Without considering the addition of two points, hash function and exclusive-OR operations, each scheme has three types of operations, that is, pairing (P), exponentiation (E), and scalar multiplication (S).We evaluate the cryptographic operations by using of MIRACL (version 5.6.1, [17]), a standard cryptographic library, on a laptop using the Intel Core i5-2400 at a frequency of 3.10?GHz with 3?GB