Black-Box Separations for Differentially Private Protocols

We study the maximal achievable accuracy of distributed differentially private protocols for a large natural class of boolean functions, in the computational setting. In the information theoretic model, McGregor et al. [FOCS 2010] and Goyal et al. [CRYPTO 2013] have demonstrated several functionalities whose differentially private computation results in much lower accuracies in the distributed setting, as compared to the client-server setting. We explore lower bounds on the computational assumptions under which this particular accuracy gap can possibly be reduced for general two-party boolean output functions. In the distributed setting, it is possible to achieve optimal accuracy, i.e. the maximal achievable accu-racy in the client-server setting, for any function, if a semi-honest secure protocol for oblivious transfer exists. However, we show the following strong impossibility results: ◦ For any boolean function and fixed level of privacy, the maximal achievable accuracy of any (fully) black-box construction based on existence of key-agreement protocols is at least a constant smaller than optimal achievable accuracy. Since key-agreement protocols imply the existence of one-way functions, this separation also extends to one-way functions