Time Consumption for Key establishment is one of the important constraints of Wireless Sensor Network. In basic schemes it is depends on the number of factors like, the number of a node neighbours N$_{nb}$, the key ring size\emph{ m}, and the key pool size \emph{P} because of shared key discovery phase and path key establishment phase .Time consumption for key establishment T$_{E}$ in E-G scheme is expressed as follow:\\ \emph{T$_{E}$= max(T$_{Ei}$)
\hspace{5mm} i=1,2,...,N\\
T$_{Ei}$ $\propto$ N$_{nb}$
\hspace{5mm} T$_{Ei}$ $\propto$ P/m}\\
Here \emph{N} is the total number of nodes in the network and T\emph{$_{Ei}$} is the time for node \emph{i} to finish its key establishment.

\paragraph*{}In the proposed scheme, the time consumption of key establishment is only depends on the time to get a key seed from the SCH. Other factors like number of nodes, number of node neighbours are not affected because of there is no need to find the shared key. So the time consumption for key establishment is unique even though the number of nodes increases. …show more content…
The shared-key discovery phase takes place after each node has finished finding shared keys with its neighbors. Each node broadcasts a list of identifiers of the keys on its key ring to all its neighbors. Two neighboring nodes will setup a secure link if they share at least one key. However, if two neighboring nodes have no keys in common, they will begin a path key establishment phase with the help of their neighbors. A path key establishment may span one or more hops. If the nodes cannot be reached via a shared key (i.e., one link or one hop), it will take at most two or three hops to contact it. We can find that the time consumption of key establishment under the basis scheme is affected by the following three factors: the number of a node neighbors, the key ring size, and the key pool