Empirical Analysis of Randomness Quality in Differential Privacy Mechanisms

Abstract

Differential Privacy (DP) relies on carefully calibrated random noise to protect individual privacy in statistical analyses. While theoretical work has analyzed DP under weakened randomness assumptions, the practical consequences of entropy degradation remain poorly understood. We present a systematic empirical investigation of how randomness quality affects differential privacy mechanisms using IBM's DiffPrivLib. We introduce progressively degraded entropy sources characterized by established test suites, starting from high-quality quantum True Random Number Generators (TRNGs) and cryptographically secure Pseudo-Random Number Generators (PRNGs) down to systematically manipulated sources with controlled entropy degradation. Through repeated experiments over one million queries on a reference database and complementary statistical tests, we directly analyze empirical Privacy Loss Random Variable distributions. Our results demonstrate that DP mechanisms reliably detect deviations when approximately 1 bit in every 8 to 16 is manipulated, with detection sensitivity varying significantly between bit-level biases and temporal correlations. We demonstrate that statistical detection of distributional anomalies does not necessarily correspond to actual privacy guarantee violations.