Horizontal SCA Attacks against $kP$ Algorithm Using K-Means and PCA

Side Channel Analysis attacks consist in, i.a., exploiting the information leaked from the implementations of cryptographic algorithms. In this paper we describe two key revealing methods which are based on machine learning algorithms: K-means and PCA. We performed the attacks against ECDSA implementations without any prior knowledge about the key and achieved 100% accuracy for an implementation without any countermeasures against horizontal attacks and 88.7% accuracy for an implementation with bus address sequencing. In the scenario where the kP operation inputs are controlled by the attacker (as during signature verification), we achieved 98.3% accuracy for the implementation with countermeasures.