Implications of Superstrong Nonlocality for Cryptography

Non-local boxes are hypothetical ``machines'' that give rise to superstrong non-local correlations, leading to a stronger violation of Bell/CHSH inequalities than is possible within the framework of quantum mechanics. We show how non-local boxes can be used to perform any two-party secure computation. We first construct a protocol for bit commitment and then show how to achieve oblivious transfer using non-local boxes. Both have been shown to be impossible using quantum mechanics alone.