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

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