A Novel Method of Correlated Laplace Noise Generation for Differential Privacy on Time-Series Data

Data correlation is crucial to privacy protection of time series data. Series indistinguishability provides a theoretical basis for ensuring differential privacy on correlated time series data and is implemented with the correlated Laplace mechanism (CLM), which has become a novel privacy-preserving method. CLM requires generating Laplace noise series with original data correlation. However, the existing method (CLM-S) can generate only Laplace noise series with nonnegative autocorrelation, which prevents it from achieving series indistinguishability on negatively correlated data, potentially compromising privacy guarantees in such scenarios. This study proposes a new method named CLM-M as well as its effective implementation (CLM-M-Delta) for generating correlated Laplace noise series through multiplication combination of four Gaussian noises. It has been theoretically proven that CLM-M can match negative correlations. The experimental results demonstrate that CLM-M-Delta effectively adapts to various data correlations and provides improved privacy performance over CLM-S.