The client in our AA scheme sends t

The client in our AA scheme sends the login message
{W, X, tc} to the application provider, where U, tc, and X
are an element of G1, the current timestamp and an element
of G1 separately and W = Ek(id, right, U). The application
provider sends the response message {Y, Auth} to the client,
where Y = y · P and Auth = MACkey(W, X, tc, Y ). Then, the
communication cost of Liu et al.’s preliminary version scheme
is 32 + 64 + 1024 + 1024 + 32 + 1024 + 160 = 3360 bits.
The communication cost comparisons among related
schemes are listed in Table IV. According to Table IV, we know
Liu et al.’s security-enhanced scheme and our AA scheme
has lighter communication cost. Besides, our AA scheme has
slightly heavier communication cost than Liu et al.’s securityenhanced scheme.
C. Computation Cost
In this section, we analyze the computation cost of our
AA scheme. We also compare the computation cost of our
AA scheme with that of Liu et al.’s schemes. The computing
capability and memory of the client’s mobile device are very
limited. However, the application provider has enough capability to execute all related operations because it is equipped
with very powerful coprocessor. Therefore, we just need to consider the computation cost of the client. For convenience, some
notations used in this section are defined as follows.
1) TGe: The execution time of executing a bilinear map
operation.
2) TGmul: The execution time of a scalar multiplication
operation.
3) TGH: The execution time of a map-to-point hash function
operation.
4) TGadd: The execution time of a point addition operation.
5) Texp: The execution time of a modular exponentiation
operation.
6) Th: The execution time of a general hash function
operation.