Feasibility Analysis of Encrypted Transmission on Security of Industrial Control Systems
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摘要: 针对需要对现场数据加密的工业控制系统（Industrial control system，ICS），基于稳定性判据设计一种加密传输机制的可行性评估模型，结合超越方程D-subdivision求解法，提出一种数据加密长度可行域求解算法.改进IAE（Integral absolute error）并提出Truncated IAE（TIAE）-based指标，用于评估可行域内不同数据长度对系统实时性能的影响.利用嵌入式平台测定的加密算法执行时间与数据长度的关系，评估了两种对称加密算法应用在他励直流电机控制系统中的可行性，验证了可行域求解算法的准确性，并获得了实时性能随数据长度的变化规律.Abstract: For those industrial control systems (ICS) whose field data need to be encrypted, a model, based on stability criterion is designed to assess the feasibility of the encrypted transmition mechanism. Combined with D-subdivision solution to transcentdental equation, a method to solve the feasible region of the length of encrypted data quantitatively is proposed. Integral absolute error (IAE) is improved to introduce the truncated IAE (TIAE)-based index, which is designed for evaluating the real-time performance influenced by the length in the feasible region. In terms of the relationship between execute time of encryption algorithm and length measured on embedded platform, two symmetric encryption algorithms for the control system of separately excited DC motor are evaluated, the accuracy of solution to the feasible region is verified, and the change law between real-time performance and length is obtained.1) 本文责任编委 陈积明
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图 1 基于加密传输机制的工控系统框架图
Fig. 1 Frame diagram of industrial control system under encrypted transmission
图 2 基于加密传输机制的MIMO控制系统结构图
Fig. 2 Structure diagram of MIMO control system under encrypted transmission
图 3 加密算法执行时间与数据加密长度关系曲线
Fig. 3 Relationship curve between the execute time of encryption algorithms and the length of encrypted data
图 4 不同AES加密数据长度下实际转速变化曲线
Fig. 4 Timely varying curves of the actual speed under different length of AES encrypted data
图 5 ${\eta _{{\rm TIAE}}}$随${t_r}$、$\sigma\% $、${t_s}$、${\rm TIAE}$变化曲线
Fig. 5 Curves of the index ${\eta _{{{\rm TIAE}}}}$ under different ${t_r}$, $\sigma\%$, ${t_s}$, ${\rm TIAE}$
图 6 ${t_r}$、$\sigma\%$、${t_s}$、${\rm TIAE}$随数据加密长度$l$变化曲线
Fig. 6 Curves of the index ${t_r}$, $\sigma\%$, ${t_s}$, ${\rm TIAE}$ under different length of AES encrypted data
图 7 ${\eta _{{\rm TIAE}}}$随数据加密长度$l$变化曲线
Fig. 7 Curves of the index ${\eta _{{\rm TIAE}}}$ under different length of AES encrypted data.
表 1 加密算法执行时间与数据加密长度测试数据
Table 1 Test data between the execute time of encryption algorithms and the length of plaintext
长度(B) 16 144 272 400 528 656 784 912 1040 时间(ms) AES加密 7.48 67.21 127.18 187.24 246.88 306.46 366.37 426.42 485.94 AES解密 9.32 83.99 158.81 233.46 308.88 383.58 458.43 533.18 608.33 DES加密 8.83 79.72 150.59 228.22 300.12 372.94 445.34 517.98 595.94 DES解密 6.97 62.46 117.91 178.22 234.84 291.86 348.74 405.94 462.94 
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表 2 集合$\Theta$判定表格
Table 2 Judging form of $\Theta$
$\tau$ $\omega $ $T$ ${\rm{RT}}$ ${\rm{NU(}}\tau {\rm{)}}$ (0, 0.321) 0 0.321 4.775 0.201867 1 (0.321, 1.637) 2 1.637 4.775 0.201867 1 (1.637, 2.953) 4 2.953 4.775 0.201867 1 $\cdots$ $\cdots$ $\cdots$ $\cdots$ 6
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表 3 实时性指标与数据加密长度测试数据
Table 3 Test data between the real-time performance index and the length of encrypted data
$l$(B) ${t_r}$(s) $\sigma\%$ ${t_s}$ (s) TIAE ${\eta _{{{\rm TIAE}}}}$ 0 20 0 1.618 99.2545 1 70 1.301 0.2438 1.972 130.2633 0.7620 80 1.305 0.3453 2.118 161.8826 0.6131 90 1.312 0.4396 2.596 206.0987 0.4816 100 1.323 0.544 3.209 274.6412 0.3614 110 1.333 0.639 4.311 372.4369 0.2665 120 1.344 0.7434 5.676 541.5546 0.1833 130 1.354 0.8383 8.749 846.1615 0.1173 140 1.365 0.9427 17.231 1.73E+03 0.0573 150 1.375 1.0376 80.985 8.52E+03 0.0117
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