Multi Party Distributed Private Matching, Set Disjointness and Cardinality of Set Intersection with Information Theoretic Security

In this paper, we focus on the specific problems of Private Matching, Set Disjointness and Cardinality of Set Intersection in information theoretic settings. Specifically, we give perfectly secure protocols for the above problems in n party settings, tolerating a computationally unbounded semi-honest adversary, who can passively corrupt at most t < n/2 parties. To the best of our knowledge, these are the first such information theoretically secure protocols in a multi-party setting for all the three problems. Previous solutions for Distributed Private Matching and Cardinality of Set Intersection were cryptographically secure and the previous Set Disjointness solution, though information theoretically secure, is in a two party setting. We also propose a new model for Distributed Private matching which is relevant in a multi-party setting.