Optimization of Binary Randomized Response Based on Lanke Privacy and Utility Analysis

Currently, it has become a consensus to enhance privacy protection. Randomized response (RR) technique, as the mainstream perturbation mechanism for local differential privacy, has been widely studied. However, most of the research in literature managed to modify existing RR schemes and propose new mechanisms with better privacy protection and utility, which are illustrated only by numerical experiments. We study the properties of generalized binary randomized response mechanisms from the perspectives of Lanke privacy and utility. The mathematical expressions of privacy and utility for the binary RR mechanism are given respectively. Moreover, the comparison principle for privacy and utility of any two mechanisms is proved. Finally, the optimization problem of the binary RR mechanism is discussed. Our work is based on a rigorous mathematical proof of privacy and utility for the general binary RR mechanism, and numerical verification illustrates the correctness of the conclusions. It can provide theoretical support for the design of binary RR mechanism and can be applied in data collection, analysis and publishing.