Data Warehouses (DW), Multidimensional (MD) Databases, and On-Line Analytical Processing Applications are used as a very powerful mechanism for discovering crucial business information. Considering the extreme importance of the information managed by these kinds of applications, it is essential to specify security measures from early stages of the DW design in the MD modeling process, and enforce them. In the past years, there have been some proposals for representing main MD modeling properties at the conceptual level. Nevertheless, none of these proposals considers security measures as an important element in their models, so they do not allow us to specify confidentiality constraints to be enforced by the applications that will use these MD models. In this paper, we discuss the confidentiality problems regarding DW's and we present an extension of the Unified Modeling Language (UML) that allows us to specify main security aspects in the conceptual MD modeling, thereby allowing us to design secure DW's. Then, we show the benefit of our approach by applying this extension to a case study. Finally, we also sketch how to implement the security aspects considered in our conceptual modeling approach in a commercial DBMS.