Information disclosure under realistic assumptions: privacy versus optimality

The problem of information disclosure has attracted much interest from the research community in recent years. When disclosing information, the challenge is to provide as much information as possible (optimality) while guaranteeing a desired safety property for privacy (such as l-diversity). A typical disclosure algorithm uses a sequence of disclosure schemas to output generalizations in the nonincreasing order of data utility; the algorithm releases the first generalization that satisfies the safety property. In this paper, we assert that the desired safety property cannot always be guaranteed if an adversary has the knowledge of the underlying disclosure algorithm. We propose a model for the additional information disclosed by an algorithm based on the definition of deterministic disclosure function (DDF), and provide definitions of p-safe and p-optimal DDFs. We give an analysis for the complexity to compute a p-optimal DDF. We show that deciding whether a DDF is p-optimal is an NP-hard problem, and only under specific conditions, we can solve the problem in polynomial time with respect to the size of the set of all possible database instances and the length of the disclosure generalization sequence. We then consider the problem of microdata disclosure and the safety condition of l-diversity. We relax the notion of p-optimality to weak p-optimality, and develop a weak p-optimal algorithm which is polynomial in the size of the original table and the length of the generalization sequence.