Privacy-preserving data splitting is a technique that aims to protect data privacy by storing different fragments of data in different locations. In this work we give a new combinatorial formulation to the data splitting problem. We see the data splitting problem as a purely combinatorial problem, in which we have to split data attributes into different fragments in a way that satisfies certain combinatorial properties derived from processing and privacy constraints. Using this formulation, we develop new combinatorial and algebraic techniques to obtain solutions to the data splitting problem. We present an algebraic method which builds an optimal data splitting solution by using Gr " o bner bases. Since this method is not efficient in general, we also develop a greedy algorithm for finding solutions that are not necessarily minimal sized.
The advent of database services has resulted in privacy concerns on the part of the client storing data with third party database service providers. Previous approaches to enabling such a service have been based on data encryption, causing a large overhead in query processing. A distributed architecture for secure database services is proposed as a solution to this problem where data is stored at multiple servers. The distributed architecture provides both privacy as well as fault tolerance to the client. In this paper we provide algorithms for (1) distributing data: our results include hardness of approximation results and hence a heuristic greedy algorithm for the distribution problem (2) partitioning the query at the client to queries for the servers implemented by a bottom up state based algorithm. Finally the results at the servers are integrated to obtain the answer at the client. We provide an experimental validation and performance study of our algorithms.