We consider the problem of processing private database queries over encrypted data in the cloud. To do this, we propose a protocol for conjunctive query and another for disjunctive query processing using somewhat homomorphic encryption in the semi-honest model. In 2016, Kim et al. [IEEE Trans. on Dependable and Secure Comput.] showed an FHE-based query processing with equality conditions over encrypted data. We improve the performance of processing private conjunctive and disjunctive queries with the low-depth equality circuits than Kim et al.’s circuits. To get the low-depth circuits, we modify the packing methods of Saha and Koshiba [APWConCSE 2016] to support an efficient batch computation for our protocols with a few multiplications. Our implementation shows that our protocols work faster than Kim et al.’s protocols for both conjunctive and disjunctive query processing along with a better security level. We are also able to provide security to both attributes and values appeared in the predicate of the conjunctive and disjunctive queries whereas Kim et al. provided the security to the values only.