  Side Channel Analysis attacks take advantage of 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.
