Efficient Linear Multiparty PSI and Extensions to Circuit/Quorum PSI

Multiparty Private Set Intersection (mPSI), enables n parties, each holding private sets (each of size m) to compute the intersection of these private sets, without revealing any other information to each other. For security parameter \lambda, this work gives secure protocols with asymptotic communication complexity O(nm\lambda) while also being over 5x more concretely efficient than prior works, even for as few as 15 parties. Finally, we introduce and consider two important variants of mPSI – circuit PSI (that allows the parties to compute a function over the intersection set without revealing the intersection itself) and quorum PSI (that allows P1 to learn all the elements in his/her set that are present in at least k other sets) and provide concretely efficient protocols for these variants.