Bistochastic privacy

Nicolas Ruiz; Josep Domingo-Ferrer

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arXiv · 2207.03940

Bistochastic privacy

Nicolas Ruiz·Josep Domingo-Ferrer

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Abstract

We introduce a new privacy model relying on bistochastic matrices, that is, matrices whose components are nonnegative and sum to 1 both row-wise and column-wise. This class of matrices is used to both define privacy guarantees and a tool to apply protection on a data set. The bistochasticity assumption happens to connect several fields of the privacy literature, including the two most popular models, k-anonymity and differential privacy. Moreover, it establishes a bridge with information theory, which simplifies the thorny issue of evaluating the utility of a protected data set. Bistochastic privacy also clarifies the trade-off between protection and utility by using bits, which can be viewed as a natural currency to comprehend and operationalize this trade-off, in the same way than bits are used in information theory to capture uncertainty. A discussion on the suitable parameterization of bistochastic matrices to achieve the privacy guarantees of this new model is also provided.

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Nicolas Ruiz, Josep Domingo-Ferrer. 2022-07-08. Bistochastic privacy. https://arxiv.org/abs/2207.03940

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