Inherit Differential Privacy in Distributed Setting: Multiparty Randomized Function Computation

How to achieve differential privacy in the distributed setting, where the dataset is distributed among the istrustful parties, is an important problem. We consider in what condition can a protocol inherit the differential privacy property of a function it computes. The heart of the problem is the secure multiparty computation of randomized function. A notion obliviousness is introduced, which captures the key security problems when computing a randomized function from a deterministic one in the distributed setting. By this observation, a sufficient and necessary condition about securely computing a randomized function from a deterministic one is given. The above result can not only be used to determine whether a protocol computing differentially private function is secure, but also be used to construct a secure one. Then we prove that the differential privacy property of a function can be inherited by the protocol computing it if the protocol securely computes it. A composition theorem of differentially private protocols is also presented. Finally, we construct protocols of Gaussian mechanism and Laplace mechanism, which inherit the differential privacy property.