“…We compare the security and the performance efficiency of our scheme to those of the known ID-based signcryption without random oracles in [23,24,26,27]. M G , E G , M G T , E G T , I G T , andê, denote the multiplication in G, the exponentiation in G, the multiplication in G T , the exponentiation in G T , the inversion in G T and the pairing operation, respectively.…”