# Dynamic Group Management Scheme for Sustainable and Secure Information Sensing in IoT
## 3 Secure Dynamic Group Management Scheme
### Group Sensor Authentication and Secure Sensor Information Transmission  
Figures 5 and 6 show the process in which an elected cluster header conducts mutual authentication for all the sensor nodes simultaneously belonging to a group, and also derives a session key value to be used for transmitting sensor information. A process for each sensor node consists of the two rounds. Figure 5: Group sensor authentication and secure sensor information transmission protocol-1. The first round consists of the mutual authentication between CH and sensor node, the transmission of filter function seed value and the process of generating a session key. The second round is the polynomial transmission process to generate a session key to be used in a group sensor node. CH and sensor node exchange RNCH_1 and RNNode_1_i 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 sensor node generates the second random number. The second random number and ID of sensor node are transmitted to CH using the challenge/response process. CH measures a time while the challenge/response process and verifies the distance between CH and sensor node. The \(n\) bits stream is conducted r\({}^{0}\), r\({}^{1}\), ad, and lr. Afterwards, IDNode_1' is derivate. CH generates different \(n\) bits stream. And it's called 'c'. 'c' and ad are used to derivate challenge bits 'C'. When 'C'  
Figure 6: Group sensor authentication and secure sensor information transmission protocol-2. is derivate, lr is used as reference point. If \(\mathrm{lr}_{i}\) is zero, 'C' is conducted \(\mathrm{c}_{i}\,|\,\mathrm{a}\mathrm{d}_{i}\). Else if \(\mathrm{lr}_{i}\) is one, 'C' is conducted \(\mathrm{a}\mathrm{d}_{i}\,|\,\mathrm{a}\mathrm{d}_{i}\). After initial process of challenge/response is run, CH sends challenge bits 'C' to sensor node. At that process started, CH also measures the time of the challenge/response process and verifies the distance between CH and sensor node against relay attack. For the response, sensor node validates 'C' and operates 'R'. Sensor node also could generate \(4n\) bits stream and derivate 'C'. While CH derivates 'C', sensor node also derivates 'C'. And while CH sends 'C', sensor node derivates 'R'. 'R' is conducted \(\mathrm{r}^{0}\), \(\mathrm{r}^{1}\), and \(\mathrm{ID}_{\mathrm{Node\_1}}\)'. When 'R' is derivate, there are two rules. The first rule is about a position of \(\mathrm{ID}_{\mathrm{Node\_1}}\)'. If \(\mathrm{lr}_{i}\) is zero, \(\mathrm{ID}_{\mathrm{Node\_1}}\)' is positioned behind of \(\mathrm{r}^{0}\) or \(\mathrm{r}^{1}\). Otherwise, if \(\mathrm{lr}_{i}\) is one, \(\mathrm{ID}_{\mathrm{Node\_1}}\)' is positioned in front of \(\mathrm{r}^{0}\) or \(\mathrm{r}^{1}\). The second rule is about a value used. If \(\mathrm{c}_{i}\) is zero, \(\mathrm{r}_{i}{}^{0}\) is used. Otherwise, if \(\mathrm{c}_{i}\) is one, \(\mathrm{r}_{i}{}^{1}\) is used. Based on the two rules, 'R' is derivate and transmitted to CH. After sensor node's ID is transmitted, the process of generating a session key between BS and CH will begin. At this time, CH executes an operation on the filter function seed value received from BS with the remainder bit occurred in the first challenge/response process and then transmits the result of this operation to a sensor node. After then, CH generates a second order polynomial with S (to be used as a session key) in the constant term. The coefficients of this polynomial are derived through the ID of a sensor node transmitted in the challenge/response process and the second random number. CH substitutes the seed value of the filter function transmitted to a sensor node. The result value of substituting ID and the random number in the filter function is utilized as a coefficient of the polynomial. Lastly, CH selects the points (P1, P2 and P3) crossing the polynomial graph. For the second round, CH and a sensor node generate a series of bit streams again.