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

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.

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BibTeX RIS

BibTeX

@misc{fabrello2026detection,
  title = {{Detection and Resolution of Periodic Artifacts in OpenDP's Discrete Laplace Sampler}},
  author = {Cesare Gerolimetto Fabrello and Valeria Rossi and Alberto Trombetta and Massimo Caccia},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01907},
  eprint = {2610.01907},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01907},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Detection and Resolution of Periodic Artifacts in OpenDP's Discrete Laplace Sampler
AU  - Cesare Gerolimetto Fabrello
AU  - Valeria Rossi
AU  - Alberto Trombetta
AU  - Massimo Caccia
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01907
UR  - https://arxiv.org/abs/2610.01907
AB  - 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.
ER  -

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