We study quantum protocols among two distrustful parties. By adopting a rather strict definition of correctness — guaranteeing that honest players obtain their correct outcomes only — we can show that every strictly correct quantum protocol implementing a non-trivial classical primitive necessarily leaks information to a dishonest player. This extends known impossibility results to all non-trivial primitives. We provide a framework for quantifying this leakage and argue that leakage is a good measure for the privacy provided to the players by a given protocol. Our framework also covers the case where the two players are helped by a trusted third party. We show that despite the help of a trusted third party, the players cannot amplify the cryptographic power of any primitive. All our results hold even against quantum honest-but-curious adversaries who honestly follow the protocol but purify their actions and apply a different measurement at the end of the protocol. As concrete examples, we establish lower bounds on the leakage of standard universal two-party primitives such as oblivious transfer.
While general secure function evaluation (SFE) with information-theoretical (IT) security is infeasible in presence of a corrupted majority in the standard model, there are SFE protocols ( [STOC'87]) that are computationally secure (without fairness) in presence of an actively corrupted majority of the participants. Now, computational assumptions can usually be well justified at the time of protocol execution. The concern is rather a potential violation of the privacy of sensitive data by an attacker whose power increases over time. Therefore, we ask which functions can be computed with long-term security, where we admit computational assumptions for the duration of a computation, but require IT security (privacy) once the computation is concluded. Towards a combinatorial characterization of this class of functions, we also characterize the classes of functions that can be computed IT securely in the authenticated channels model in presence of passive, semi-honest, active, and quantum adversaries.