Algorithm 2. the algorithm of a trust-based secure routing (TBSR) scheme

INPUT: receive a packet // $t_{i,j}\left(0\le j\le 23\right)$ is the $j$ th hour of the $i$ th day; $U_{i,j}$ is the available energy at $t_{i,j}$, // ${\alpha }_{i,j}$ is the probability of marking at $t_{i,j}$, ${\beta }_{i,j}$ is the probability of logging at $t_{i,j}$, and $h$ is the hop from the sink. OUTPUT: Forward a new packet to next hop node (1) aggregate signature stage 1: For each node Do     running aggregator determining algorithm which is similar to cluster-head selection algorithm in Reference [59];  End for  // now, nodes either belong to aggregators or belong to member nodes 2: For each member node Do    send its data and node ID, data time to its aggregator  End for 3: For each aggregator node ${\mathrm{s}}_0$ Do     ${\mathrm{s}}_0$ aggregate its member nodes’ data into a data packet ${\mathfrak{D}}_0$   using ID-based aggregate signature technology as Reference [58];     ${\mathrm{s}}_0$ aggregate its member nodes’ abstract into an abstract ${\mathfrak{A}}_0$   using ID-based aggregate signature technology as Reference [58];  End for (2) Adopt the variable probability marking and logging $\left({\alpha }_{i,j},{\beta }_{i,j}\right)$ stage 4: For each receive packet $\mathrm{P}$ in node $n_h$ and $n_h$ is not sink Do     Mark all received packets P with ${\alpha }_{i,j}$.    //${\alpha }_{i,j}$ using Equation (41).  End for 5: For each receive packet ${\mathrm{P}}_1$ generated by last node $n_{h+1}$ Do     Log the amount of notification in packet ${\mathrm{P}}_1$ with ${\beta }_{i,j}$.    //${\beta }_{i,j}$ using Equation (50);  End for 6: Forward New packets ${\mathrm{P}}^{\prime }$ to next hop node.