Comparison of Pearson correlation coefficient and distance correlation in Correlation Power Analysis on Digital Multiplier

Abstract

Correlation power analysis (CPA) is a side-channel attack (SCA) which exploits the information leaked through the power supply current and voltage, or the electromagnetic emissions of the attacked digital system. It uses statistical analysis of a large number of power supply measurements to retrieve the secrets of the digital system. Correlation power analysis uses a number of hypothetical secret keys which are correlated to the measurements of the attacked system. Usually correlation power analysis uses the Pearson correlation coefficient, but the intermediary values and the power supply measurements can have a nonlinear relationship. The paper investigates the application of the distance correlation in the correlation power analysis and compares it to the Pearson correlation coefficient. The comparison is based on a side-channel attack on a multiplication operation of an input message and a secret key. The results of the comparison show that the distance correlation achieves a higher prominence of the correct secret key than the Pearson correlation coefficient.