. 2015 Aug 11;10(8):e0131368. doi: 10.1371/journal.pone.0131368

Table 3. Login and authentication phases of the proposed user authentication scheme.

User U_i/Smartcard		Server S
User U_i:
Insert ⟨ID _i, PW _i⟩
Smartcard:
Compute B _i = H(ID _i∣∣PW _i), A _i = C _i⊕B _i
Compute $D_{i}^{'}$ = H(A _i∣∣B _i)
If ( $D_{i}^{'} \neq D_{i}$ )
terminate the session
Else
compute c _i = c _i + 1
Choose $a \in_{R} Z_{n}^{*}$
Compute M ₁ = (ID _i∣∣A _i∣∣a∣∣c _i)² mod n
	$\to_{(via a public channel)}^{M_{1}}$
		Obtain ID _i, A _i, a, c _i from M ₁
		Retrieve ⟨ID _i, $c_{i}^{'}$ , b _i⟩ from database
		If ( $c_{i}^{'} \leq c_{i}$ )
		terminate the session
		Else
		update ⟨ID _i, $c_{i}^{'}$ , b _i⟩ to ⟨ID _i, c _i, b _i⟩
		Compute $A_{i}^{'}$ = H(ID _i∣∣K∣∣b _i)
		If ( $A_{i}^{'} \neq A_{i}$ )
		terminate the session
		Else
		select $b \in_{R} Z_{n}^{*}$
		Compute d = a⊕b and
		Session key SK = H(ID _i∣∣a∣∣b∣∣A _i)
		Compute M ₂ = H(ID _i∣∣A _i∣∣d∣∣SK)
	$\leftarrow_{(via a public channel)}^{{d, M_{2}}}$
Smartcard:
Compute b = d⊕a and
Session key SK = H(ID _i∣∣a∣∣b∣∣A _i)
Compute $M_{2}^{'}$ = H(ID _i∣∣A _i∣∣d∣∣SK)
If ( $M_{2}^{'} \neq M_{2}$ )
terminate the session
Else
authenticate S and
Accept SK as session key