Kernel Discriminant Analysis for Information Extraction in the Presence of Masking
Résumé
To reduce the memory and timing complexity of the Side-Channel Attacks (SCA), dimensionality reduction techniques are usually applied to the measurements. They aim to detect the so-called Points of Interest (PoIs), which are time samples which (jointly) depend on some sensitive information (e.g. secret key sub-parts), and exploit them to extract information. The extraction is done through the use of functions which combine the measurement time samples. Examples of combining functions are the linear combinations provided by the Principal Component Analysis or the Linear Discriminant Analysis. When a masking countermeasure is properly implemented to thwart SCAs, the selection of PoIs is known to be a hard task: almost all existing methods have a combinatorial complexity explosion, since they require an exhaustive search among all possible d-tuples of points. In this paper we propose an efficient method for informative feature extraction in presence of masking countermeasure. This method, called Kernel Discriminant Analysis, consists in completing the Linear Discriminant Analysis with a so-called kernel trick, in order to efficiently perform it over the set of all possible d-tuples of points without growing in complexity with d. We identify and analyse the issues related to the application of such a method. Afterwards, its performances are compared to those of the Projection Pursuit (PP) tool for PoI selection up to a 4th-order context. Experiments show that the Kernel Discriminant Analysis remains effective and efficient for high-order attacks, leading to a valuable alternative to the PP in constrained contexts where the increase of the order d does not imply a growth of the profiling datasets.