Imbalanced Data Problems in Deep Learning-Based Side-Channel Attacks: Analysis and Solution

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.