One-Sided Bounded Noise: Theory, Optimization Algorithms and Applications

We investigate the optimal trade-off between utility and privacy using one-sided perturbation. Unlike conventional privacy-preserving statistical releases, randomization for obfuscating side-channel information is often constrained by infrastructure limitations. In practical scenarios, these constraints may only allow positive and bounded perturbations. For example, extending processing time or sending and storing dummy messages/data is typically feasible. However, implementing modifications in the opposite direction is challenging due to restrictions imposed by hardware capacity, communication protocols, and data management systems. In this paper, we establish the foundation of the positive noise mechanism within three semantic privacy frameworks: Differential Privacy (DP), Maximal Leakage (MaxL), and Probably Approximately Correct (PAC) Privacy. We then present a series of results that characterize or approximate the optimal one-sided noise distribution, subject to a second-moment budget and a bounded maximal magnitude. Building on this theoretical foundation, we develop efficient tools to solve the underlying optimization problems. Through experiments conducted in various scenarios, we demonstrate that existing techniques, such as Truncated Biased Laplace noise, are often suboptimal and result in excessive performance degradation. For instance, in an anonymous communication system with a 250K message budget, our optimized DP noise mechanism achieves a 21× reduction in dummy messages and an 18× reduction in dummy message latency overhead compared to traditional methods.