On the Optimality of Correlation Power Attack on Embedded Cryptographic Systems

In this paper, we answer the question of what are the necessary conditions under which Correlation Power Attack (CPA), that essentially targets embedded cryptographic implementations, is optimal with regards to attacks that exploit the same leakage model. For this purpose, we offer an in-depth theoretical study which aims at determining the conditions under which the Pearson correlation coefficient is maximized. Moreover, we propose theoretical metrics to practically verify the validity of those conditions. Besides, we illustrate our theoretical study by an experiment on real electromagnetic traces acquired from a DES cryptographic implementation.