Impossibility Results for Static Input Secure Computation

Consider a setting of two mutually distrustful parties Alice and Bob who want to securely evaluate some function on pre-specified inputs. The well studied notion of two-party secure computation allows them to do so in the stand-alone setting. Consider a deterministic function (e.g., 1-out-of-2 bit OT) that Alice and Bob can not evaluate trivially and which allows only Bob to receive the output. We show that Alice and Bob can not securely compute any such function in the concurrent setting even when their inputs are pre-specified. Our impossibility result also extends to all deterministic functions in which both Alice and Bob get the same output. Our results have implications in the boundedconcurrent setting as well.