The use of TLS by malware poses new challenges to network threat detection because traditional pattern-matching techniques can no longer be applied to its messages. However, TLS also introduces a complex set of observable data features that allow many inferences to be made about both the client and the server. We show that these features can be used to detect and understand malware communication, while at the same time preserving the privacy of benign uses of encryption. These data features also allow for accurate malware family attribution of network communication, even when restricted to a single, encrypted flow. We provide a general analysis on millions of TLS encrypted flows, and a targeted study on 18 malware families composed of thousands of unique malware samples and ten-of-thousands of malicious TLS flows.