Analysis of Multiplicative Low Entropy Masking Schemes Against Correlation Power Attack

Low Entropy Masking Schemes (LEMS) had been proposed to mitigate the high-performance overhead results from the Full Entropy Masking Schemes (FEMS) while offering good protection against side-channel attacks. The masking schemes usually rely on Boolean masking, however, splitting sensitive variables in a multiplicative way is more amenable to non-linear functions and it had been applied to both software and hardware with a competitive alternative to state-of-the-art masked design. Compared to the comprehensive analysis done for Boolean LEMS, the specific leakage characteristics of Multiplicative LEMS have not yet been analyzed. In this paper, we introduce security models for LEMS to characterize the balance of the mask set. Based on the security model, we present an inherent weakness of Multiplicative LEMS. We prove that this defect of Multiplicative LEMS cannot be compensated by choosing a proper mask set, and the security of FEMS is guaranteed thanks to the Dirac function which is used to resist zero-value attack. Then, we exhibit the leakages in the implementation of Multiplicative LEMS. In particular, we propose a new attack against Multiplicative LEMS more efficient by utilizing the distribution of masked intermediate values. The feasibility of the attack is verified by both simulation and practical experiments.