The　secure　group　communication　is　essential　to　the　group-oriented　applications.　The　problem　of　the　one-to-many　communication　is　investigated　and　an　efficient　and　secure　resolution　is　presented　in　this　paper.　To　achieve　the　confidentiality,　integrity　and　authenticity　simultaneously,　a　new　signcryption　scheme　based　on　Rabin　cryptosystem　is　proposed　firstly.　Then,　it　is　extended　to　the　one-to-many　scenario,　and　a　parallel　multi-recipient　signcryption　scheme　is　proposed,　in　which　a　single　sender　broadcasts　a　message　to　several　recipients　in　confidential　and　authenticated　way.　Each　of　the　recipient　could　decode　the　message　by　his　private　key　and　verify　the　signature　by　the　sender＇s　public　key.　The　parallel　scheme　exploits　the　advantages　of　multi-core　processor　and　multithread,　and　the　nature　of　wireless　broadcast.　Compared　with　the　trivial　parallel　scheme,　the　communication　overheads　has　been　reduced　up　to　3/4.　©　2011　ICIC　International.