Over the last five years, on-line analytical processing (OLAP) became one of the essential information processing technologies. OLAP technology has been successfully used in different areas: retail, financial services, telecommunication, health care etc. Because of this security of data stored in Data Warehouses became one of the most important aspect of this technology, especially when we speaking about data privacy. We review existing privacy-preserving OLAP techniques and identify new challenges of this technology. In particular, OLAP databases are placed often in the untrusted clouds, so it is crucial to create techniques for evaluating widely used statistical functions (mean value, standard deviation, minimum, maximum, and so on) over the encrypted data. For this purpose, we review and compare encryption schemes with special features (partly homomorphic, order-preserving, deterministic etc.) and suggest architecture of application for private OLAP over the encrypted database.