基于流形学习能量数据预处理的模板攻击优化方法

袁庆军; 王安; 王永娟; 王涛

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

doi: 10.11999/JEIT190598

袁庆军^{1, 2},
王安³,
王永娟^{1, 2, ,},
王涛^{1, 2}

1.
战略支援部队信息工程大学郑州 450001
2.
河南省网络密码技术重点实验室郑州 450001
3.
北京理工大学计算机学院北京 100081

基金项目: 国家自然科学基金(61872040)，河南省网络密码技术重点实验室开放基金(LNCT2019-S02)，“十三五”国家密码发展基金(MMJJ20170201)

详细信息

作者简介:
袁庆军：男，1993年生，讲师，研究方向为机器学习侧信道分析

王安：男，1983年生，副教授，研究方向为侧信道分析与防护技术

王永娟：女，1982年生，研究员，研究方向为侧信道分析与密码系统安全

王涛：男，1995年生，硕士生，研究方向为机器学习侧信道分析

通讯作者:
王永娟　pinkywyj@163.com

中图分类号: TP309.7
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出版历程
- 收稿日期: 2019-08-07
- 修回日期: 2019-10-31
- 网络出版日期: 2019-11-27
- 刊出日期: 2020-08-18

An Improved Template Analysis Method Based on Power Traces Preprocessing with Manifold Learning

Qingjun YUAN^{1, 2},
An WANG³,
Yongjuan WANG^{1, 2
, ,},
Tao WANG^{1, 2}

1.
PLA Strategic Support Force Information Engineering University , Zhengzhou 450001, China
2.
Henan Key Laboratory of Network Cryptography Technology, Zhengzhou 450001, China
3.
School of Computer Science, Beijing Institute of Technology, Beijing 100081, China

Funds: The National Natural Science Foundation of China (61872040), The Fund of Henan Key Laboratory of Network Cryptography Technology (LNCT2019-S02), The National Cryptographic Development Fund of the 13th Five-Year Plan (MMJJ20170201)

摘要

摘要: 能量数据作为模板攻击过程中的关键对象，具有维度高、有效维度少、不对齐的特点，在进行有效的预处理之前，模板攻击难以奏效。针对能量数据的特性，该文提出一种基于流形学习思想进行整体对齐的方法，以保留能量数据的变化特征，随后通过线性投影的方法降低数据的维度。使用该方法在Panda 2018 challenge1标准数据集进行了验证，实验结果表明，该方法的特征提取效果优于传统的PCA和LDA方法，能大幅度提高模板攻击的成功率。最后采用模板攻击恢复密钥，仅使用两条能量迹密钥恢复成功率即可达到80%以上。
- 信息安全 /
- 模板攻击 /
- 流形学习 /
- 能量数据 /
- 对齐算法 /
- 降维算法
Abstract: As the key object in the process of template analysis, power traces have the characteristics of high dimension, less effective dimension and unaligned. Before effective preprocessing, template attack is difficult to work. Based on the characteristics of energy data, a global alignment method based on manifold learning is proposed to preserve the changing characteristics of power traces, and then the dimensionality of data is reduced by linear projection. The method is validated in Panda 2018 challenge1 standard datasets respectively. The experimental results show that the feature extraction effect of this method is superior over that of traditional PCA and LDA methods. Finally, the method of template analysis is used to recover the key, and the recovery success rates can reach 80% with only two traces.
- Information security /
- Template analysis /
- Manifold learning /
- Power traces /
- Alignment algorithm /
- Dimension reduction algorithm

HTML全文

图 1 PANDA 2018 Challenge1 前3条能量迹

下载: 全尺寸图片幻灯片

图 2 PANDA 2018 Challenge1 能量迹与密钥相关系数

下载: 全尺寸图片幻灯片

图 3 PANDA 2018 Challenge1能量数据对齐后

下载: 全尺寸图片幻灯片

图 4 PANDA 2018 Challenge1 能量迹降维后

下载: 全尺寸图片幻灯片

图 5 PANDA 2018 Challenge1 能量迹PCA-20和LDA-20降维后

下载: 全尺寸图片幻灯片

表 1 向量矩阵计算算法

　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${ {{W} }_{{j} } } = \dfrac{ {\left( { {{C} }_i^{ - 1} \cdot { {{1} }_k} } \right)} }{ { { {{\textit{1} } } }_k^{\rm T} \cdot {{C} }_i^{ - 1} \cdot { {{{\textit{1}}} }_k} } }$，其中${ { C}_i} $为
　　　 ${\rm{\{ }}{T_{j1}},{T_{j2}}, ··· ,{T_{jk}}\} $的协方差矩阵，${ {{{\textit{1}}} }_k}$为$k$维全1向量；

　(6)　end

　(7)　计算矩阵${{M} } = ({{ {I} } } - {{W} }){({{I} } - {{W} })^{\rm{T} } }$;

　(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 $。

下载: 导出CSV

表 2 PANDA 2018 Challenge1数据集预处理后方差(×10⁴)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

下载: 导出CSV

表 3 PANDA 2018 Challenge1数据集预处理后方差(×10⁴)表(汉明重量相同)

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

下载: 导出CSV

表 4 PANDA 2018 Challenge1数据集PCA-20处理后方差(×10⁴)表(汉明重量不同)

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

下载: 导出CSV

表 5 PANDA 2018 Challenge1数据集LDA-20处理后方差(×10⁴)表(汉明重量不同)

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

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