In the Naive Bayes classification problem using a vertically partitioned dataset, the conventional scheme to preserve privacy of each partition uses a secure scalar product and is based on the assumption that the data is synchronized amongst common unique identities. In this paper, we attempt to discard this assumption in order to develop a more efficient and secure scheme to perform classification with minimal disclosure of private data. Our proposed scheme is based on the work by Vaidya and Clifton [2], which uses commutative encryption to perform secure set intersection so that the parties with access to the individual partitions have no knowledge of the intersection. The evaluations presented in this paper are based on experimental results, which show that our proposed protocol scales well with large sparse datasets*.

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.

Random substitutions are very useful and practical method for privacy-preserving schemes. In this paper we obtain the exact relationship between the estimation errors and three parameters used in the random substitutions, namely the privacy assurance metric γ, the total number n of data records, and the size N of transition matrix. We also demonstrate some simulations concerning the theoretical result.