In this talk, we focus our attention on privately computing functions of the intersection of two sets, held by two different parties. To exemplify, assume that $U$ is an ordered ground set, that Alice holds a subset of elements $X \subset U$, and that Bob holds a subset of elements $Y \subset U$. Alice and Bob would like to privately compute the minimum or the maximum of $X \cap Y$, in such a way that no further information is leaked on $X \cap Y$ and on the rest of the elements held by Alice and Bob in their respective sets. We quickly survey the main available approaches for privately computing $X \cap Y$ and point out that current custom protocols cannot trivially be adapted to privately compute some specific functions of the intersection like the minimum or the maximum functions, mentioned before. And it seems not easy to come up with a design strategy different from the circuit-based general solution for secure two-party computation. Nevertheless, we suggest some hybrid protocols for certain functions and discuss some interesting issues, which could be addressed by future research.

Bio: Paolo D'Arco is a Computer Science professor at the University of Salerno (Italy). He was a postdoctoral fellow at the Centre for Applied Cryptographic Research (CACR), in the Department of Combinatorics and Optimization (University of Waterloo), from November 2001 to October 2002. His main research interests are in Cryptography. He has worked on the design and the analysis of cryptographic primitives and protocols: secret sharing, key distribution, authentication, anonymous communication, oblivious transfer, visual cryptography, broadcast encryption, and secure multiparty computation. He has also done some cryptanalysis of lightweight and ultra-lightweight protocols.