The　invariant　bilinear　form　is　an　important　tool　in　the　representation　theory　of　algebras.　Constructing　representation　for　some　algebra　groups　is　desirable　for　study　of　the　properties　of　the　underlying　group.　This　representation　is　also　very　useful　for　some　applications,　e.g.　the　application　of　cyclic　group　in　information　security　(cryptographic　protocol).　This　paper　we　will　construct　the　invariant　bilinear　forms　on　the　modules　of　the　simple-pointed　Hopf　algebra　R(q,α).　In　addition,　we　discuss　its　application　in　information　security.　This　construction　will　provide　a　new　group　for　cryptographic　protocol　design.　It　is　motivated　by　the　current　wide　applications　of　multi-bilinear　mappings　to　information　security,　especially　for　the　design　of　multivariable　cryptographic　protocols,　signature　schemes,　public　key　encryptions.　©　2005　IEEE.