Efficient and Security Enhanced Anonymous Authentication with Key Agreement Scheme in Wireless Sensor Networks

. 2017 Mar 21;17(3):644. doi: 10.3390/s17030644

Algorithm 1: Algorithm

E X P 1_{H A S H, A}^{A U A K A S}

1. Eavesdrop login request message

〈D I D_{i}, M_{U_{i}, G}, C_{i}, T_{1}〉

during the login phase.
2. Call the Reveal oracle. Let

(T I D_{i}^{'}, H P W_{i}^{'}, H I D_{i}^{'}, T_{1}^{'}) \leftarrow R e v e a l (M_{U_{i}, G})

3. Call the Reveal oracle. Let

(I D_{i}^{'}, u^{'}) \leftarrow R e v e a l (T I D_{i}^{'})

4. Computes

D I D_{i}^{'} = h (I D_{i}^{'} | | u^{'}) \oplus H I D_{i}^{'}

5. if $(D I D_{i}^{'} = D I D_{i})$ then
6.    Accepts $I D_{i}^{'}$ as the correct $I D_{i}$ of user $U_{i}$
7.    Call the Reveal oracle. Let $(P W_{i}^{'}, B i o_{i}^{'}) \leftarrow R e v e a l (H P W_{i}^{'})$
8.    Computes $M_{U_{i}, G}^{'} = h (T I D_{i}^{'} | | h (P W_{i}^{'} | | B i o_{i}^{'}) | | H I D_{i}^{'} | | T_{1}^{'})$
9.    if $(M_{U_{i}, G}^{'} = M_{U_{i}, G})$ then
10.       Accepts $B i o_{i}^{'}$ and $P W_{i}^{'}$ as the correct $B i o_{i}$ and $P W_{i}$ of user $U_{i}$
11.       Call the Reveal oracle. Let $(H I D_{i}^{''}, K^{'}) \leftarrow R e v e a l (C_{i})$
12.       if $(H I D_{i}^{''} = H I D_{i}^{'})$ then
13.          Accept $K^{'}$ as the correct secret key K of gateway node $G W N$
14.          return 1 (Success)
15.       else
16.          return 0
17.       end if
18.    else
19.       return 0
20.    end if
21. else
22.    return 0
23. end if