## 7 Module III: Temporal Privacy
### Energy Controlled Anti Temporal Scheme (ECAT)
#### 7.2.1 Changing \(\omega_{i}\) from Fixed to Variable  
Having a fixed interval time, \(\omega_{i}\) could be a glitch for network performance. If \(\omega_{i}\) is set to be a large value, then the delay will be high which could be a serious problem in some time sensitive applications. If \(\omega_{i}\) is set to be a small value, then a huge amount of fake messages will be sent at the end of each interval, which will reduce the lifetime of SNs and accordingly the lifetime of the WSN. We propose that we have variable \(\omega_{i}\) as presented in [17]. Every node will be calculating its \(\omega_{i}\) using a pseudo-random number generator (PRNG). We suggest a uniform distribution algorithm such as multiplicative congruential algorithm [45,46], which is the basis for many of the random number generators in use today. [PERSON]'s generators [47] involve three integer parameters, \(r\), \(s\), and \(m\), and an initial value, \(x_{0}\), called the seed. A sequence is generated by the following modified formula:  
\[\mathrm{X_{k+1}=b\ \times((r\ \mathrm{X_{k}+s})\ mod\ m+f)} \tag{43}\]  
The result of the modified PRNG will be a sequence of integer values between (b \(\times\)f) and (b \(\times(m+f-1)\)). Each SN needs to be preloaded with the seed \(\times 0\), r, s, m, b and f values. The seed range is 0 to (m \(-1\)) and it is uniformly assigned to the sensor nodes. If b = 2, f = 1 and m = 4 then sequence of four intervals will be: \(\omega_{i}\in\) [2,4,6,8] time-units as exhibited in Figure 13. We could have up to (m!) different sequences that are uniformly distributed on the SNs. For instance, we can have Equation (24) different sequences for our example and if we have Equation (48) nodes in the network, so each sequence should be provided to two nodes only.  
Figure 12: Anonymity with fake messages. (**a**) Sensors sense events and send real messages while the rest send fake messages. With Fake MSG’s: \(P_{r}=\frac{1}{N}=\frac{1}{48}=2\%\), Without Fake MSG’s: \(P_{r}=\frac{1}{n}=\frac{1}{11}=9\%\); (**b**) Sensors send or forward real messages will not send fake messages. The more the network gets busy the less fake messages are transmitted.  
Each node will be dynamically assigned an interval value, which needs to change after each transmission. Taking the example above, the first \(\frac{1}{m}\) th (more or less) of the sensors will send data after 2 time-units. Then, the second \(\frac{1}{m}\) th will transmit after 4 time-units, and so on. At any point of time, the adversary will be faced by enough transmissions in the network that it could divert its attention far away from the SNs sending real data. By having (m) interval values where each SN will be generating one \(\omega_{i}\) using the PRNG, we have reduced the average interval time from \(\omega_{\max}\) to \(\omega_{\text{ave}}\). That is explained in the inequality Equation (44):  
\[\omega_{max}>\omega_{ave}=\frac{T_{1}+\cdots+T_{m}}{m}>\omega_{min} \tag{44}\]  
Considering the earlier example, we have \(\omega_{max}=8\), \(\omega_{min}=2\) and \(\omega_{ave}=5\). That is: we have reduced the delay interval by 37.5%. If \(\mathrm{m}=8\), then delay reduced by 44%. The transmission of real and fake messages is exhibited in Figure 14.  
Figure 14: SN is assigned a sequence of intervals, which repeat until sensor lifetime ends. At the end of each interval, the sensor sends a fake message if it does not have an event to report. This should cause different delay times depending on the event relative arrival time and the length of the interval.  
Figure 13: The generation of the sequence of intervals assigned for each sensor. The sequence keeps repeating for the sensor. Fake messages transmitted only at the end of the interval. However, real message could be transmitted at any subinterval.