Differential privacy is a widely-used metric, which provides rigorous privacy definitions and strong privacy guarantees. Much of the existing studies on differential privacy are based on datasets where the tuples are independent, and thus are not suitable for correlated data protection. In this paper, we focus on correlated differential privacy, by taking the data correlations and the prior knowledge of the initial data into account. The data correlations are modeled by Bayesian conditional probabilities, and the prior knowledge refers to the exact values of the data. We propose general correlated differential privacy conditions for the discrete and continuous random noise-adding mechanisms, respectively. In case that the conditions are inaccurate due to the insufficient prior knowledge, we introduce the tuple dependence based on rough set theory to improve the correlated differential privacy conditions. The obtained theoretical results reveal the relationship between the correlations and the privacy parameters. Moreover, the improved privacy condition helps strengthen the mechanism utility. Finally, evaluations are conducted over a micro-grid system to verify the privacy protection levels and utility guaranteed by correlated differential private mechanisms.

2022 IEEE 19th International Conference on Mobile Ad Hoc and Smart Systems (MASS)