Secure Computability of Functions in the IT Setting With Dishonest Majority and Applications to Long-Term Security

It is well known that general Secure Function Evaluation (SFE) with Information-Theoretical (IT) security is infeasible in presence of a corrupted majority in the standard model. On the other hand, there are SFE protocols (Goldreich et al. [STOC'87]) that are computationally secure (without fairness) in presence of an actively corrupted majority of the participants. Now, the issue with computational assumptions is not so much that they might be unjustified at the time of protocol execution. Rather, the authors are usually worried about a potential violation of the privacy of sensitive data by an attacker whose power increases over time (e.g. due to new technical developments).