Detection and Resolution of Periodic Artifacts in OpenDP's Discrete Laplace Sampler
Cesare Gerolimetto Fabrello, Valeria Rossi, Alberto Trombetta, Massimo Caccia
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 bernoulliexp1 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 106 samples confirms that the corrected sampler produces outputs indistinguishable from the theoretical distribution at the tested precision level.
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