Cloud computing helps reduce costs, increase business agility and deploy solutions with a high return on investment for many types of applications, including data warehouses and on-line analytical processing. However, storing and transferring sensitive data into the cloud raises legitimate security concerns. In this paper, we propose a new multi-secret sharing approach for deploying data warehouses in the cloud and allowing on-line analysis processing, while enforcing data privacy, integrity and availability. We first validate the relevance of our approach theoretically and then experimentally with both a simple random dataset and the Star Schema Benchmark. We also demonstrate its superiority to related methods.