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%.

翻译：针对数值数据的本地差分隐私技术通常会对数据集进行变换，以确保给定查询时恶意用户无法从原始样本中推断出信息的概率。查询往往仅基于用户及其需求，这限制了扰动过程的设计——该过程在实现结果私有化的同时，不能损害其可用性。本文提出一种名为Zeal的私有化技术，该技术将扰动器与聚合器设计为一个整体，形成一种本地差分隐私机制，该机制在设计上提升了扰动数据集相对于原始数据集的压缩性，节省了数据收集的传输比特数，并防止了因浮点运算导致的隐私漏洞（这些漏洞影响了其他先进方案）。我们证明，在广泛条件下，查询均值时的效用误差与Zeal引入的偏差无关，且在同一条件下，Zeal还能保证针对上述漏洞的保护。数值实验表明，在保持效用误差在2%以内的同时，压缩效率最高提升94%，数据传输效率最高提升95%。