Profiling attacks, especially those based on machine learning proved as very successful techniques in recent years when considering side-channel analysis of block ciphers implementations. At the same time, the results for implementations of public-key cryptosystems are very sparse. In this paper, we consider several machine learning techniques in order to mount a power analysis attack on EdDSA using the curve Curve25519 as implemented in WolfSSL. The results show all considered techniques to be viable and powerful options. Especially convolutional neural networks (CNNs) are effective as we can break the implementation with only a single measurement in the attack phase while requiring less than 500 measurements in the training phase. Interestingly, that same convolutional neural network was recently shown to perform extremely well for attacking the implementation of the AES cipher. Our results show that some common grounds can be established when using deep learning for profiling attacks on distinct cryptographic algorithms and their corresponding implementations.