A Robust and Effective Smart-Card-Based Remote User Authentication Mechanism Using Hash Function

Table 5

Comparison of computational overhead between our scheme and other schemes during all phases.

Phase	[13]	[14]	[3]	[15]	Ours
Registration	2𝑡ℎ	4𝑡ℎ	2𝑡ℎ	7𝑡ecm+6𝑡eca+8𝑡ℎ	4𝑡ℎ
Login + authentication	2𝑡me+10𝑡ℎ	2𝑡me+14𝑡ℎ	13𝑡ℎ	10𝑡ecm+3𝑡eca+10𝑡ℎ	14𝑡ℎ
Password change	2𝑡ℎ	5𝑡ℎ	4𝑡ℎ	2𝑡ecm+2𝑡eca+8𝑡ℎ	6𝑡ℎ
Total	2𝑡me+14𝑡ℎ	2𝑡me+23𝑡ℎ	19𝑡ℎ	19𝑡ecm+11𝑡eca+26𝑡ℎ	24𝑡ℎ

Note: 𝑡_ℎ: the time to compute a one-way hash function; 𝑡_me: the time to compute a modular exponentiation; 𝑡_ecm: the time to compute a point multiplication on the elliptic curve group; 𝑡_eca: the time to compute a point addition on the elliptic curve group.