The cloud paradigm enables users to outsource their data to computationally powerful third-party service providers for data management. Many data management tasks rely on the data dependencies in the outsourced data. This raises an important issue of how the data owner can protect the sensitive information in the outsourced data while preserving the data dependencies. In this paper, we consider functional dependency FD, an important type of data dependency. We design a FD-preserving encryption scheme, named F2, that enables the service provider to discover the FDs from the encrypted dataset. We consider the frequency analysis attack, and show that the F2 encryption scheme can defend against the attack under Kerckhoff's principle with provable guarantee. Our empirical study demonstrates the efficiency and effectiveness of F2.