Security Under Message-Derived Keys: Signcryption in iMessage

At the core of Apple's iMessage is a signcryption scheme that involves symmetric encryption of a message under a key that is derived from the message itself. This motivates us to formalize a primitive we call Encryption under Message-Derived Keys (EMDK). We prove security of the EMDK scheme underlying iMessage. We use this to prove security of the signcryption scheme itself, with respect to definitions of signcryption we give that enhance prior ones to cover issues peculiar to messaging protocols. Our provable-security results are quantitative, and we discuss the practical implications for iMessage.