Detection and Resolution of Periodic Artifacts in OpenDP's Discrete Laplace Sampler

2026-10-01

AI Summary

This study addresses periodic artifacts in the OpenDP discrete Laplace sampler caused by underlying library defects, which compromise the statistical reliability of differential privacy mechanisms. To resolve this, we propose a fault diagnosis strategy that isolates nested sampling layers to precisely identify failing components, and reconstructs Bernoulli primitives using exact rational arithmetic to eliminate artifacts at their source. Statistical validation over one million samples demonstrates that the corrected sampler output exhibits no significant deviation from the theoretical distribution. This work effectively resolves sampling bias in the discrete Laplace distribution within differential privacy frameworks, enhancing the robustness of privacy-preserving algorithms in safety-critical scenarios.

Abstract

Differential privacy implementations rely on precise sampling from noise distributions to provide formal privacy guarantees. We report the discovery of systematic artifacts in OpenDP's discrete Laplace sampler that manifest as periodic distortions in the output distribution. Through systematic testing, we trace these artifacts to a faulty implementation in the rational arithmetic library used by the bernoulli_exp1 function, a low-level primitive that implements sampling from Bernoulli(e^(-x)) distributions. We present a diagnostic methodology that isolates the faulty component in the nested sampling hierarchy and propose an alternative implementation based on exact rational arithmetic that eliminates the artifacts. Statistical validation with 10^6 samples confirms that the corrected sampler produces outputs indistinguishable from the theoretical distribution at the tested precision level.

Problem

• differential privacy
• discrete Laplace sampler
• periodic artifacts
• OpenDP
• rational arithmetic

Innovation

• Differential Privacy
• Discrete Laplace Sampler
• Periodic Artifacts
• Exact Rational Arithmetic
• Diagnostic Methodology