All-or-Nothing Disclosure of Secrets

Alice disposes of some number of secrets. She is willing to disclose one of them to Bob. Although she agrees to let him choose wich secret he wants, she is not willing to allow him to gain any information on more than one secret. On the other hand, Bob does not want Alice to know which secret he wishes. This is a useful building block in crypto-protocols. For instance, it can be used to easily implement a multi-party mental Poker protocol similar to that of [Cr1], i.e. : safe against player coalitions. An all-or-nothing disclosure is one by which, as soon as Bob has gained any information whatsoever on one of Alice’s secrets, he has wasted his chances to learn anything about the other secrets. In particular, it must be impossible for Bob to gain joint information on several secrets, such as their exclusive-or. Notice that this is crucial, because it is well-known in classical cryptography that the exclusive-or of two plaintext English messages allows easy recovery of them both, just as a running stream Vigenère would [D].