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


L-1	U_i inserts U_i's smart card into a terminal and inputs $I D_{i}^{}$ and. $p w_{i}^{}$
L-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.
L-3	The smart card generates a random nonce R_Ni and computes the following. T_i is the current timestamp of U_i system.
	$D I D_{i} = h (H_P W_{i}^{} ‖ X s_{i}^{}) \oplus h (X s_{i}^{*} ‖ R N_{i} ‖ T_{i})$
	$M_{U_{i} - G} = h (A_{i} ‖ X s_{i}^{*} ‖ R N_{i} ‖ T_{i})$
	$v_{i} = R N_{i} \oplus X s_{i}^{*}$
	The smart card sends the authentication request {DID_i, M_Ui₋_G, v_i, T_i, H_{_}ID_i } to GW.