A deterministic privacy metric using non-stochastic information theory is developed. Particularly, maxi min information's 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 anon-stochastic uncertain private data set. 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 data set). The optimal privacy-preserving policy is proved to be a piece wise 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 k-anonymity (a popular deterministic mechanism for privacy-preserving release of data sets using suppression and generalization techniques), proving that it is in fact not privacy preserving.
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