ma post the solution to #3.

 #3

Gregory and the merchant would be incredibly hard-pressed to cheat the bank, even if hacking was allowed. It is very secure against their cheating, collusion or no, in many levels.

Someone eavesdropping on the communications line between Gregory and the merchant can actually get a copy of the money order. Let's call this person Lloyd. Lloyd isn't part of the protocol; he's an outsider. If the merchant hasn't cashed in his money order yet, Lloyd can come to the bank with his copy of the money order and cash it in. The spender of the money order is anonymous, and thus for all the bank knows (unless they check his background), Lloyd is a merchant. Thus, when the merchant comes up with the "real" money order, he'll be identified as a cheater! So will Gregory, if he tries to back up the merchant. And since Lloyd never wrote a money order, he's getting free cash.

Folks, we have a serious problem here!

Even though we had some assumptions and ground rules in here, we still broke these protocols. Now imagine what would happen if anything were allowed (though obviously in reality you don't have unlimited resources; finding a 128-bit key by brute force is virtually undo-able). What if there was noise along the communication lines, corrupting the money orders? What if the bank were not to be trusted? What if the hardware fails? What if someone hacks into the databases the bank houses? Even worse, what if an employee of the bank were attempting to steal the cash? Yet even worse, what if the president of the bank was plotting to haul off with everyone's deposits and flee?

Moral: Don't use these protocols.