In recent years, the threat of profiling attacks using deep learning has emerged. Successful attacks have been demonstrated against various types of cryptographic modules. However, the application of deep learning to side-channel attacks (SCAs) is often not adequately assessed because the labels that are widely used in SCAs, such as the Hamming weight (HW) and Hamming distance (HD), follow an imbalanced distribution. This study analyzes and solves the problems caused by dataset imbalance during training and inference. First, we state the reasons for the negative effect of data imbalance in classification for deep-learning-based SCAs and introduce the Kullback-Leibler (KL) divergence as a metric to measure this effect. Using the KL divergence, we demonstrate through analysis how the recently reported cross-entropy ratio loss function can solve the problem of imbalanced data. We further propose a method to solve dataset imbalance at the inference phase, which utilizes a likelihood function based on the key value instead of the HW/HD. The proposed method can be easily applied in deep-learning-based SCAs because it only needs an extra multiplication of the inverted binomial coefficients and inference results (i.e., the output probabilities) from the conventionally trained model. The proposed solution corresponds to data-augmentation techniques at the training phase, and furthermore, it better estimates the keys because the probability distributions of the training and test data are preserved. We demonstrate the validity of our analysis and the effectiveness of our solution through extensive experiments on two public databases.

中文翻译：

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基于深度学习的侧通道攻击中的数据不平衡问题：分析与解决方案


近年来，使用深度学习进行分析攻击的威胁已经出现。已针对各种类型的加密模块进行了成功的攻击。然而，深度学习在侧信道攻击（SCA）中的应用往往没有得到充分的评估，因为SCA中广泛使用的标签，例如汉明权重（HW）和汉明距离（HD），遵循不平衡的分布。本研究分析并解决了训练和推理过程中数据集不平衡带来的问题。首先，我们阐述了基于深度学习的 SCA 分类中数据不平衡产生负面影响的原因，并引入 Kullback-Leibler (KL) 散度作为衡量这种影响的指标。利用KL散度，我们通过分析证明了最近报道的交叉熵比损失函数如何解决数据不平衡的问题。我们进一步提出了一种在推理阶段解决数据集不平衡的方法，该方法利用基于键值而不是 HW/HD 的似然函数。该方法可以很容易地应用于基于深度学习的 SCA，因为它只需要对传统训练模型的倒二项式系数和推理结果（即输出概率）进行额外的乘法。所提出的解决方案对应于训练阶段的数据增强技术，此外，由于保留了训练和测试数据的概率分布，因此它可以更好地估计密钥。我们通过在两个公共数据库上进行大量实验来证明我们分析的有效性和解决方案的有效性。