Fair Games against an All-Powerful Adversary

Suppose that a weak (i.e., polynomially-bounded) device needs to interact over a clear channel with an infinitely-powerful and adversarial device which he does not trust. Notice that throughout this interaction (game) the infinitely-powerful device can hide information from the weak device using encryption. The weak device, however, is not so fortunate: to keep the game fair, he must hide information from the strong device in the information-theoretic sense. Nevertheless, we show that the weak player can play any polynomial length partial-information game (or secure protocol) with the strong player using any one-way function. More specifically, we show that oblivious transfer protocol can be implemented in this model using any one-way function and we establish related impossibility results concerning oblivious transfer.

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