Mathematical Problems in Engineering

Research Article

Strongly Secure Certificateless Signature Scheme Supporting Batch Verification

Table 1

The comparisons between [5, 7, 11, 13, 14, 16, 27–34] and our scheme.
  Signing phase Verification phase Security level Formally proved Security model
[5] Girault’s level-3 Yes
ROM
 
[7] Girault’s level-2 Yes
ROM
 
 
[27] Girault’s level-1 Yes ROM
  
[28] Cha-based Girault’s level-1
No
ROM
[28] Waters-based
Girault’s level-1
No
STD
[28] Hess-based
Girault’s level-1
No
ROM
[29] Geng-based
Girault’s level-2
No
ROM
[32]
Girault’s level-1
No
ROM
[11] Girault’s level-2
No
—
[13] Girault’s level-3
Yes
 ROM
[30]
Girault’s level-1
No
—
[14] Girault’s level-2
Yes
ROM
[33]
Girault’s level-1
No
ROM
[34]
Girault’s level-1
No
—
[16] Girault’s level-2
Yes
STD
[31] Girault’s level-1
No
—
Ours
Girault’s level-3
Yes
ROM
According to [41–43], ,   , and .
: the number of -bit chunks in Waters scheme; : the number of registered users in Qin scheme; : the number of individual signatures; : the time cost of a pairing operation; : the time cost of a scalar multiplication in ; : the time cost of a map-to-point hash operation; : the time cost of a point addition operation; : the time cost of a modular multiplication in ; : the time cost of a hash operation; ROM: random oracle model; STD: standard model.