Broadcast encryption is conventionally formalized as broadcast encapsulation in which, instead of a cipher-text, a session key is produced, which is required to be indistinguishable from random. Such a scheme can provide public encryption functionality in combination with a symmetric encryption through the hybrid encryption paradigm. The boneh-gentry-waters scheme of 2005 proposed a broadcast scheme with constant-size cipher-text. It is one of the most efficient broadcast encryption schemes regarding overhead size. In this paper the authors consider the improved scheme of Phan-Pointcheval-Shahandashi-Stefler [PPSS12] which provides an adaptive CCA broadcast encryption scheme.