In many emerging security applications, a system designer frequently needs to ensure that a certain property of a given system (that may reveal important details about the system’s operation) be kept secret (opaque) to outside observers (eavesdroppers). Motivated by such applications, several researchers have formalized, analyzed, and described methods to verify notions of opacity in discrete event systems of interest. This paper introduces and analyzes a notion of opacity in systems that can be modeled as probabilistic finite automata or hidden Markov models. We consider a setting where a user needs to choose a specific hidden Markov model (HMM) out of m possible (different) HMMs, but would like to “hide” the true system from eavesdroppers, by not allowing them to have an arbitrary level of confidence as to which system has been chosen. We describe necessary and sufficient conditions (that can be checked with polynomial complexity), under which the intruder cannot distinguish the true HMM, namely, the intruder cannot achieve a level of certainty about its decision, which is above a certain threshold that we can a priori compute.

中文翻译：

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离散事件系统中的概率系统不透明度

在许多新兴的安全应用程序中，系统设计人员经常需要确保给定系统的某些属性（可能会透露有关系统操作的重要细节）对外部观察者（窃听者）保密（不透明）。在此类应用的推动下，一些研究人员已经正式化、分析和描述了验证感兴趣的离散事件系统中不透明度概念的方法。本文介绍并分析了可以建模为概率有限自动机或隐马尔可夫模型的系统中的不透明度概念。我们考虑这样一种设置：用户需要从 m 个可能的（不同的）HMM 中选择一个特定的隐马尔可夫模型（HMM），但希望通过不允许窃听者具有任意级别的“隐藏”真实系统对选择了哪个系统的信心。