  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.
