Communication-Efficient Inner Product Private Join and Compute with Cardinality.

Private join and compute (PJC) is a paradigm where two parties owing their private database securely join their databases and compute a function over the combined database. Inner product PJC, introduced by Lepoint et al. (Asiacrypt'21), is a class of PJC that has a wide range of applications such as secure analysis of advertising campaigns. In this computation, two parties, each of which has a set of identifier-value pairs, compute the inner product of the values after the (inner) join of their databases with respect to the identifiers. They proposed inner product PJC protocols that are specialized for the unbalanced setting where the input sizes of both parties are significantly different and not suitable for the balanced setting where the sizes of two inputs are relatively close. We propose an inner product PJC protocol that is much more efficient than that by Lepoint et al. for balanced inputs in the setting where both parties are allowed to learn the intersection size additionally. Our protocol can be seen as an extension of the private intersection-sum protocol based on the decisional Diffie-Hellman assumption by Ion et al. (EuroS&P'20) and is especially communication-efficient as the private intersection-sum protocol. In the case where both input sizes are 216, the communication cost of our inner-product PJC protocol is 46x less than that of the inner product PJC protocol by Lepoint et al.