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 ${A_{i}, D I D_{i}, T_{1}, M_{1}, I D_{S N_{j}}, I D_{G W N_{j}}}$ from $U_{i}$ , the $B S$ checks if $T_{2} - T_{1} \leq ∆ T$ holds. If this does not true then session expires. Otherwise, $B S$ calculates $(I D_{i} ‖ R_{U}) = D I D_{i} \oplus h (h (A_{i} ‖ X) ‖ T_{1})$ and computes $M_{1}^{} = h (R_{U} ‖ I D_{i} ‖ T_{1} ‖ h (A_{i} ‖ X))$ , then verifies if $M_{1}^{}$ equals $M_{1}$ or not. If this holds, $B S$ goes to next step. Otherwise, the session is rejected.
Step 2:	Now, $B S$ generates a random nonce $R_{B S}$ and computes a new $A_{i}^{n e w}$ , where $A_{i}^{n e w}$ = $h (R_{U} ‖ h (A_{i} ‖ X)) .$ Then, $B S$ computes $M_{2}$ = $h (A_{i}^{n e w} ‖ X)$ ⊕ $h (h (A_{i} ‖ X) ‖ R_{B S})$ , $M_{3} = (R_{U} ‖ R_{B S} ‖ I D_{i}) \oplus h (X_{B S - G W N_{j}} ‖ T_{3})$ , $M_{4} = h (M_{1} ‖ M_{2} ‖ I D_{i} ‖ T_{3} ‖ R_{B S} ‖ R_{U})$ and $M_{5} = R_{B S}$ ⊕ $h (h (I D_{S N_{j}} ‖ X) ‖ T_{3})$ and sends ${M_{1}, M_{2}, M_{3}, M_{4}, M_{5}, T_{3}}$ to $G W N_{j}$ via public channel.
Step 3:	After getting the request message from $B S$ , the $G W N_{j}$ checks if $T_{4} - T_{3} \leq ∆ T$ holds. If this does not true then session expires. Otherwise, $G W N_{j}$ calculates $(R_{U} ‖ R_{B S} ‖ I D_{i}) = M_{3} \oplus h (X_{B S - G W N_{j}} ‖ T_{3})$ and $M_{4}^{} = h (M_{1} ‖ M_{2} ‖ I D_{i} ‖ T_{3} ‖ R_{B S} ‖ R_{U})$ , then checks if $M_{4}^{}_{=}^{?} M_{4}$ holds. If the condition is true then it proceeds further. Otherwise, the session is terminated.
Step 4:	Now, the $G W N_{j}$ generates a random nonce $R_{G W N_{j}}$ , calculates $M_{6}$ = $(R_{U} ‖ R_{G W N_{j}} ‖ I D_{i}) \oplus h (R_{B S} ‖ M_{5} ‖ T_{5})$ and $M_{7} = h (M_{1} ‖ M_{2} ‖ R_{B S} ‖ R_{G W N_{j}} ‖ I D_{i} ‖ R_{U})$ , then sends ${M_{1}, M_{2}, M_{5}, M_{6}, M_{7}, T_{3}, T_{5}}$ to $S N_{j}$ .
Step 5:	Upon obtaining the message from $G W N_{j}$ , the $S N_{j}$ checks if $T_{6} - T_{5} \leq ∆ T$ holds. If this does not true then session expires. Otherwise, $S N_{j}$ calculates $R_{B S}^{} = M_{5} \oplus h (R I_{j} ‖ T_{3})$ , $(R_{U} ‖ R_{G W N_{j}} ‖ I D_{i}) = M_{6} \oplus h (R_{B S}^{} ‖ M_{5} ‖ T_{5})$ and $M_{7}^{} = h (M_{1} ‖ M_{2} ‖ R_{B S}^{} ‖ R_{G W N_{j}} ‖ I D_{i} ‖ R_{U})$ . Then, $S N_{j}$ verifies if $M_{7}^{*}_{=}^{?} M_{7}$ holds. If the condition is true then it proceeds further. Otherwise, the session is terminated.
Step 6:	Now, the $S N_{j}$ generates a random nonce $R_{S N_{j}}$ , computes $M_{8} = R_{S N_{j}} \oplus h (R_{G W N_{j}} ‖ R_{B S}^{} ‖ T_{7})$ , $S K = h (R_{G W N_{j}} ‖ R_{U} ‖ R_{S N_{j}} ‖ R_{B S}^{} ‖ I D_{i} ‖ M_{1})$ and $M_{9} = h (S K ‖ R_{B S}^{*} ‖ R_{U} ‖ M_{2} ‖ T_{7})$ . Then, $S N_{j}$ sends ${M_{1}, M_{2}, M_{8}, M_{9}, T_{7}}$ to $G W N_{j}$ .
Step 7:	Upon receiving the message from $S N_{j}$ , $G W N_{j}$ firstly verifies if $T_{8} - T_{7} \leq ∆ T$ holds. If this is not true then the session expires. Otherwise, $G W N_{j}$ calculates $R_{S N_{j}}^{} = M_{8} \oplus h (R_{G W N_{j}} ‖ R_{B S} ‖ T_{7})$ , $S K^{} = h (R_{G W N_{j}} ‖ R_{U} ‖ R_{S N_{j}}^{} ‖ R_{B S} ‖ I D_{i} ‖ M_{1})$ and $M_{9}^{} = h (S K^{} ‖ R_{B S} ‖ R_{U} ‖ M_{2} ‖ T_{7})$ , then checks if $M_{9}^{}_{=}^{?} M_{9}$ holds. If the condition is true then further is proceeded. Otherwise, the session is terminated.
Step 8:	The $G W N_{j}$ computes $M_{10} = h (R_{U} ‖ I D_{i}) \oplus (R_{G W N_{j}} ‖ R_{S N_{j}}^{} ‖ R_{B S})$ and $M_{11} = h (R_{U} ‖ R_{S N_{j}}^{} ‖ M_{2} ‖ S K ‖ T_{9})$ . Then, $G W N_{j}$ sends ${M_{2}, M_{10}, M_{11}, T_{9}}$ to $U_{i}$ .
Step 9:	Upon receiving the message from $G W N_{j}$ , $U_{i}$ firstly verifies if $T_{8} - T_{7} \leq ∆ T$ holds. If this does not true then session expires. Otherwise, $U_{i}$ computes $(R_{G W N_{j}} ‖ R_{S N_{j}}^{} ‖ R_{B S})$ = $h (R_{U} ‖ I D_{i})$ ⊕ $M_{10}$ , $S K^{}$ = $h (R_{G W N_{j}} ‖ R_{U} ‖ R_{S N_{j}}^{} ‖ R_{B S} ‖ I D_{i} ‖ M_{1})$ , $h (A_{i}^{n e w} ‖ X) = M_{2} \oplus h (h (A_{i} ‖ X) ‖ R_{B S})$ , $M_{11}^{} = h (R_{U} ‖ R_{S N_{j}}^{} ‖ M_{2} ‖ S K^{} ‖ T_{9})$ and verifies if $M_{11}^{*}_{=}^{?} M_{11}$ holds. If the condition is true then mutual authentication and session key agreement holds. Otherwise, the session is terminated.
Step 10:	The $U_{i}$ computes $B_{i}^{n e w} = h (A_{i}^{n e w} ‖ X) \oplus h (I D_{i} ‖ R P W_{i})$ and $D_{i}^{n e w} = h (A_{i}^{n e w} ‖ R P W_{i} ‖ I D_{i})$ . Then, $U_{i}$ replaces $A_{i}, B_{i}, D_{i}$ with $A_{i}^{n e w}$ , $B_{i}^{n e w}$ , $D_{i}^{n e w}$ , respectively.