# Precision-based attacks and interval refining: how to break, then fix, differential privacy on finite computers

arXiv: https://arxiv.org/abs/2207.13793 · HTML: https://mlsanity.com/paper/2207.13793/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2022.

## Built on by (most cited first, 8 of 8)

- [Correlated Privacy Mechanisms for Differentially Private Distributed Mean Estimation](https://mlsanity.com/paper/2407.03289/) (2024)
- [dpmm: Differentially Private Marginal Models, a Library for Synthetic Tabular Data Generation](https://mlsanity.com/paper/2506.00322/) (2025)
- [ResidualPlanner+: a scalable matrix mechanism for marginals and beyond](https://mlsanity.com/paper/2305.08175/) (2023)
- [Rethinking Anonymity Claims in Synthetic Data Generation: A Model-Centric Privacy Attack Perspective](https://mlsanity.com/paper/2601.22434/) (2026)
- [Tight Auditing of Differential Privacy in MST and AIM](https://mlsanity.com/paper/2604.18352/) (2026)
- [PPFL-RDSN: Privacy-Preserving Federated Learning-based Residual Dense Spatial Networks for Encrypted Lossy Image Reconstruction](https://mlsanity.com/paper/2507.00230/) (2025)
- [DPSQL+: A Differentially Private SQL Library with a Minimum Frequency Rule](https://mlsanity.com/paper/2602.22699/) (2026)
- [Dithered Gaussian Mechanism for Randomness-Efficient Differential Privacy](https://mlsanity.com/paper/2607.06320/) (2026)

## Abstract (arXiv)

Despite being raised as a problem over ten years ago, the imprecision of floating point arithmetic continues to cause privacy failures in the implementations of differentially private noise mechanisms. In this paper, we highlight a new class of vulnerabilities, which we call precision-based attacks, and which affect several open source libraries. To address this vulnerability and implement differentially private mechanisms on floating-point space in a safe way, we propose a novel technique, called interval refining. This technique has minimal error, provable privacy, and broad applicability. We use interval refining to design and implement a variant of the Laplace mechanism that is equivalent to sampling from the Laplace distribution and rounding to a float. We report on the performance of this approach, and discuss how interval refining can be used to implement other mechanisms safely, including the Gaussian mechanism and the exponential mechanism.