Signcryption tag-KEM (Key Encapsulation Mechanism with a tag) is an authenticated tag-KEM for generic construction of hybrid signcryption. Signcryption tagKEM allows the sender to encapsulate a symmetric key along with a tag so that the receiver can authenticate the sender, the key, and the tag. We present a definition for the security of signcryption tag-KEM which is suitable for a recent signcryption setting. We also present a proof of security for the previous generic construction of hybrid signcryption according to the given definition. Key words: key encapsulation, privacy, authentication, signcryption, signcryption tag-KEM