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

Understand

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 \emph{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 \emph{interval refining}.
• This technique has minimal error, provable privacy, and broad applicability.