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 standalone 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 bounded-concurrent
setting as well.