Mind the Balance: Revealing the Vulnerabilities in Low Entropy Masking Schemes
Jingdian Ming, Yongbin Zhou, Wei Cheng, Huizhong Li, Guang Yang, Qian Zhang · IEEE Transactions on Information Forensics and Security · 2020
Low Entropy Masking Schemes (LEMS) have attracted wide attention due to their implementations simplicity and relatively good performance in protecting cryptographic implementations against Side-Channel-Attacks (SCAs). To achieve desired security, it is necessary (but not sufficient) to find proper low entropy mask sets to protect all sensitive secret-dependant intermediate variables. However, one crucial problem concerning this intuitive idea is that what `proper' mask sets should be. To formally capture such crucial qualification, we introduce the notion of balancedness to characterize this natural attribute of mask sets themselves. Considering that this notion is limited to characterize first-order security, we generalize it to d-dimension balancedness to accommodate dth-order security, then we exhibit lower and upper bounds on d-dimension balancedness for any d. With the help of these essential definitions, we prove that no balanced low entropy mask set really exists, which implies that LEMS implementations always have vulnerabilities in theory due to the unbalancedness of underlying mask sets. In order to further demonstrate the practical implications of balancedness, we show 4 different kinds of attacks on three state-of-the-art LEMS implementations. Specifically, the distribution attack proposed in this paper is a general first-order attack on LEMS. The results demonstrate that unbalanced mask sets actually do lead to serious vulnerabilities.