Differential privacy is a confidentiality metric and quantitatively guarantees the confidentiality of individuals. A noise criterion, called sensitivity, must be calculated when constructing a probabilistic disturbance mechanism that satisfies differential privacy. Depending on the statistical process, the sensitivity may be very large or even impossible to compute. As a result, the usefulness of the constructed mechanism may be significantly low; it might even be impossible to directly construct it. In this paper, we first discuss situations in which sensitivity is difficult to calculate, and then propose a differential privacy with additional dummy data as a countermeasure. When the sensitivity in the conventional differential privacy is calculable, a mechanism that satisfies the proposed metric satisfies the conventional differential privacy at the same time, and it is possible to evaluate the relationship between the respective privacy parameters. Next, we derive sensitivity by focusing on correlation coefficients as a case study of a statistical process for which sensitivity is difficult to calculate, and propose a probabilistic disturbing mechanism that satisfies the proposed metric. Finally, we experimentally evaluate the effect of noise on the sensitivity of the proposed and direct methods. Experiments show that privacy-preserving correlation coefficients can be derived with less noise compared to using direct methods.

We present a privacy preserving method based on inserting dummy data into original data on the data structure called Zero-suppressed BDDs (ZDDs). Our task is distributed itemset mining, which is frequent itemset mining from horizontally partitioned databases stored in distributed places called sites. We focus on the fundamental case in which there are two sites and each site has a database managed by its owner. By dividing the process of distributed itemset mining into the set union and the set intersection, we show how to make the operations secure in the sense of undistinguishability of data, which is our criterion for privacy preserving based on the already proposed criterion, p-indistinguishability. Our method conceals the original data in each operation by inserting dummy data, where ZDDs, BDD-based directed acyclic graphs, are adopted to represent sets of itemsets compactly and to implement the set operations in constructing the distributed itemset mining process. As far as we know, this is the first technique which gives a concrete representation of sets of itemsets and an implementation of set operations for privacy preserving in distributed itemset mining. Our experiments show that the proposed method provides undistinguishability of dummy data. Furthermore, we compare our method with Secure Multiparty Computation (SMC), which is one of the well-known techniques of secure computation.