基于均匀流型逼近与投影的高级加密标准算法相关功耗分析方法

doi:10.11772/j.issn.1001-9081.2024060867

《计算机应用》唯一官方网站 ›› 2025, Vol. 45 ›› Issue (6): 1895-1901.DOI: 10.11772/j.issn.1001-9081.2024060867

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基于均匀流型逼近与投影的高级加密标准算法相关功耗分析方法

张润莲(), 唐瑞锋, 王蒿, 武小年

桂林电子科技大学计算机与信息安全学院，广西桂林 541004

收稿日期:2024-06-25 修回日期:2024-11-06 接受日期:2024-11-07 发布日期:2024-11-25 出版日期:2025-06-10
通讯作者: 张润莲
作者简介:张润莲（1974—），女，山西太原人，副教授，博士，主要研究方向：信息安全、分布式计算 zhangrl@guet.edu.cn
唐瑞锋（1998—），男，广西钦州人，硕士研究生，主要研究方向：信息安全
王蒿（1997—），男，河南驻马店人，硕士研究生，主要研究方向：信息安全
武小年（1972—），男，湖北监利人，教授，硕士，主要研究方向：信息安全、分布式计算。
基金资助:
国家自然科学基金资助项目(62062026);广西重点研发计划项目(桂科AB23026131);广西研究生教育创新计划项目(YCSW2024347)

Correlation power analysis method of advanced encryption standard algorithm based on uniform manifold approximation and projection

Runlian ZHANG(), Ruifeng TANG, Hao WANG, Xiaonian WU

School of Computer Science and Information Security，Guilin University of Electronic Technology，Guilin Guangxi 541004，China

Received:2024-06-25 Revised:2024-11-06 Accepted:2024-11-07 Online:2024-11-25 Published:2025-06-10
Contact: Runlian ZHANG
About author:ZHANG Runlian， born in 1974， Ph. D.， associate professor. Her research interests include information security， distributed computing.
TANG Ruifeng， born in 1998， M. S. candidate. His research interests include information security.
WANG Hao， born in 1997， M. S. candidate. His research interests include information security.
WU Xiaonian， born in 1972， M. S.， professor. His research interests include information security， distributed computing.
Supported by:
National Natural Science Foundation of China(62062026);Key Research and Development Program of Guangxi(Guike AB23026131);Innovation Program of Guangxi Graduate Education(YCSW2024347)

摘要/Abstract

摘要：

侧信道攻击（SCA）中所采集的能量迹数据的高噪声和高维度大幅降低了SCA的效率和密钥恢复的准确率。针对上述问题，提出一种基于均匀流型逼近与投影（UMAP）的高级加密标准（AES）算法相关功耗分析（CPA）方法。所提方法基于欧氏距离计算能量迹数据的邻近点集合。首先，通过构建邻接图并计算邻近点之间的相似度得到加权邻接图，从而捕获能量迹数据之间的位置关系以保留数据的局部结构特征；其次，利用拉普拉斯矩阵描述邻接图的结构关系，并通过特征分解取特征值较小的特征向量作为初始化的低维数据；同时，为了保留数据的全局结构特征，使用二进制交叉熵作为优化函数调整数据在低维空间中的位置；此外，为了提升计算效率，在梯度下降过程中使用力导向图布局算法；最后，对降维后的数据进行相关功耗攻击以恢复密钥。实验结果表明，UMAP方法能够有效保留原始能量迹数据的局部和全局结构特征；所提方法能够提高能量迹数据和假设功耗泄露模型之间的相关性，减少恢复密钥所需的能量迹条数，具体地，所提方法恢复单个密钥字节需要的能量迹条数为180，恢复全部16个密钥字节需要的能量迹条数为700；相较于等距特征映射（ISOMAP）降维方法，所提方法恢复所有密钥字节所需的能量迹条数减少了36.4%。

关键词: 侧信道攻击, 均匀流型逼近与投影, 相关功耗分析, 数据降维, 加权邻接图

Abstract:

The efficiency of Side Channel Attack （SCA） and the accuracy of key recovery are reduced by the high noise and dimension of energy trace data collected in SCA greatly. To solve these problems， a Correlation Power Analysis （CPA） method of Advanced Encryption Standard （AES） algorithm based on Uniform Manifold Approximation and Projection （UMAP） was proposed. In the proposed method， Euclidean distance was used as a basis to calculate the set of proximate points of energy traces. Firstly， in order to capture position relationships of the energy trace data to preserve local structural features of the data， a weighted adjacency matrix was obtained by constructing an adjacency graph and calculating the similarity among proximate nodes. Then， structure relationships of the adjacency graph were described using the Laplacian matrix， and the eigenvectors with small eigenvalues were extracted as the initialized low-dimensional data from the adjacency graph by feature decomposition. Meanwhile， in order to preserve global structural features of the data， the binary cross-entropy was used as optimization function to adjust position of the data in the low-dimensional space. Furthermore， in order to improve the computational efficiency， the force-directed graph layout algorithm was adopted in the gradient descent process. Finally， correlation power attacks were performed on the dimensional reduced data to recover the key. Experimental results show that UMAP method can preserve local and global structural features of the original energy trace data effectively； the proposed method can improve the correlation between energy trace data and assumed power leakage models， and reduce the number of energy traces required for key recovery，specifically， the number of energy traces required to recover a single key byte is 180， and the number of energy traces required to recover all 16 key bytes is 700 by the proposed method； compared to the ISOmetric MAPping （ISOMAP） dimension reduction method， the proposed method reduces the number of energy traces required to recover all key bytes by 36.4%.

Key words: Side Channel Attack (SCA), Uniform Manifold Approximation and Projection (UMAP), Correlation Power Analysis (CPA), data dimension reduction, weighted adjacency graph

中图分类号:

TP309.7

张润莲, 唐瑞锋, 王蒿, 武小年. 基于均匀流型逼近与投影的高级加密标准算法相关功耗分析方法[J]. 计算机应用, 2025, 45(6): 1895-1901.

Runlian ZHANG, Ruifeng TANG, Hao WANG, Xiaonian WU. Correlation power analysis method of advanced encryption standard algorithm based on uniform manifold approximation and projection[J]. Journal of Computer Applications, 2025, 45(6): 1895-1901.

图/表 9

图1 采集设备连接

Fig.1 Connection of collection equipment

图2 AES软件采集的某条能量迹波形

Fig.2 Waveform of energy trace collected by AES software

图3 基于能量迹构建的加权k邻图

Fig. 3 Weighted k-adjacency graph based on energy traces

图4 降维后数据中相似度为1的2条能量迹波形

Fig. 4 Waveforms of two energy traces with similarity of 1 after dimension reduction

图5 降维后数据中邻近点集合中的2条能量迹波形

Fig.5 Waveforms of two energy traces in proximate point set after dimension reduction

图6 降维后数据中非邻近点集合中的3条能量迹波形

Fig.6 Waveforms of three energy traces in non-proximate point set after dimension reduction

图7 使用不同预处理方法后的CPA相关系数图

Fig. 7 Correlation coefficient graphs of CPA with different preprocessing methods

图8 使用不同预处理方法后的CPA攻击分数排名

Fig. 8 Score ranking of CPA with different preprocessing methods

图9 采用不同方法进行CPA密钥恢复所需的能量迹条数

Fig.9 Number of energy traces required for key recovery using CPA based on different methods

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基于均匀流型逼近与投影的高级加密标准算法相关功耗分析方法

Correlation power analysis method of advanced encryption standard algorithm based on uniform manifold approximation and projection

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