A cloud data warehouse (cloud DW) is a subject-oriented, integrated, time-variant, voluminous, nonvolatile and multidimensional distributed database that is hosted in a cloud. A solution to ensure data confidentiality for a cloud DW is cryptography. In this article, the authors propose an encryption methodology for a cloud DW stored according to the star schema, considering both the data confidentiality maintenance of the DW and the capability of processing analytical queries directly over the encrypted DW. The proposed encryption methodology comprises an encryption strategy for DW called MV-HO (MultiValued and HOmomorphic) for the definition of how the different types of DW's attributes must be encrypted. The proposed MV-HO encryption strategy was compared with encryption strategies based on symmetric encryption, order preserving symmetric encryption and homomorphic encryption. Results indicated that MV-HO is the best solution found, as MV-HO is pareto-optimal with respect to other strategies investigated.