An Enhanced Lightweight Dynamic Pseudonym Identity Based Authentication and Key Agreement Scheme Using Wireless Sensor Networks for Agriculture Monitoring

. 2019 Mar 6;19(5):1146. doi: 10.3390/s19051146

Step 1:	Upon obtaining the message ${B_{i}, D I D_{i}, M_{1}, M_{2}}$ from $U_{i}$ , the $B S$ computes $I D_{i}^{} = D I D_{i} \oplus h (B_{i} ‖ X)$ , $(R_{U}^{} ‖ I D_{S N_{j}}^{} ‖ I D_{G W N_{j}}^{} ‖ T_{1}) = D_{A i} (M_{1})$ and checks if $T_{2} - T_{1} \leq ∆ T$ holds. If this does not true, then session expires. Otherwise, $B S$ computes $M_{2}^{} = h (R_{U}^{} ‖ I D_{i}^{} ‖ T_{1}^{} ‖ h (B_{i} ‖ X))$ and verifies if $M_{2}^{*}$ equals $M_{2}$ or not. If it holds, then $U_{i}$ is legal and $B S$ goes to next step. Otherwise, the session is rejected.
Step 2:	Now, the $B S$ produces a random nonce $R_{B S}$ and computes $M_{3} = E_{h (X_{B S - G W N_{j}})} (I D_{i} ‖ R I_{j} ‖ I D_{S N_{j}} ‖ R_{U} ‖ R_{B S} ‖ T_{3})$ , $M_{5} = h (M_{2} ‖ I D_{i} ‖ T_{3} ‖ R_{B S} ‖ R_{U})$ and then sends ${M_{3}, M_{2}, M_{5}}$ to $G W N_{j}$ via public channel.
Step 3:	After getting request message ${M_{3}, M_{2}, M_{5}}$ from $B S$ , the $G W N_{j}$ computes $(I D_{i} ‖ R I_{j} ‖ I D_{S N_{j}} ‖ R_{U} ‖ R_{B S} ‖ T_{3}) = D_{h (X_{B S - G W N_{j}})} (M_{3})$ and $(R_{U}^{} ‖ I D_{S N_{j}}^{} ‖ I D_{G W N_{j}}^{} ‖ T_{1}) = D_{A_{i}} (M_{1})$ , then checks if two condition $T_{4} - T_{3} \leq ∆ T$ and $M_{5}^{}_{=}^{?} M_{5}$ hold. If both conditions are true then it proceeds further. Otherwise, the session is terminated.
Step 4:	Now, the $G W N_{j}$ generates a random nonce $R_{G W N_{j}}$ and calculates $M_{6} = E_{R I_{j}} (R_{B S} ‖ T_{5} ‖ R_{U} ‖ R_{G W N_{j}} ‖ I D_{i})$ , $M_{7} = h (M_{2} ‖ R I_{j} ‖ R_{G W N_{j}} ‖ I D_{i} ‖ R_{U})$ and then sends ${M_{2}, M_{6}, M_{7}}$ to $S N_{j}$ .
Step 5:	Upon obtaining the message from $G W N_{j}$ , the $S N_{j}$ computes $(R_{B S} ‖ T_{5} ‖ R_{U} ‖ R_{G W N_{j}} ‖ I D_{i}) = D_{R I_{j}} (M_{6})$ , $M_{7}^{} = h (M_{2} ‖ R I_{j} ‖ R_{G W N_{j}} ‖ I D_{i} ‖ R_{U})$ and then verifies if two conditions $T_{6} - T_{5} \leq ∆ T$ and $M_{7}^{}_{=}^{?} M_{7}$ hold. If both are true, then $S N_{j}$ goes to the next step, Otherwise, the session is terminated.
Step 6:	Now, the $S N_{j}$ generates a random nonce $R_{S N_{j}}$ , computes $M_{8} = R_{S N_{j}} \oplus h (R I_{j} ‖ R_{G W N_{j}})$ , $S K = h (R_{G W N_{j}} ‖ R_{U} ‖ R_{S N_{j}} ‖ R I_{j} ‖ M_{2})$ , $M_{9} = h (S K ‖ I D_{i})$ and sends ${M_{8}, M_{9}, T_{7}}$ to $G W N_{j}$ via public channel.
Step 7:	After getting the message from $S N_{j}$ , $G W N_{j}$ firstly verifies if $T_{8} - T_{7} \leq ∆ T$ holds. If true, the process continues. Otherwise, the session expires. Then, $G W N_{j}$ calculates $R_{S N_{j}}^{} = M_{8} \oplus h (R I_{j} ‖ R_{G W N_{j}})$ , $S K^{} = h (R_{G W N_{j}} ‖ R_{U} ‖ R_{S N_{j}}^{} ‖ R I_{j} ‖ M_{2})$ and $M_{9}^{} = h (S K^{} ‖ I D_{i})$ , then checks if $M_{9}^{}_{=}^{?} M_{9}$ . If it holds, the next step proceeds. Otherwise, the session is terminated.
Step 8:	The $G W N_{j}$ computes $M_{10} = E_{h (R_{U} ‖ I D_{i})} (R I_{j} ‖ T_{9} ‖ R_{G W N_{j}} ‖ R_{S N_{j}} ‖ M_{2})$ and sends ${M_{9}, M_{10}}$ to $U_{i}$ via public channel.
Step 9:	After getting the message from $G W N_{j}$ , $U_{i}$ computes $(R I_{j} ‖ T_{9} ‖ R_{G W N_{j}} ‖ R_{S N_{j}} ‖ M_{2}) = D_{h (R_{U} ‖ I D_{i})} (M_{10})$ and verifies if $T_{10} - T_{9} \leq ∆ T$ holds. If it holds, the next step proceeds.
Step 10:	The $U_{i}$ calculates $S K^{}$ = $h (R_{G W N_{j}} ‖ R_{U} ‖ R_{S N_{j}} ‖ R I_{j} ‖ M_{2})$ , $M_{9}^{} = h (S K^{} ‖ I D_{i})$ and checks if $M_{9}^{}_{=}^{?} M_{9}$ holds. If it holds, mutual-authentication and session-key agreement holds.