Another look on the relation between template attack and higher order DPA

Template attacks are widely discussed as one of the serious threats against cryptographic modules. Standaert et al. showed that, in multivariate setting, the template attack is more powerful than the differential-of-mean and the correlation analysis in extracting the secret key. Their results match the experiments of Oswald et al. Both Standaert et al. and Oswald et al. discussed the template attack against the implementation with DPA countermeasure called random masking; however, they assumed that the attacker is able to use the information of the random mask in the classification. This paper introduces the notion of higher order template attack and shows that the first order template attack, whereas the attacker has no knowledge of the random mask, also defeats the random masking. From this viewpoint, the template attacks of are the second order template attack, and, as shown in this paper, they can defeat the second order masking. We also discuss the relation between the template attack and the higher order DPA.