差分隐私与定量信息流
Differential Privacy versus Quantitative Information Flow
摘要：
差分隐私是数据库社区中非常流行的隐私概念。粗略地说，这个想法是，如果两个不同条目产生某个答案的概率之比受e^ε约束，则随机化查询机制提供了足够的隐私保护。在匿名性和信息流领域，存在类似的对控制信息泄漏的关注，即限制从可观察量推断秘密信息的可能性。近年来，研究人员提出用信息论中的互信息概念来量化泄漏。有两种主要的方法属于这一类：一种是基于香农熵，另一种是基于雷尼最小熵。后者与所谓的贝叶斯风险有关，贝叶斯风险表示猜测秘密的概率。在本文中，我们将展示如何建模的查询系统中的信息理论的渠道，我们比较的概念差分隐私与互信息。我们表明，差分隐私的概念是严格强，在这个意义上，它意味着一个绑定的互信息，但不是反之亦然。
英文摘要：
Differential privacy is a notion of privacy that has become very popular in the database community. Roughly, the idea is that a randomized query mechanism provides sufficient privacy protection if the ratio between the probabilities of two different entries to originate a certain answer is bound by e^ε. In the fields of anonymity and information flow there is a similar concern for controlling information leakage, i.e. limiting the possibility of inferring the secret information from the observables. In recent years, researchers have proposed to quantify the leakage in terms of the information-theoretic notion of mutual information. There are two main approaches that fall in this category: One based on Shannon entropy, and one based on Rényi's min entropy. The latter has connection with the so-called Bayes risk, which expresses the probability of guessing the secret. In this paper, we show how to model the query system in terms of an information-theoretic channel, and we compare the notion of differential privacy with that of mutual information. We show that the notion of differential privacy is strictly stronger, in the sense that it implies a bound on the mutual information, but not viceversa.
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