Kovtun Viacheslav, Izonin Ivan, Gregus Michal
Vinnytsia National Technical University, Vinnytsia, 21000, Ukraine.
Lviv Polytechnic National University, Lviv, 79013, Ukraine.
Sci Rep. 2022 Jul 27;12(1):12849. doi: 10.1038/s41598-022-17254-4.
The article's main contribution is the description of the process of the security subsystem countering the impact of typed cyber-physical attacks as a model of end states in continuous time. The input parameters of the model are the flow intensities of typed cyber-physical attacks, the flow intensities of possible cyber-immune reactions, and the set of probabilities of neutralization of cyber-physical attacks. The set of admissible states of the info-communication system is described taking into account possible variants of the development of the modeled process. The initial parameters of the model are the probabilities of the studied system in the appropriate states at a particular moment. The dynamics of the info-communication system's life cycle are embodied in the form of a matrix of transient probabilities. The mentioned matrix connects the initial parameters in the form of a system of Chapman's equations. The article presents a computationally efficient concept based on Gershgorin's theorems to solve such a system of equations with given initiating values. Based on the presented scientific results, the article proposes the concept of calculating the time to failure as an indicator of the reliability of the info-communication system operating under the probable impact of typical cyber-physical attacks. The adequacy of the model and concepts presented in the article is proved by comparing a statically representative amount of empirical and simulated data. We emphasize that the main contribution of the research is the description of the process of the security subsystem countering the impact of typed cyber-physical attacks as a model of end states in continuous time. Based on the created model, the concept of computationally efficient solution of Chapman's equation system based on Gershgorin's theorems and calculating time to failure as an indicator of the reliability of the info-communication system operating under the probable impact of typed cyber-physical attacks are formalized. These models and concepts are the highlights of the research.
本文的主要贡献在于将安全子系统应对类型化网络物理攻击影响的过程描述为连续时间内的终态模型。该模型的输入参数包括类型化网络物理攻击的流量强度、可能的网络免疫反应的流量强度以及网络物理攻击的中和概率集。考虑到建模过程发展的可能变体，描述了信息通信系统的一组可允许状态。该模型的初始参数是所研究系统在特定时刻处于适当状态的概率。信息通信系统生命周期的动态性以转移概率矩阵的形式体现。上述矩阵以查普曼方程组的形式连接初始参数。本文基于格什戈林定理提出了一种计算效率高的概念，用于求解具有给定初始值的此类方程组。基于所呈现的科学成果，本文提出了将故障时间作为在典型网络物理攻击可能影响下运行的信息通信系统可靠性指标的计算概念。通过比较具有统计代表性的大量经验数据和模拟数据，证明了本文所提出模型和概念的充分性。我们强调，该研究的主要贡献在于将安全子系统应对类型化网络物理攻击影响的过程描述为连续时间内的终态模型。基于所创建的模型，基于格什戈林定理的查普曼方程组的高效计算解概念以及将故障时间作为在类型化网络物理攻击可能影响下运行的信息通信系统可靠性指标的计算概念得以形式化。这些模型和概念是该研究的亮点。
