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.