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Two parties with private data sets can find shared elements using a PrivateSet Intersection (PSI) protocol without revealing any information beyond theintersection. Circuit PSI protocols privately compute an arbitrary function ofthe intersection - such as its cardinality, and are often employed in anunbalanced setting where one party has more data than the other. Existingprotocols are either computationally inefficient or require extensiveserver-client communication on the order of the larger set. We introducePractically Efficient PSI or PEPSI, a non-interactive solution where only theclient sends its encrypted data. PEPSI can process an intersection of 1024client items with a million server items in under a second, using less than 5MB of communication. Our work is over 4 orders of magnitude faster than anexisting non-interactive circuit PSI protocol and requires only 10% of thecommunication. It is also up to 20 times faster than the work of Ion et al.,which computes a limited set of functions and has communication costsproportional to the larger set. Our work is the first to demonstrate thatnon-interactive circuit PSI can be practically applied in an unbalancedsetting.

PEPSI: Practically Efficient Private Set Intersection in the Unbalanced Setting