Security Analysis and Improvements of Two-Factor Mutual Authentication with Key Agreement in Wireless Sensor Networks

. 2014 Apr 9;14(4):6443–6462. doi: 10.3390/s140406443


P-1	U_i inserts its smart card into a terminal and inputs, $I D_{i}^{}$ , $p w_{i}^{}$ and pw_ni. is U_i's new password.
P-2	The smart card computes the following.
	$R N_{r}^{} = h (p w_{i}^{}) \oplus X_P W_{i}$
	$H_P W_{i}^{} = h (p w_{i}^{} ‖ R N_{r}^{*})$
	$X s_{i}^{} = C_{i} \oplus h (I D_{s} ‖ H_P W_{i}^{})$
	$B_{i}^{} = h (H_P W_{i}^{} \oplus X s_{i}^{*})$
	The smart card compares $B_{i}^{}$ with B_i. If $B_{i}^{} = B_{i}$ , then the next step proceeds; otherwise, this phase is aborted.
P-3	The smart card computes the following.
	$H_P W_{n i} = h (p w_{n i} ‖ R N_{r}^{*})$
	$A_{n i} = A_{i} \oplus h (H_P W_{i}^{} ‖ X s_{i}^{}) \oplus h (H_P W_{n i} ‖ X s_{i}^{*})$
	$B_{n i} = h (H_P W_{n i} \oplus X s_{i}^{*})$
	$C_{n i} = X s_{i}^{*} \oplus h (I D_{s} ‖ H_P W_{n i})$
	The smart card replaces the existing values A_i, B_i and C_i with the new values A_ni, B_ni and C_ni.