Less is More Dimensionality Reduction from a Theoretical Perspective

Reducing the dimensionality of the measurements is an important problem in side-channel analysis. It allows to capture multi-dimensional leakage as one single compressed sample, and therefore also helps to reduce the computational complexity. The other side of the coin with dimensionality reduction is that it may at the same time reduce the efficiency of the attack, in terms of success probability. In this paper, we carry out a mathematical analysis of dimensionality reduction. We show that optimal attacks remain optimal after a first pass of preprocessing, which takes the form of a linear projection of the samples. We then investigate the state-of-the-art dimensionality reduction techniques, and find that asymptotically, the optimal strategy coincides with the linear discriminant analysis.