Differential privacy is a formal mathematical framework for quantifying the degree of individual privacy in a statistical database.To guarantee differential privacy, a typical method is to add random noise to the original data for data release. In this paper, we investigate the conditions of differential privacy (single-dimensional case) considering the general random noise adding mechanism, and then apply the obtained results for privacy analysis of the privacy-preserving consensus algorithm. Specifically, we obtain a necessary and sufficient condition of $\epsilon$-differential privacy, and the sufficient conditions of $(\epsilon, \delta)$-differential privacy. We apply them to analyze various random noises. For the special cases with known results, our theory not only matches with the literature, but also provides an efficient approach to the privacy parameters’ estimation; for other cases that are unknown, our approach provides a simple and effective tool for differential privacy analysis. Applying the obtained theory on privacy-preserving consensus algorithm, we obtain the necessary condition and the sufficient condition to ensure differential privacy.

中文翻译：

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差分私人噪声添加机制及其在共识算法中的应用

差分隐私是在统计数据库中量化个体隐私程度的正式数学框架。为保证差分隐私，典型的方法是在原始数据中加入随机噪声进行数据发布。在本文中，我们研究了考虑一般随机噪声添加机制的差分隐私（单维情况）的条件，然后将所得结果应用于隐私保护共识算法的隐私分析。具体来说，我们得到一个充分条件$\epsilon$- 差分隐私，充分条件 $(\epsilon, \delta)$- 差异隐私。我们应用它们来分析各种随机噪声。对于已知结果的特殊情况，我们的理论不仅与文献相符，而且还提供了一种有效的隐私参数估计方法；对于其他未知的情况，我们的方法为差异隐私分析提供了一种简单有效的工具。应用得到的隐私保护共识算法理论，我们得到了保证差分隐私的必要条件和充分条件。