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

Table 3

Summary of the authentication phase of our scheme.

User (𝑈𝑖)/smart card (𝐶𝑖)	Remote server (𝑆𝑗)
	Checks the validity of 𝑇𝑐.
	If it holds, computes
	𝑀4=ℎ(𝐼𝐷𝑖‖𝑋𝑠),
	𝑀5=𝑀2⊕𝑀4⊕𝑇𝑐,
	and 𝑀6=ℎ𝐼𝐷𝑖‖𝑀5‖𝑇𝑐.
	Checks if 𝑀6=𝑀3. If it holds,
	computes 𝑀7=𝑀4⊕𝑅𝑠⊕𝑇𝑠,
	𝑀8=ℎ(𝑅𝑠‖𝑇𝑠‖𝑀5‖𝑇𝑐)⊕𝑁𝐼𝐷^new𝑖,
	and 𝑀9=ℎ(𝐼𝐷𝑖‖𝑀5+1‖𝑇𝑐+1
	‖𝑅𝑠‖𝑇𝑠‖𝑁𝐼𝐷^new𝑖).
	←−−−−−−−−−−−−−−−−−−^⟨𝑀7,𝑀8,𝑀9,𝑇𝑠⟩−−−−−−−
Checks the validity of 𝑇𝑠.	(via a public channel)
If it holds, computes
𝑀10=𝑀7⊕𝑀1⊕𝑇𝑠,
𝑀11=ℎ(𝑀10‖𝑇𝑠‖𝑅𝑐‖𝑇𝑐),
𝑁𝐼𝐷^new∗𝑖=𝑀8⊕𝑀11,
and 𝑀12=ℎ(𝐼𝐷𝑖‖𝑅𝑐+1‖𝑇𝑐+1‖𝑀10‖𝑇𝑠
‖𝑁𝐼𝐷^new∗𝑖). Checks if 𝑀12=𝑀9. If it
holds, updates 𝑇𝐷𝑖 and 𝐷𝑖. Computes
𝑀13=ℎ(𝑀10+1‖𝑇𝑠+1‖𝑅𝑐+1‖𝑇𝑐+1 ‖𝑁𝐼𝐷^new∗𝑖‖𝐼𝐷𝑖).
	−−−−−→^𝑀13
(via a public channel)	Computes 𝑀14= ℎ(𝑅𝑠+1‖𝑇𝑠+1
	‖𝑀5+1‖𝑇𝑐+1‖𝑁𝐼𝐷𝑖^𝑛𝑒𝑤‖𝐼𝐷𝑖).
	Checks if 𝑀14=𝑀13. If it holds,
	𝑆𝑗 authenticates 𝑢𝑖.
Computes 𝐾𝑈𝑖,𝑆𝑗= ℎ(𝐼𝐷𝑖‖𝑅𝑐‖𝑇𝑐‖𝑀10‖𝑇𝑠‖𝑀1).	Computes 𝐾𝑆𝑗,𝑈𝑖=ℎ(𝐼𝐷𝑖‖𝑀5‖𝑇𝑐‖𝑆𝑅𝑠‖𝑇𝑠‖𝑀4).