The framework of differential privacy protects an individual's privacy while publishing query responses on congregated data. In this work, a new noise addition mechanism for differential privacy is introduced where the noise added is sampled from a hybrid density that resembles Laplace in the centre and Gaussian in the tail. With a sharper centre and light, sub-Gaussian tail, this density has the best characteristics of both distributions. We theoretically analyze the proposed mechanism, and we derive the necessary and sufficient condition in one dimension and a sufficient condition in high dimensions for the mechanism to guarantee (${\epsilon}$,${\delta}$)-differential privacy. Numerical simulations corroborate the efficacy of the proposed mechanism compared to other existing mechanisms in achieving a better trade-off between privacy and accuracy.

翻译：差分隐私框架能够在发布聚合数据查询结果的同时保护个人隐私。本文提出了一种新的差分隐私噪声添加机制，其噪声采样自一种混合密度分布——中心区域呈拉普拉斯分布特征，尾部则表现为高斯分布特性。该密度分布兼具中心更尖锐与尾部更轻缓（亚高斯尾部）的双重优势。我们从理论上分析了所提机制，推导出该机制在单维条件下保证（ε，δ）-差分隐私的充要条件，以及在高维条件下保证该机制的充分条件。数值模拟验证了该机制相对于现有其他机制，在实现隐私与精度之间更优权衡方面的有效性。