输入:能量数据${T_\alpha } = {\rm{\{ } }{T_i},0 \le i \le \alpha ,i \in N\}$,对齐参数$k$。 |
输出:对齐后的能量数据${T'_\alpha }$ |
(1) for j in range(α), do |
(2) 计算与${T_j}$ 欧式距离最近的$k$条能量迹${\rm{\{ }}{T_{j1}},{T_{j2}}, ··· ,{T_{jk}}\} $; |
(3) end |
(4) for j in range (α), do |
(5) 计算关系向量矩阵${{{W}}_{{j}}} = \frac{{\left( {{{C}}_i^{ - 1} \cdot {{{1}}_k}} \right)}}{{{{1}}_k^T \cdot {{C}}_i^{ - 1} \cdot {{{1}}_k}}}$,其中${C_i}$为 ${\rm{\{ }}{T_{j1}},{T_{j2}}, ··· ,{T_{jk}}\} $的协方差矩阵,${{{1}}_k}$为$k$维全1向量; |
(6) end |
(7) 计算矩阵${{M}} = ({{{\rm I}}} - {{W}}){({{I}} - {{W}})^{\rm{T}}}$; |
(8) 设$\beta = \alpha /2$从矩阵M中选择较小的$\beta $个特征值,记为${{{M}}_\beta }$, 计算${T'_\alpha } = T \cdot {{{M}}_\beta }$; |
(9) return ${T_\alpha }^\prime $ |

Citation: Qingjun YUAN, An WANG, Yongjuan WANG, Tao WANG. An Improved Template Analysis Method Based on Power Traces Preprocessing with Manifold Learning[J]. Journal of Electronics and Information Technology, doi: 10.11999/JEIT190598

基于流形学习能量数据预处理的模板攻击优化方法
English
An Improved Template Analysis Method Based on Power Traces Preprocessing with Manifold Learning
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[1]
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表 1 向量矩阵计算算法
表 2 PANDA 2018 Challenge1数据集预处理后方差表(汉明重量不同)
方差 0 1 3 7 15 31 63 127 255 0 4.08 10.99 14.31 16.61 9.80 15.80 18.32 13.02 10.19 1 10.99 2.67 12.49 8.83 7.34 9.50 11.48 5.00 6.33 3 14.31 12.49 8.53 13.62 15.21 12.67 11.73 13.00 15.81 7 16.61 8.83 13.62 3.62 16.24 8.13 11.60 4.99 10.73 15 9.80 7.34 15.21 16.24 4.23 12.21 12.85 9.23 9.84 31 15.80 9.50 12.67 8.13 12.21 4.17 11.62 8.86 9.61 63 18.32 11.48 11.73 11.60 12.85 11.62 4.54 9.26 9.73 127 13.02 5.00 13.00 4.99 9.23 8.86 9.26 1.97 5.23 255 10.19 6.33 15.81 10.73 9.84 9.61 9.73 5.23 4.26 表 3 PANDA 2018 Challenge1数据集预处理后方差表(汉明重量相同)(单位:万)
方差 7 11 13 14 19 35 67 131 224 7 3.62 11.23 23.70 12.19 13.35 13.52 11.55 14.04 9.86 11 11.23 2.60 18.80 11.73 12.07 11.85 12.43 10.97 10.21 13 23.70 18.80 31.91 23.04 27.09 22.52 23.58 56.33 19.22 14 12.19 11.73 23.04 3.89 12.54 9.52 14.47 14.96 12.70 19 13.35 12.07 27.09 12.54 4.78 13.86 15.33 17.68 11.98 35 13.52 11.85 22.52 9.52 13.86 3.15 15.07 15.10 10.67 67 11.55 12.43 23.58 14.47 15.33 15.07 4.98 17.73 9.50 131 14.04 10.97 56.33 14.96 17.68 15.10 17.73 37.04 20.31 224 9.86 10.21 19.22 12.70 11.98 10.67 9.50 20.31 3.91 表 4 PANDA 2018 Challenge1数据集PCA-20处理后方差表(汉明重量不同)(单位:万)
方差 0 1 3 7 15 31 63 127 255 0 33.00 27.97 30.58 29.58 28.96 30.91 29.07 31.04 31.06 1 27.97 13.72 15.97 16.05 15.23 16.10 15.99 20.49 14.26 3 30.58 15.97 13.79 16.97 15.97 17.57 15.58 23.60 16.56 7 29.58 16.05 16.97 17.04 16.70 17.60 17.34 22.65 17.31 15 28.96 15.23 15.97 16.70 14.53 16.83 16.07 21.60 16.43 31 30.91 16.10 17.57 17.60 16.83 16.64 16.65 22.57 17.06 63 29.07 15.99 15.58 17.34 16.07 16.65 15.41 22.27 16.76 127 31.04 20.49 23.60 22.65 21.60 22.57 22.27 24.36 22.35 255 31.06 14.26 16.56 17.31 16.43 17.06 16.76 22.35 13.91 表 5 PANDA 2018 Challenge1数据集LDA-20处理后方差表(汉明重量不同)(单位:万)
方差 0 1 3 7 15 31 63 127 255 0 0.95 1.21 0.93 0.99 1.07 1.09 1.08 1.12 1.13 1 1.21 1.13 1.07 1.17 1.20 1.11 1.24 1.15 1.20 3 0.93 1.07 0.65 0.90 0.99 0.93 1.00 1.05 1.01 7 0.99 1.17 0.90 0.84 0.97 1.02 1.10 1.09 1.06 15 1.07 1.20 0.99 0.97 0.92 1.08 1.17 1.16 1.11 31 1.09 1.11 0.93 1.02 1.08 0.89 1.10 1.10 1.02 63 1.08 1.24 1.00 1.10 1.17 1.10 1.07 1.18 1.15 127 1.12 1.15 1.05 1.09 1.16 1.10 1.18 0.98 1.15 255 1.13 1.20 1.01 1.06 1.11 1.02 1.15 1.15 0.97 -