The confidentiality of encrypted data depends on how well the key under which it was encrypted is maintained. If a session key was exchanged encrypted under a long-term key, exposure of the long-term key may reveal the session key and hence the data encrypted with it. The problem of key-dependencies between keys can be mapped onto connectivity of a graph, and the resulting graph can be inspected. This article presents a structured method (an algorithm) with which key-dependencies can be detected and analysed. Several well-known protocols are examined, and it is shown that they are vulnerable to certain attacks exploiting key-dependencies. Protocols which are free from this defect do exist. That is, when a session is terminated it is properly closed.