Each　member　entering　into　a　confidential　group　is　unwilling　to　make　the　private　information,　i.e.,　which　group　he　wants　to　join,　who　is　the　group　manager　and　who　issues　the　admission　token,　available　to　the　general　public　and　hence　to　any　adversary.　The　group　key　initial　distribution　based　on　basic　signature　can　not　efficiently　protect　the　privacy　of　the　entering　member　since　the　basic　signature　can　be　verified　by　anyone　using　the　corresponding　public　key.　In　this　paper,　we　propose　a　directed　signature　scheme　based　on　the　elliptic　curve　ElGamal　cryptosystems　and　apply　it　to　the　group　key　initial　distribution　for　a　confidential　group　communication.　Through　comparing　to　the　elliptic　curve　ElGamal　digital　signature　scheme　in　terms　of　computational　cost　using　statistical　hypothesis　t-test　two　samples　for　means　and　Wilcoxon　rank　sum　test,　the　results　of　the　experiment　show　that　our　directed　signature　scheme　is　not　significantly　different　from　the　digital　signature　scheme　in　statistics　so　that　the　group　key　initial　distribution　based　on　our　directed　signature　scheme　not　only　efficiently　protects　the　privacy　of　the　entering　member　but　also　saves　the　computation　resources.　Copyright　©　2009　ACM.