On Perfect Privacy

The problem of private data disclosure is studied from an information theoretic perspective. Considering a pair dependent random variables (X, Y), where X and Y denote the useful data, respectively, following addressed: What maximum that can be revealed about Y, measured by mutual I(Y; U), in which U denotes while disclosing no X, captured condition statistical independence, i.e., ⊥ U, henceforth called perfect privacy)? We analyze supremization utility, U) under privacy for two scenarios: output perturbation full observation models, correspond to cases Markov kernel, privacy-preserving mapping, applies respectively. When both have finite alphabet, linear algebraic analysis involved solution provides some interesting results, such as upper/lower bounds on size released alphabet utility. Afterwards, it shown jointly Gaussian not possible model contrast model. Finally, asymptotic provided obtain rate when sufficiently small leakage allowed. In particular, context model, this always feasible, lower are it; mild conditions, becomes unbounded.