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

Table 1

Operation costs for the GQ-SM-IBI scheme.

Algorithm	A	M1	M2	E
Setup	0	0	0	0
Extract	1	0	0	3
SEM-Prove	0	0	1	2
User-Prove	0	0	3	2
Verify	0	0	1	2

A: addition in ℤ_𝜙(𝑁), M1: multiplication in ℤ_𝜙(𝑁), M2: multiplication in ℤ^∗_𝑁, and E: exponentiation in ℤ^∗_𝑁.