Algorithm 1 Initiation.

GW: Calculate $R_{gw}=PU{F}_{gw}\left(C_{gw}\right)$            $GW\to CS:M_1=\left\{C_{gw}\right\}$ CS:  Generate a random number $N_{cs1}$            Calculate $X_1=NLF\left(R_{gw}\right)\oplus N_{cs1}$, $H_1=h\left(N_{cs1}\right)$            $CS\to GW:M_2=\{H_1,X_1\}$            $S{K}_1=N_{cs1}\Vert R_{gw}$ GW: Calculate $N_{cs1}^{\prime }=X_1\oplus NLF\left(R_{gw}\right)$, $N_{cs1}^{\prime }=X_1\oplus NLF\left(R_{gw}\right)$, $H_1^{\prime }=h\left(N_{cs1}^{\prime }\right)$            If $H_1^{\prime }\ne H_1$, the message is discarded. Otherwise, the gateway generates a new CRP.            $S{K}_1=N_{cs1}^{\prime }\Vert R_{gw}$            Calculate $$E_1={\left(C_{gwnew}\Vert R_{gwnew}\right)}_{Enc}^{S{K}_1}$$ $$H_2=h(C_{gwnew}\Vert R_{gwnew}\Vert N_{cs1}^{\prime })$$            $GW\to CS:M_3=\{H_2,E_1\}$ CS:  Calculate $D_1={\left(E_1\right)}_{Dec}^{S{K}_1}$, $H_2^{\prime }=h(D_1\Vert N_{cs1})$            If $H_2^{\prime }=H_2$, we store the updated value $C_{gwnew}$ and $R_{gwnew}$.