Page Realization -Bilinear Map Let a bilinear map tuple be(a, 9, 9, G1, G2, Gr, e), where G1, G2(G1 and G2 are not the same group)and GT are multiplicative cyclic groups of prime order g, lql= k, and g is a random generator of G1, 9 is a random generator of G2. The mapping e: G1 X G2,Gr has three properties (1)Bilinearity: for all a, bER Z,e(9,9)=e(g, 9);(2) No on-degeneracy:e(g, 9)+IGr, where lGr is the unit of gT; (3) Computability: e can be efficiently computedPage . Realization – Bilinear Map