An Energy Efficient Mutual Authentication and Key Agreement Scheme Preserving Anonymity for Wireless Sensor Networks

. 2016 Jun 8;16(6):837. doi: 10.3390/s16060837

Algorithm 2

E X P 2_{A}^{H a s h}

1:
Eavesdrop the authenticated message ${G_{i}, F_{i}}$ , where $G_{i} = h (T I D_{i}, I D_{S N_{j}}, h (I D_{S N_{j}} \oplus S_{r a n}), I D_{G W N}, T_{2}, r_{k}, r_{i})$ , $F_{i} = E_{h (I D_{S N_{j}} \oplus S_{r a n})} (r_{k} \oplus r_{i}, T I D_{i}, T_{1}, T_{2})$
2:
Call Reveal2 oracle. Let $(T I D_{i}^{^{'}}, I D_{S N_{j}}^{^{'}}, h (I D_{S N_{j}} \oplus$
3:
Eavesdrop the communicated message ${I_{i}, H_{i}}$ , $I_{i} = h (I D_{S N_{j}}, T I D_{i}, T_{3}, S K)$ , $H_{i} = E n c_{h (I D_{S N_{j}} \oplus S_{r a n})} (r_{j}, T_{3}, r_{k}, r_{i})$
4:
Call Reveal2 oracle. Let $(I D_{S N_{j}}^{^{″}}, T I D_{i}^{^{″}}, T_{3}^{^{″}}, S K^{^{″}}) \leftarrow R e v e a l 2 (D_{i})$
5:
If ( $T I D_{i}^{^{'}} = T I D_{i}^{^{″}}$ ) then
6:
Accept $S K^{'}$ as the session key among $U_{i}$ , $G W N$ and $S N_{j}$
7:
return 1
8:
else
9:
return 0
10:
end if