The signcryption is a relatively new cryptographic technique that is supposed to fulfill the functionalities of encryption and digital signature in a single logical step. Several signcryption schemes are proposed throughout the years, each of them having its own problems and limitations. In this paper, the security of a recent signcryption scheme, i.e. Hwang et al.'s scheme is analyzed, and it is proved that it involves several security flaws and shortcomings. Several devastating attacks are also introduced to the mentioned scheme whereby it fails all the desired and essential security attributes of a signcryption scheme.