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.