# Dynamic Group Management Scheme for Sustainable and Secure Information Sensing in IoT
## 3 Secure Dynamic Group Management Scheme
### Cluster Header Authentication and Encryption Key's Elements Transmission  
Figures 3 and 4 show the process of transmitting the filter function seed values, which the elected cluster headers (hereinafter referred to as CH) and the base station (hereinafter referred to as BS) will use for authentication and information transmission in mutual authentication and sensor group. The process thereof consists of the two rounds. The first round carries out the mutual authentication between BS and CH and the process of generating secret key. The second round is the process of transmitting filter function seed value for generating secret key and group sensor node secret key. BS and CH exchange RNCH_1 and RNBS_1 and generate 4\(n\) bits stream {0, 1}\({}^{n}\) by utilizing the expansion substitution-box operator. The generated bits stream is separated into \(n\) bits stream, while the CH generates the second random number. The second random number and ID of CH are transmitted to BS using the challenge/response process. BS measures the time of the challenge/response process and verifies the distance between BS and CH. The \(n\) bits stream is conducted r\({}^{0}\), r\({}^{1}\), ad, and lr. Afterwards, IDCH' is derivate. BS generates different \(n\) bits stream, called 'c'. 'c' and ad are used to derivate challenge bits 'C'. When 'C' is derivate, lr is used as reference point. If lr\({}_{i}\) is zero, 'C' is conducted c\({}_{i}\,|\,\mathrm{ad}_{i}\). Otherwise, if lr\({}_{i}\) is one, 'C' is conducted ad\({}_{i}\,|\,\mathrm{ad}_{i}\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbols** & **Explanation** \\ \hline RN & Random Number \\ S-Box & Substitution-Box (S-box having no inverse matrix) \\ ID & Identification \\ K & Secret Shared Key \\ RB & Redundancy Bits \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The symbols used in the scheme. Figure 2: Filter Function. After an initial process of challenge/response is run, BS sends challenge bits 'C' to CH. With that process started, BS also measures a time while the challenge/response process and verifies the distance between BS and CH against of relay attack. For response, CH validates 'C' and operates 'R'. CH also could generate \(4n\) bits stream and derivate 'C'. While BS derivates 'C', CH also derivates 'C'. And while BS sends 'C', CH derivates 'R'. 'R' is conducted \(r^{0}\), \(r^{1}\), and \(\text{ID}_{\text{CH}}\)'. When 'R' is derivate, there are two rules. The first rule is about a position of \(\text{ID}_{\text{CH}}\)'. If \(\text{Ir}_{i}\) is zero, \(\text{ID}_{\text{CH}}\)' is positioned behind of \(r^{0}\) or \(r^{1}\). Otherwise, if \(\text{Ir}_{i}\) is one, \(\text{ID}_{\text{CH}}\)' is positioned in front of \(r^{0}\) or \(r^{1}\). The second rule is about a value used. If \(c_{i}\) is zero, \(\text{r}_{i}^{0}\) is used. Otherwise, if \(c_{i}\) is one, \(\text{r}_{i}^{1}\) is used. Based on the two rules, 'R' is derivate and transmitted to BS. Figure 3: Cluster header authentication and encryption key’s elements transmission protocol-1. After CH's ID is transmitted, the process of generating a session key between BS and CH will begin. BS generates a second order polynomial with S (to be used as a session key) in the constant term. The coefficients of this polynomial will be derived by using ID of CH, which was transmitted in the challenge/response process, and the second random number. BS is the seed value of the filter function that was shared in advance. The resulting value of substituting ID and the random number in the filter function after substituting the secret key of CH is used as a coefficient of the polynomial. Lastly, BS selects the points (P1, P2 and P3) crossing the polynomial graph. In this process, only multiplication and addition is used to create P1, P2 and P3. For the second round, BS and CH shall create a series of bit streams again.