Instant Messaging has gained popularity by users for both private and business communication as low-cost short message replacement on mobile devices. However, before releases about mass surveillance performed by intelligence services such as NSA and GCHQ and Facebook's acquisition of WhatsApp, most mobile messaging apps did not protect confidentiality or integrity of the messages. A messaging app that claims to provide secure instant messaging and has attracted a lot of attention is TextSecure. Besides numerous direct installations, its protocol is part of Android's most popular aftermarket firmware Cyanogen-Mod. TextSecure's successor Signal continues to use the underlying protocol for text messaging. In this paper, we present the first complete description of TextSecure's complex cryptographic protocol, provide a security analysis of its three main components (key exchange, key derivation and authenticated encryption), and discuss the main security claims of TextSecure. Furthermore, we formally prove that - if key registration is assumed to be secure - TextSecure's push messaging can indeed achieve most of the claimed security goals.