Zip to Zip-it: Compression to Achieve Local Differential Privacy

Abstract: Local differential privacy techniques for numerical data typically transform a dataset to ensure a bound on the likelihood that, given a query, a malicious user could infer information on the original samples. Queries are often solely based on users and their requirements, limiting the design of the perturbation to processes that, while privatizing the results, do not jeopardize their usefulness. In this paper, we propose a privatization technique called Zeal, where perturbator and aggregator are designed as a unit, resulting in a locally differentially private mechanism that, by-design, improves the compressibility of the perturbed dataset compared to the original, saves on transmitted bits for data collection and protects against a privacy vulnerabilities due to floating point arithmetic that affect other state-of-the-art schemes. We prove that the utility error on querying the average is invariant to the bias introduced by Zeal in a wide range of conditions, and that under the same circumstances, Zeal also guarantee protection against the aforementioned vulnerability. Our numerical results show up to 94% improvements in compression and up to 95% more efficient data transmissions, while keeping utility errors within 2%.