Higher order side channel attacks (HOSCAs) exploit the side channel leakages of a masked crypto device at multiple leakage samples to recover the secret key used by the target crypto device. The attack price of HOSCA increases exponentially with the attack order, and HOSCA becomes infeasible when the attack order is high. Therefore, it is utmost important to employ the higher order optimal distinguishers (HOODs) to effectively decrease the attack price of HOSCA and make it applicable in a wide scenario. Recently, under the assumption that noises at different leakage samples are independent and that the noise at a single leakage sample follow the Gaussian distribution, Bruneau et al. proposed one HOOD. However, the two assumptions made by Bruneau et al. do not fit in with the real cases well. In light of this, the HOOD proposed by Bruneau et al. cannot be strictly speaking the optimal. Therefore, in this paper we propose the mahalanobis distance similarity measure (MDSM)-based HOOD. In the MDSM-based HOOD, no unsuitable assumptions are made. Therefore, the key-recovery efficiency of the MDSM-based HOOD should be higher than that of the maximum likelihood principle-based HOOD. In fact, both empirical and real evaluations are performed to support our point.

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