Efficient and Provable Secure Pairing-Free Security-Mediated Identity-Based Identification Schemes

Table 3

Operation costs for the BNN-SM-IBI scheme.

Algorithm	A	M	GM	E
Setup	0	0	0	1
Extract	3	1	0	3
SEM-Prover	1	1	0	2
User-Prover	2	1	3	2
Verifier	0	1	2	3

H: hash operation, A: addition mod 𝑞, M: multiplication mod 𝑞, GM: group multiplication, and E: exponentiation mod 𝑞.