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摘要: 针对传统动态水印(Dynamic-watermarking, DWM)检测方法无法适用模型不确定系统的攻击检测问题, 首先分析模型不确定项导致的传统动态水印检测失效原因, 然后考虑模型不确定项和过程噪声的统计规律, 将其影响转化为对方差变化特性进行分析, 提出两个具有鲁棒性的攻击检测式以及检测式中关键时变方差阈值的确定方法; 其次采用系统失真信号功率定量刻画攻击信号造成系统性能损失程度, 理论证明了系统失真信号功率上界; 在此基础上考虑最坏情况下攻击能够躲过检测, 基于水印信号与其他混合信号相互独立性新增第三检测式, 同时理论证明了系统失真信号功率上界进一步受限范围, 进而提升不确定系统的安全性; 最后仿真算例验证了所提方法的有效性和可行性.Abstract: The traditional dynamic-watermarking (DWM) cyber-attack detection cannot directly apply to uncertain systems. In this paper, we first analyze this failure due to model uncertainty. Secondly, based on the statistics of model uncertainty and process noise, we derive two robust attack-detection formulas, and the method of determining the critical time-varying-variance threshold in the formulas. Then, the system performance loss caused by the attack signal, and the upper limit of the distortion signal power are quantified. Furthermore, in the worst case, to avoid that an attack can pass-through the above two-formula detection, the third detection formula is derived. In addition, the upper limit of the distorted signal power of the system is also derived. This is based on the mutual independence of the watermark signal and other mixed signals. Thus, the three-formula detection strengthens the security of the system with model uncertainty. Finally, we use a simulation example to demonstrate our theoretical results.
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图 6 基于Test 1的虚假数据注入攻击检测结果 (数值仿真)
Fig. 6 Detection results based on Test 1 under false data injection attack (numerical simulation)
图 7 基于Test 2的虚假数据注入攻击检测结果 (数值仿真)
Fig. 7 Detection results based on Test 2 under false data injection attack (numerical simulation)
图 8 基于Test 3的虚假数据注入攻击检测结果(数值仿真)
Fig. 8 Detection results based on Test 3 under false data injection attack (numerical simulation)
图 10 基于阈值检测的虚假数据注入攻击检测结果(实例仿真)
Fig. 10 Detection results based on threshold detection under false data injection attack (real example simulation)
图 12 基于Test 2的虚假数据注入攻击检测结果(实例仿真)
Fig. 12 Detection results based on Test 2 under false data injection attack (real example simulation)
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