Table 2. Login and Authentication phases of Wen’s scheme [3].

User Ui/Smartcard		Server S
User Ui:
Insert ⟨ID i, PW i⟩
Smartcard:
Select a random number r
Compute s 2 = H(H(PW i∣∣s 1), c i = c i + 1
Compute M 1 = (ID i∣∣N∣∣s 2∣∣r∣∣c i)2 mod n
	$\underset{(\mathrm{\text{via a public channel}})}{\overset{M_1}{\to }}$
		Extract ⟨ID i, N, s 2, r, c i⟩ from M 1
		Obtain ⟨ID i, $c_i^{\prime }⟩$ from database
		If ($c_i^{\prime }\le c_i$)
		abort the session
		Else
		update ⟨ID i, $c_i^{\prime }⟩$ to ⟨ID i, c i⟩
		Compute v = H(K⊕ID i), $s_2^{\prime }=N\oplus v$
		If ($s_2^{\prime }\ne s_2$)
		abort the session
		Else
		authenticate U i
		Compute the session key SK = H(s 2∣∣r∣∣1)
		Compute M 2 = H(s 2∣∣r∣∣0)
	$\underset{(\mathrm{\text{via a public channel}})}{\overset{M_2}{\leftarrow }}$
Smartcard:
Compute $M_2^{\prime }$ = H(s 2∣∣r∣∣0)
If ($M_2^{\prime }$ M 2)
abort the session
Else
authenticate S
Compute the session key SK = H(s 2∣∣r∣∣1)