Multi-Party Private Set Intersection: An Information-Theoretic Approach

We investigate the problem of multi-party private set intersection (MP-PSI). In MP-PSI, there are M parties, each storing a data P i over N replicated and non-colluding databases, we want to calculate sets ∩ xmlns:xlink="http://www.w3.org/1999/xlink">i=1 M without leaking any information beyond parties. consider specific communication protocol where one called leader party, initiates MP-PSI by sending queries remaining parties which client The not allowed communicate with other. propose an information-theoretic scheme that privately calculates download cost D = min xmlns:xlink="http://www.w3.org/1999/xlink">t ∈ {1,... xmlns:xlink="http://www.w3.org/1999/xlink">, M} Σ xmlns:xlink="http://www.w3.org/1999/xlink">i {1,..., M}\t ⌈[| xmlns:xlink="http://www.w3.org/1999/xlink">t |N ]/[N -1]⌉. Similar 2-party PSI problem, our builds on connection between multi-message symmetric retrieval (MM-SPIR) problem. Our is non-trivial generalization as it needs intricate design shared common randomness. Interestingly, in terms cost, does incur penalty due more stringent privacy constraints compared