Graphics processing units (GPUs) are increasingly common on desktops, servers, and embedded platforms. In this article, we report on new security issues related to CUDA, which is the most widespread platform for GPU computing. In particular, details and proofs-of-concept are provided about novel vulnerabilities to which CUDA architectures are subject. We show how such vulnerabilities can be exploited to cause severe information leakage. As a case study, we experimentally show how to exploit one of these vulnerabilities on a GPU implementation of the AES encryption algorithm. Finally, we also suggest software patches and alternative approaches to tackle the presented vulnerabilities.