Large-scale multi-party counting set intersection using a space efficient global synopsis

Privacy-preserving set intersection (PPSI) of very large data sets is increasingly being required in many real application areas including health-care, national security, and law enforcement. Various techniques have been developed to address this problem, where the majority of them rely on computationally expensive cryptographic techniques. Moreover, conventional data structures cannot be used efficiently for providing count estimates of the elements of the intersection of very large data sets. We consider the problem of efficient PPSI by integrating sets from multiple (three or more) sources in order to create a global synopsis which is the result of the intersection of efficient data structures, known as Count-Min sketches. This global synopsis furthermore provides count estimates of the intersected elements. We propose two protocols for the creation of this global synopsis which are based on homomorphic computations, a secure distributed summation scheme, and a symmetric noise addition technique. Experiments conducted on large synthetic and real data sets show the efficiency and accuracy of our protocols, while at the same time privacy under the Honest-but-Curious model is preserved.