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The private collection of multiple statistics from a population is afundamental statistical problem. One possible approach to realize this is torely on the local model of differential privacy (LDP). Numerous LDP protocolshave been developed for the task of frequency estimation of single and multipleattributes. These studies mainly focused on improving the utility of thealgorithms to ensure the server performs the estimations accurately. In thispaper, we investigate privacy threats (re-identification and attributeinference attacks) against LDP protocols for multidimensional data followingtwo state-of-the-art solutions for frequency estimation of multiple attributes.To broaden the scope of our study, we have also experimentally assessed fivewidely used LDP protocols, namely, generalized randomized response, optimallocal hashing, subset selection, RAPPOR and optimal unary encoding. Finally, wealso proposed a countermeasure that improves both utility and robustnessagainst the identified threats. Our contributions can help practitioners aimingto collect users' statistics privately to decide which LDP mechanism best fitstheir needs.

On the Risks of Collecting Multidimensional Data Under Local Differential Privacy