The Symmetric alpha-Stable Privacy Mechanism

With the rapid growth of digital platforms, there is increasing apprehension about how personal data is being collected, stored, and used by various entities. These concerns range from data breaches and cyber-attacks to potential misuse of personal information for targeted advertising and surveillance. As a result, differential privacy (DP) has emerged as a prominent tool for quantifying a system's level of protection. The Gaussian mechanism is commonly used because the Gaussian density is closed under convolution, a common method utilized when aggregating datasets. However, the Gaussian mechanism only satisfies approximate differential privacy. In this work, we present novel analysis of the Symmetric alpha-Stable (SaS) mechanism. We prove that the mechanism is purely differentially private while remaining closed under convolution. From our analysis, we believe the SaS Mechanism is an appealing choice for privacy focused applications.