Development and Analysis of Deterministic Privacy-Preserving Policies Using Non-Stochastic Information Theory

• Published in: arXiv.org
• Main Author: Farokhi, Farhad
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 23.01.2019
• Subjects: Computation; Computer Science - Cryptography and Security; Computer Science - Information Theory; Computer Science - Systems and Control; Information theory; Mathematics - Information Theory; Mathematics - Optimization and Control; Minimax technique; Optimization; Policies; Privacy; Queries
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1810.11153

A deterministic privacy metric using non-stochastic information theory is developed. Particularly, minimax information is used to construct a measure of information leakage, which is inversely proportional to the measure of privacy. Anyone can submit a query to a trusted agent with access to a non-stochastic uncertain private dataset. Optimal deterministic privacy-preserving policies for responding to the submitted query are computed by maximizing the measure of privacy subject to a constraint on the worst-case quality of the response (i.e., the worst-case difference between the response by the agent and the output of the query computed on the private dataset). The optimal privacy-preserving policy is proved to be a piecewise constant function in the form of a quantization operator applied on the output of the submitted query. The measure of privacy is also used to analyze the performance of \(k\)-anonymity methodology (a popular deterministic mechanism for privacy-preserving release of datasets using suppression and generalization techniques), proving that it is in fact not privacy-preserving.