Statistical Higher-Order Correlation Attacks against Code-Based Masking

Masking is one of the most well-established methods to thwart side-channel attacks. Many masking schemes have been proposed in the literature, and code-based masking emerges and unifies several masking schemes in a coding-theoretic framework. In this work, we investigate the side-channel resistance of code-based masking from a non-profiling perspective by utilizing correlation-based side-channel attacks. We present a systematic evaluation of correlation attacks with various higher-order (centered) moments and then present the form of optimal correlation attacks. Interestingly, the Pearson correlation coefficient between the hypothetical leakage and the measured traces is connected to the signal-to-noise ratio in higher-order moments, and it turns out to be easy to evaluate rather than launch repeated attacks. We also identify some ineffective higher-order correlation attacks at certain orders when the device leaks under the Hamming weight leakage model. Our theoretical findings are verified through both simulated and real-world measurements.