Hiding Alice in Wonderland: A Case for the Use of Signal Processing Techniques in Differential Privacy

A transformation of data in statistical databases is proposed to hide the presence of an individual. The transformation employs a cascade of spectral whitening and colouring (named recolouring for brevity) that preserves the first- and second-order statistical properties of the true data (i.e. mean and correlation). A measure of practical indistinguishability is introduced for the presence of the individual to be hidden (the Impact Factor), and the transformation is applied to a toy model for the case of correlated data following a Gaussian copula model. It is shown that the Impact Factor is a multiple of what would be achieved with noise addition: the proposed recolouring transformation significantly enlarges the range of attribute values for which the presence of the individual of interest cannot be reliably inferred.

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