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Despite being raised as a problem over ten years ago, the imprecision offloating point arithmetic continues to cause privacy failures in theimplementations of differentially private noise mechanisms. In this paper, wehighlight a new class of vulnerabilities, which we call \emph{precision-basedattacks}, and which affect several open source libraries. To address thisvulnerability and implement differentially private mechanisms on floating-pointspace in a safe way, we propose a novel technique, called \emph{intervalrefining}. This technique has minimal error, provable privacy, and broadapplicability. We use interval refining to design and implement a variant ofthe Laplace mechanism that is equivalent to sampling from the Laplacedistribution and rounding to a float. We report on the performance of thisapproach, and discuss how interval refining can be used to implement othermechanisms safely, including the Gaussian mechanism and the exponentialmechanism.

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