# A Secure and Lightweight Group Mobility Authentication Scheme for 6 LoWPAN Networks
## 4 System Models
### The Proposed Scheme (SL_GAS)
#### 4.3.2 Initial Group Authentication Phase  
Upon the first joining of a group of registered 6L\({}_{\text{MNSI}}\) to the domine, it is necessary to authenticate with the server. During this stage, a set of 6L\({}_{\text{MNI}}\), 6L\({}_{\text{MAGGs}}\), LMA, and AAA with each other will establish mutual initial AKE, as depicted in Figure 4 and outlined as follows:  
* Upon a group of 6L\({}_{\text{MNSI}}\) joining the 6 LoWPAN network, 6L\({}_{\text{MNGL}}\) will be selected based on its capabilities. Every 6L\({}_{\text{MNI}}\) of the group denoted as 6L\({}_{\text{MNI}}\)\(1\leq i\leq n\) produces a \(Tag_{i}=MAC_{ki}\)+\({}_{A}\) (\(AID_{i}\)\(1\)\(1\)\(T_{i}\)\(1\)\(R_{i}\)\({}^{2}\)), which is the tag in a standard MAC using the node pairwise key. Therefore, each group member sends its verification message \(\{AID_{i}\)\(1\)\(1\)\(T_{i}\)\(Tag_{i}\}\) to the 6L\({}_{\text{MNGL}}\) (FFD node).
* The 6L\({}_{\text{MNGL}}\) collects all the authentication messages and then generates a 64-bit random number, \(N_{1}\). It then combines this number with its own authentication information, represented as \(Tag_{GL}=MAC_{KGL}\)+\({}_{A}\) (\(AID_{GL}\)\(1\)\(1\)\(T_{GL}\)\(1\)\(1\)\(N_{1}\)), including the messages from all the members of the group. 6L\({}_{\text{MNGL}}\) incorporates all \(M\) group tags and combines its tag into 6\(GLM\) = \(\{(AID_{1}\), \(Tag_{1})\),..., \((AID_{N}\), \(Tag_{N})\), \((AID_{GL}\), \(Tag_{GL})\}\). Next, a router solicitation (RS) message is transmitted to the 6L\({}_{\text{MAG}}\) as \(\{AID_{GL}\)\(1\)\(1\)\(T_{GL}\)\(1\)\(M\)\(  
the pairwise key, \(K_{i}{\leftrightarrow}_{A}\). This technique examines the Illegitimate node; if a 6L\({}_{\text{MN}i}\) message is sent to the 6L\({}_{\text{MAGs}}\) and the 6L\({}_{\text{MNGL}}\) to notify them that this 6L\({}_{\text{MN}i}\) is an unauthorized device, that should be terminated.
* Then, the AAA generates two nonces of 64 bits, \(N_{2}\) and \(N_{3}\), that will be transmitted to the 6L\({}_{\text{MNGL}}\) for generating session keys with either the 6L\({}_{\text{MAG}}\) or the LMA, as well as assigning an \(ID_{6G}\) to each group member and a key calculating function for pairwise keys that are established between each group leader and its group member, \(F(X)\) = \(\sum_{i=1}^{N}\left(K_{i+GL}.\prod_{1\leq j\leq N,\ j\
eq i}\frac{x-AID_{j}}{AID _{j}-AID_{j}}\right)\), used to compute the ciphertext (\(CT_{GL}\)) and send it to 6L\({}_{\text{MN}i}\) within a router advertisement message (RA). Then, AAA calculates a unique ticket of 64 bits in size, \(T_{C}\) = \((ID_{6G}\oplus N_{2}\oplus N_{3}\oplus SP)\), and _Texp_ is the ticket expiry time of 64 bits of size used during the handover process. After that, a message \(\{T_{C}\mid\text{$1 TD_{A}\mid\text{$1T_{A}\mid\text{$1 Texp\mid\text{$1E_{ \text{KLMA}}$}$}$}$}\)\(  
* Once the authentication response message is received, each member decrypts \(CT_{i}\) to verify \(ID_{6G}\) and \(K_{i}{\leftrightarrow}_{GL}\). This enables the recovery of \(HNP_{i}\) from the encrypted message using \(K_{i}{\leftrightarrow}_{GL}\). \(T_{C}\) and _Texp_ are stored in each 6L-MNi for use in the handover process.