# Lightweight Sensor Authentication Scheme for Energy Efficiency in Ubiquitous Computing Environments
## 3 Proposed Scheme  
In the suggested method, while routing protocol motion is based on the LEACH routing protocol [37], a lightweight protocol for existing sensor network environments, it forms a group using energy information for greater efficiency. The suggested IoT environment has the following characteristics: every sensor node in the specific area can transmit to the sync node in one hop; sensors give the intensity of received power and changes in transmission power are possible; and sensor nodes regularly transmit data to the base station.  
For the battery life, each sensor periodically selects a random Middle Node (MN) and forms a group through it. After the sensor nodes belonging to the specific group collect data to transmit to MN, MN aggregates this information and transmits it to MD. At this time, MN consumes relatively more energy compared to other nodes and may negatively influence the whole network if specific nodes become overloaded. Thus, after a specified time period, MN is selected in order to distribute its energy consumption by round.  
At this time, to consider the energy efficiency of sensor nodes, nodes belonging to each group transmit their energy quantity and MN aggregates this information and transmits it to MD. MD selects the top 30% nodes that do not play a role in MN through a probability algorithm, as follows:  
\[P_{i}\left(\mathrm{x}\right)=\frac{K_{opt}}{N-K_{opt}\left(r\ mod\frac{N}{K_{opt}} \right)}C_{i}\left(t\right)=0\ or\ 1 \tag{1}\]  
where \(i\) represents each sensor and has a value ranging from 1 to the total number of sensors, \(N\); \(t\) is time; \(P_{i}(t)\) is the probability of selecting \(i\) as MN at \(t\); \(r\) represents the round; \(K_{opt}\) is the number of rounds that ends at Group of Round; and \(C_{i}(t)\) represents either 0 or 1, according to whether it was selected as MN before \(t\). One round is performed from when a new cluster is formed to when the new cluster is expired. When all nodes have each cluster head, the nodes can be eligible to become cluster heads, which state is defined as Group of Round. As the round progresses, since the number of sensors participating in MN selection decreases, the probability of becoming MN increases. At this point, the probability of becoming MN is \(K_{opt}\).  
The sensor that calculated \(P_{i}(t)\) will pick a \(p\) value between 0 and 1; if \(p<P_{i}(t)\), it selects itself as MN. If \(p>P_{i}(t)\), the node will be used for forming a cluster. If the current node became MN at Group-of-Round, \(P_{i}(t)=0\), so it is impossible to become MN until a new round begins. In the final round, \(P_{i}(t)=1\), so nodes that never have been MN are selected as MN. The parameters for the proposed protocol are described in Table 1.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Meaning** \\ \hline \(N_{v},N_{p}\) & Nonce \\ \(MN\) & Middle Node \\ \(CA\) & Certificate Authority \\ \(ID\) & Node ID \\ \(C_{id}\) & Middle Node ID \\ \(R_{i}^{o},R_{i}^{o},R_{i}^{o},R_{i}^{o}\) & 3n Bit Divided Value \\ \(Sk\) & Session Key \\ \(Nk\) & \(f(0)\) Function Shared Key \\ \(N_{i}\) & After distance bounding remaining bits \\ \(C_{i}\) & Random bit \\ \(g(k)\) & Group Key Polynomial \\ \(\sigma(x,y)\) & Group Key Encryption Polynomial \\ \(g^{\prime}(x)\) & Encrypted Polynomial to \(e(x,y)\) \\ \(E(0,D0)\) & Encryption, Decryption \\ \hline \hline \end{tabular}
\end{table}
Table 1: Proposed protocol parameters.