Communication-Efficient and Privacy-Preserving Protocol for Computing Over-Threshold Set-Union

In a variety of applications, the data items of multiple participants are collected and analyzed, and meanwhile the participants' privacy needs to be protected. This paper studies an over-threshold data aggregation problem, i.e., over-threshold set-union. In our model, we assume there are n participants, an untrusted data aggregator and a proxy, and each participant has a sensitive data item. The over-threshold set-union is normally defined as follows: given a threshold t, the aggregator only learns the data items which appear at least t times in the union of data items of all participants without learning anything else. Existing solutions either suffer from high communication cost or leak the multiplicity information of data items. In order to handle this defect, we present an efficient protocol in the honest-but-curious model by leveraging threshold secret sharing and dual pairing vector spaces. We prove that the proposed protocol not only has O(n log(2) n) communication complexity which nearly matches the lower bound Omega(n/ log n) but also protects the data privacy.