泄漏的加法和乘法概念及其容量

M. Alvim, K. Chatzikokolakis, Annabelle McIver, Carroll Morgan, C. Palamidessi, Geoffrey Smith
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引用次数: 75

摘要

保护敏感信息不被不当泄露是一个基本的安全目标。这很复杂,很难实现,通常是因为不可避免甚至不可预测的操作条件可能导致计划的安全防御遭到破坏。一种有吸引力的方法是将目标定义为定量问题,然后设计方法,根据泄漏的信息量来度量系统漏洞。其结果是,精确的操作条件和对先验知识的假设,可以在评估任何可测量脆弱性的严重程度方面发挥至关重要的作用。我们通过关注漏洞度量来发展这个主题,这些漏洞度量在允许将一般泄漏边界置于程序上的意义上是稳健的,这些边界适用于任何操作条件和任何先验知识。特别地,我们提出了一个信道容量理论,推广了信息论的香农容量,它可以应用于最近提出的一种称为g泄漏的测量的加法和乘法形式。此外,我们探索了计算这些(新)能力的计算方面:其中一种情况可以通过将其表示为坎托罗维奇距离来有效地解决,但另一种情况证明是np完全的。我们还发现了与通道不直接访问的数据的任意相关性的容量界限,如在Dalenius's Desideratum的场景中。
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Additive and Multiplicative Notions of Leakage, and Their Capacities
Protecting sensitive information from improper disclosure is a fundamental security goal. It is complicated, and difficult to achieve, often because of unavoidable or even unpredictable operating conditions that can lead to breaches in planned security defences. An attractive approach is to frame the goal as a quantitative problem, and then to design methods that measure system vulnerabilities in terms of the amount of information they leak. A consequence is that the precise operating conditions, and assumptions about prior knowledge, can play a crucial role in assessing the severity of any measured vunerability. We develop this theme by concentrating on vulnerability measures that are robust in the sense of allowing general leakage bounds to be placed on a program, bounds that apply whatever its operating conditions and whatever the prior knowledge might be. In particular we propose a theory of channel capacity, generalising the Shannon capacity of information theory, that can apply both to additive- and to multiplicative forms of a recently-proposed measure known as g-leakage. Further, we explore the computational aspects of calculating these (new) capacities: one of these scenarios can be solved efficiently by expressing it as a Kantorovich distance, but another turns out to be NP-complete. We also find capacity bounds for arbitrary correlations with data not directly accessed by the channel, as in the scenario of Dalenius's Desideratum.
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