Over-threshold multi-party private set operation protocols for lightweight clients

The problem of private set operation (PSO) can realize the function of data set analysis on the premise of privacy protection, which has been widely concerned by researchers in academia and industry. Over-threshold multi-party private set operation (OT-MP-PSO) is a special class of PSO, where multiple parties hold their own private set respectively and want to securely compute which element appears in at least t private sets of all parties for an adjustable threshold t. In practical scenarios, this primitive has many applications, such as voting systems and network operations centers collaborating to identify common threats. However, in current studies, the computational costs of existing protocols are exponentially related to the threshold t thus the range of t is limited to keep the protocols efficient. In this paper, we designed an efficient OT-MP-PSO protocol in a dual cloud setting and the range of t is not limited. In addition, we also design a series of private set fine-grained computation protocols that combine threshold, such as the cardinality of the result set and the sum of the element labels that satisfy the threshold condition. Moreover, we give formal security proofs for the proposed protocols and validate the efficiency of our protocols through experiments. On small data sets, our protocol has very little computational and communication overhead. When the set size ranges from 101 to 103, the experimental results show that our protocol is significantly better than the state-of-the-art approach. Finally, we introduce a typical application of our protocols in the field of voting. •We construct a novel over-threshold multi-party private set operation protocol.•We design corresponding secure statistical protocols in threshold conditions.•We introduce an anonymous voting application based on our protocol.