Many implementations making use of

Many implementations making use of pairing-based operations have been reported in last decade [37]–[39]. Recently,
Xiong et al. [40] implemented bilinear pairing on the MICAz,
which has been used extensively in wireless sensor networking
research and has only 4 KB RAM,128 KB ROM, and a
7.3828-MHz ATmega128L microcontroller. In Xiong et al.’s
implementation, the RAM and ROM usage by each operation
was obtained using the TinyOS toolchain. We use their implementation to evaluate the computation cost of the client and
the application provider separately. According to Xiong et al.’s
experiment and the relationship among different operations,
the running time of different pairing-based operations is listed
in Table V [40]. Besides, the running time of a symmetric
encryption/decryption operation and a message authentication
code operation is the same with that of a hash function
operation [41].
The client in Liu et al.’s preliminary version scheme calculates four scalar multiplication operations, one map-to-point
hash function operation, one-point addition operation, one
modular exponentiation operation, and one general hash function operation. The computation cost at the client side is
4 TGmul + 1 TGH + 1 Texp + 1 TGadd + 3 Th ≈ 11.95 s.
The client in Liu et al.’s preliminary version scheme calculates four scalar multiplication operations, one map-to-point
hash function operation, two-point addition operations, one
modular exponentiation operation, and three general hash function operations. The computation cost at the client side is
4 TGmul + 1 TGH + 2 TGadd + 1 Texp + 3 Th ≈ 11.95 s.
The client in our AA scheme calculates four scalar multiplication operations, one map-to-point hash function operation,
one-point addition operations, and four general hash function
operations. Then, the computation cost at the client side is
4 TGmul + 1 TGH + 1 TGadd + 4 Th ≈ 10.69 s.
The computation cost comparisons among related schemes
are listed in Table VI. According to Table VI, our AA scheme
has lower computation cost than both Liu et al.’s scheme.