Two-Factor User Authentication with Key Agreement Scheme Based on Elliptic Curve Cryptosystem

Table 1

Computation cost comparison among our scheme and others.

	Yang and Chang [15]	Islam and Biswas [16]	Our scheme
Registration phase	1𝑇𝑚+1𝑇ℎ	1𝑇𝑚+1𝑇ℎ	2𝑇𝑚+1𝑇𝑎+3𝑇ℎ
Authentication phase	8𝑇𝑚+5𝑇𝑎+8𝑇ℎ	7𝑇𝑚+4𝑇𝑎+6𝑇ℎ	9𝑇𝑚+5𝑇𝑎+13𝑇ℎ
Total computation cost	9𝑇𝑚+5𝑇𝑎+9𝑇ℎ	8𝑇𝑚+4𝑇𝑎+7𝑇ℎ	11𝑇𝑚+8𝑇𝑎+14𝑇ℎ

𝑇_𝑚: the time complexity of ECC multiplication operation; 𝑇_𝑎: the time complexity of ECC addition/subtraction operation; 𝑇_ℎ: the time complexity of hashing function operation.