Privacy-preserving disjunctive normal form operations on distributed sets

Privacy-preserving set operations such as set union and set intersection on distributed sets are widely used in data mining in which the preservation of privacy is of the utmost concern. In this paper, we extended privacy-preserving set operations and considered privacy-preserving disjunctive normal form (DNF) operations on distributed sets. A privacy-preserving DNF operation on distributed sets can be used to find a set SF satisfying SF=(S1,1∩…∩S1,t2)∪…∪(St1,1∩…∩St1,t2)SF=(S1,1∩…∩S1,t2)∪…∪(St1,1∩…∩St1,t2) without revealing any other information besides just the information which could be inferred from the DNF operations, where Si,j∈{A1,…,An,A1¯,…,An¯} and set Ak is known only to a party Pk. A complement set Ak¯ is defined as Ak¯=(A1∪…∪An)-Ak. Using privacy-preserving DNF operations on distributed sets, it is possible to find set union, (threshold) set intersection, and a set of k-repeated elements.