The safety of cryptosystems, mainly based on algorithmic improvement, is still vulnerable to side-channel attacks (SCA) based on machine learning. Multi-class classification based on neural networks and principal components analysis (PCA) can be powerful tools for pattern recognition and classification of side-channel information. In this paper, an experimental investigation was conducted to explore the efficiency of various architectures of feed-forward back-propagation (FFBP) neural networks and PCA against side-channel attacks. The experiment is performed on the data leakage of an FPGA implementation of elliptic curve cryptography (ECC). Our results show that the proposed method is a promising method for SCA with an overall accuracy of 88% correct classification.