The wide use of cloud computing and of data outsourcing rises important concerns with regards to data security resulting thus in the necessity of protection mechanisms such as encryption of sensitive data. The recent major theoretical breakthrough of finding the Holy Grail of encryption, i.e. fully homomorphic encryption guarantees the privacy of queries and their results on encrypted data. However, there are only a few studies proposing a practical performance evaluation of the use of homomorphic encryption schemes in order to perform database queries. In this paper, we propose and analyse in the context of a secure framework for a generic database query interpreter two different methods in which client requests are dynamically executed on homomorphically encrypted data. Dynamic compilation of the requests allows to take advantage of the different optimizations performed during an off-line step on an intermediate code representation, taking the form of boolean circuits, and, moreover, to specialize the execution using runtime information. Also, for the returned encrypted results, we assess the complexity and the efficiency of the different protocols proposed in the literature in terms of overall execution time, accuracy and communication overhead.