Privacy-preserving techniques for processing sets of information have attracted the research community's attention in recent years due to society's increasing dependency on the availability of data at any time. One of the fundamental problems in set operations is known as Private Set Intersection (PSI). The problem requires two parties to compute the intersection between their sets while preserving correctness and privacy. Although several efficient two-party PSI protocols already exist, protocols for PSI in the multi-party setting (MPSI) currently scale poorly with a growing number of parties, even though this applies to many real-life scenarios. This paper fills this gap by proposing two multi-party protocols based on Bloom filters and threshold homomorphic PKEs, which are secure in the semi-honest model. The first protocol is a multi-party PSI, whereas the second provides a more subtle functionality -threshold multi-party PSI (T-MPSI) - which outputs items of the server that appear in at least some number of other private sets. The protocols are inspired by the Davidson-Cid protocol based on Bloom filters. We compare our MPSI protocol against Kolesnikov et al., which is among the fastest known MPSI protocols. Our MPSI protocol performs better than Kolesnikov et al. in terms of run time, given that the sets are small and there is a large number of parties. Our T-MPSI protocol performs better than other existing works: the computational and communication complexities are linear in the number of elements in the largest set given a fixed number of colluding parties. We conclude that our MPSI and T-MPSI protocols are practical solutions suitable for emerging use-case scenarios with many parties, where previous solutions did not scale well.

Millions of shipping containers filled with goods move around the world every day. Before such a container may enter a trade bloc, the customs agency of the goods’ destination country must ensure that it does not contain illegal or mislabeled goods. Due to the high volume of containers, customs agencies make a selection of containers to audit through a risk analysis procedure. Customs agencies perform risk analysis using data sourced from a centralized system that is potentially vulnerable to manipulation and malpractice. Therefore we propose an alternative: DEFenD, a decentralized system that stores data about goods and containers in a secure and privacy-preserving manner. In our system, economic operators make claims to the network about goods they insert into or remove from containers, and encrypt these claims so that they can only be read by the destination country’s customs agency. Economic operators also make unencrypted claims about containers with which they interact. Unencrypted claims can be validated by the entire network of customs agencies. Our key contribution is a data partitioning scheme and several protocols that enable such a system to utilize blockchain and its powerful validation principle, while also preserving the privacy of the involved economic operators. Using our protocol, customs agencies can improve their risk analysis and economic operators can get through customs with less delay. We also present a reference implementation built with Hyperledger Fabric and analyze to what extent our implementation meets the requirements in terms of privacy-preservation, security, scalability, and decentralization.