Protecting private information for two classes of aggregated database queries

An important direction of informatics is devoted to the protection of privacy of confidential information while providing answers to aggregated queries that can be used for analysis of data. Protecting privacy is especially important when aggregated queries are used to combine personal information stored in several databases that belong to different owners or come from different sources. Malicious attackers may be able to infer confidential information even from aggregated numerical values returned as answers to queries over large collections of data. Formal proofs of security guarantees are important, because they can be used for implementing practical systems protecting privacy and providing answers to aggregated queries. The investigation of formal conditions which guarantee protection of private information against inference attacks originates from a fundamental result obtained by Chin and Ozsoyoglu in 1982 for linear queries. The present paper solves similar problems for two new classes of aggregated nonlinear queries. We obtain complete descriptions of conditions, which guarantee the protection of privacy of confidential information against certain possible inference attacks, if a collection of queries of this type are answered. Rigorous formal security proofs are given which guarantee that the conditions obtained ensure the preservation of privacy of confidential data. In addition, we give necessary and sufficient conditions for the protection of confidential information from special inference attacks aimed at achieving a group compromise.