Two Dimensional SOST: Extract Multi-Dimensional Leakage for Side-Channel Analysis on Cryptosystems

In 2021, Perin et al. proposed a horizontal attack framework against elliptic curve scalar multiplication (ECSM) operation based on the work of Nascimento et al. Their framework consists roughly of three steps. First, they apply k-means on the iteration traces from multiple ECSM executions, then, the results of clustering are used to make a leakage metric trace by using sum-of-squared t-values (SOST), based on the leakage metric trace, the points of interest (POI) are selected. Second, they apply k-means on those POIs to get initial labels for the scalar bits, the accuracy of initial labels is only 52%. Third, wrong bits are corrected by using an iterative deep learning framework. Our work focus on improving the horizontal attack framework by replacing SOST with our proposed two dimensional SOST (2D-SOST) to improve the efficiency of POI selection under unsupervised context. 2D-SOST can extract leakage information between dimensions while SOST can only extract information on one dimension which limits its performance. By replacing SOST with 2D-SOST, our method improves the accuracy of clustering algorithm from an average of 58% to an average of 74%. We also simplified the framework used in original paper and finally recover scalar bits successfully under the configuration where the original paper can not.