Abstract Opacity is a privacy property which aims to determine whether the “secret” of a system can be deduced by an outside intruder. In this paper, we investigate the enforcement of opacity using insertion functions which insert additional events if necessary to modify the output of the system. Inspired by the existing insertion mechanisms, we propose a mechanism named k -memory-embedded insertion mechanism for the enforcement of opacity. In our k -memory-embedded insertion mechanism, the insertion functions are determined based on the knowledge of system’s exact states and the stored next sequence of events with length k . Especially, we define the property of i k -E-enforceability that a k -memory-embedded insertion function needs to satisfy for opacity enforcement, and further construct a verifier to determine whether a given opacity notion of the system is i k -E-enforceable or not. Our mechanism improves the embedded insertion mechanism by applying to a broader class of systems. Also, we improve the k -memory insertion mechanism by requiring a smaller number of consecutive events which need to be stored.

中文翻译：

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用于执行不透明度的 K 内存嵌入插入机制

摘要 不透明度是一种隐私属性，旨在确定系统的“秘密”是否可以被外部入侵者推断出来。在本文中，我们使用插入函数来研究不透明度的实施，这些函数在必要时插入额外的事件来修改系统的输出。受现有插入机制的启发，我们提出了一种名为 k-memory-embedded 的插入机制来强制执行不透明度。在我们的 k 内存嵌入插入机制中，插入函数是根据系统确切状态的知识和存储的下一个长度为 k 的事件序列来确定的。特别是，我们定义了 ik -E-enforceability 的属性，即 ak -memory-embedded 插入函数需要满足不透明度强制，并进一步构造一个验证器来确定系统的给定不透明度概念是否可以执行 ik -E-enforceable。我们的机制通过应用于更广泛的系统来改进嵌入式插入机制。此外，我们通过需要更少数量的需要存储的连续事件来改进 k 内存插入机制。