Biblio

Private Set Intersection (PSI) allows two parties, the sender and the receiver, to compute the intersection of their private sets without revealing extra information to each other. We are interested in the unbalanced PSI setting, where (1) the receiver's set is significantly smaller than the sender's, and (2) the receiver (with the smaller set) has a low-power device. Also, in a Labeled PSI setting, the sender holds a label per each item in its set, and the receiver obtains the labels from the items in the intersection. We build upon the unbalanced PSI protocol of Chen, Laine, and Rindal (CCS\textbackslashtextasciitilde2017) in several ways: we add efficient support for arbitrary length items, we construct and implement an unbalanced Labeled PSI protocol with small communication complexity, and also strengthen the security model using Oblivious Pseudo-Random Function (OPRF) in a pre-processing phase. Our protocols outperform previous ones: for an intersection of 220 and \$512\$ size sets of arbitrary length items our protocol has a total online running time of just \$1\$\textbackslashtextasciitildesecond (single thread), and a total communication cost of 4 MB. For a larger example, an intersection of 228 and 1024 size sets of arbitrary length items has an online running time of \$12\$ seconds (multi-threaded), with less than 18 MB of total communication.

Private Set Intersection (PSI) is a cryptographic technique that allows two parties to compute the intersection of their sets without revealing anything except the intersection. We use fully homomorphic encryption to construct a fast PSI protocol with a small communication overhead that works particularly well when one of the two sets is much smaller than the other, and is secure against semi-honest adversaries. The most computationally efficient PSI protocols have been constructed using tools such as hash functions and oblivious transfer, but a potential limitation with these approaches is the communication complexity, which scales linearly with the size of the larger set. This is of particular concern when performing PSI between a constrained device (cellphone) holding a small set, and a large service provider (e.g. WhatsApp), such as in the Private Contact Discovery application. Our protocol has communication complexity linear in the size of the smaller set, and logarithmic in the larger set. More precisely, if the set sizes are Ny textless Nx, we achieve a communication overhead of O(Ny log Nx). Our running-time-optimized benchmarks show that it takes 36 seconds of online-computation, 71 seconds of non-interactive (receiver-independent) pre-processing, and only 12.5MB of round trip communication to intersect five thousand 32-bit strings with 16 million 32-bit strings. Compared to prior works, this is roughly a 38–115x reduction in communication with minimal difference in computational overhead.