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Assessment of Addition-Chain-Based Masked S-Box Using Deep-Learning-Based Side-Channel Attacks

Masking schemes are considered to be effective countermeasures to protect Internet-of-Things devices from side-channel attacks. Deep-learning-based side-channel attacks (DL-SCAs) have been demonstrated to be very effective targeting on masked implementations. In this paper, we investigate the resistance of a popular computation-based masking scheme against DL-SCAs, that is, the addition-chain-based one. We find that addition chain introduces computations of intermediate monomials over 
 
 
 
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 with smaller output sizes, which decreases its resistance against DL-SCAs. Specifically, we first use mutual information metric to evaluate the side-channel resistance of different monomials from an information theory point of view. Next, we further propose the Kullback–Leibler divergence ratio as an evaluation metric to analyze the impact of monomial output size on DL-SCAs. The measurement values show that the monomial with smaller output size is less-resistant against DL-SCAs. Then we conduct simulated and practical experiments respectively to verify it. In simulated experiments, we perform DL-SCAs on first-order masked implementations with different noise levels and training trace numbers. The results demonstrate that monomials with smaller output size are more vulnerable. Moreover, with the increase (resp. decrease) in noise level (resp. training trace number), the resistance difference of these monomials becomes more significant. In addition, we obtain similar results through simulated experiments on second-order masked scenario. In practical experiments based on an ARM Cortex-M4 architecture, we collect power and electromagnetic traces in consideration of low and high noise levels. The results show that the number of required traces for targeting the S-Box output is at least three times as much that for targeting the weakest monomial.