On the relation between identifiability, differential privacy, and mutual-information privacy

Weina Wang, Lei Ying, Junshan Zhang
2014 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
This paper investigates the relation between three different notions of privacy: identifiability, differential privacy and mutual-information privacy. Under a privacy-distortion framework, where the distortion is defined to be the expected Hamming distance between the input and output databases, we establish some fundamental connections between these three privacy notions. Given a maximum distortion D, let * i (D) denote the smallest (best) identifiability level, and * d (D) the smallest
more » ... ntial privacy level. Then we characterize * i (D) and * d (D), and prove that * for D in some range, where X is a constant depending on the distribution of the original database X, and diminishes to zero when the distribution of X is uniform. Furthermore, we show that identifiability and mutual-information privacy are consistent in the sense that given a maximum distortion D in some range, there is a mechanism that optimizes the identifiability level and also achieves the best mutual-information privacy.
doi:10.1109/allerton.2014.7028576 dblp:conf/allerton/WangYZ14 fatcat:njgqkad7ezfefcpiynuzt6ysmu