## 7 Module III: Temporal Privacy
### Simple Global Anti Temporal Scheme (SGAT)  
When an event-driven message is sent out, the adversary can trace back the message to the SN or forward to the BS. Sending few other transmissions in the network within the range of the adversary confuses it and prevents the adversary from having known path to follow. In this work, we presume the lifetime of the network (\(\Omega\)) is divided into a number of intervals (\(I\)) and each interval time is (\(\omega\)), where:  
Figure 9: Having multiple colluding nodes will reduce system anonymity exponentially [34,42,44]. \[\Omega=I\times\omega_{i} \tag{33}\]  
The value of \(\Omega\) can be predicted as a range between a minimum value (worst case) \(\Omega_{min}\) and a maximum value (best case) \(\Omega_{max}\). It all depends on how real/fake transmissions are facilitated. The SNs will send either a fake or a real message during one interval. The message is sent at the end of each interval or it is adjusted to be sent during the interval to create some variable delays through the route to the BS, which would confuse the adversary more and would prevent it from gaining useful knowledge about the network based on time correlation. SNi that has sensed the event or received the real data from another SNj, will send the real message (\(M_{r}\)) through a hop-by-hop path to the BS, and some other nodes will send fake messages (\(M_{f}\)) during the same time to disrupt the adversary. There are two questions: _How long the message will be held in the SN after it is sensed?_ Simplistically, Mr and Mf are sent at the end of the interval \(I\). The time from arrival of the data to the end of the period time (\(\tau_{w}\)) expressed in Equation (34):  
\[\tau_{w}=\omega_{i}-t_{a}\quad\quad\text{where: }t_{0}\leq t_{a}\leq t_{s}\leq \omega_{i} \tag{34}\]  
where: to is the beginning of the interval \(I_{i}\), \(t_{a}\) is the arrival time, \(t_{0}\leq t_{a}\). Ideally, the message will be sent immediately after it is sensed or received which makes \(\tau_{w}=0\). Theoretically, \(\tau_{w}\) could be a value: \(0\leq\tau_{w}\leq\omega_{i}\) as exhibited in Figure 10.  
_How many SNs in the network will send fake message during one interval time and which ones?_ Simplistically, every SN in the network, which is in the range of the adversary and in the range of source SN, should send a fake message while SNs that have real messages will send the real messages only. There are many technical issues regarding the determination of the optimal configuration for both questions mentioned earlier. For instance, it is not possible for the neighboring nodes to know in advance when a SN is going to sense an event. It is a completely unpredictable random-distribution for the events. The need to transmit fake messages becomes even much more crucial if we do not have busy-network. Therefore, all SNs with no real messages need to send fake messages during the interval \(I_{i}\), in the worst  
Figure 10: Timing for receiving a real message and then sending it out during the interval period assigned to the sensor node. The total delay will include the processing time, transmission time and the withhold time [42]. case, or only selected nodes according to a probabilistic protocol. Having high number of fake message transmissions will reduce the lifetime of the network in favor of privacy. Doing the reverse will jeopardize the privacy of the sensor nodes. The adversary could learn the mechanism of sending real and fake messages at the end of the interval. However, it is not very dangerous if the network sends enough fake messages at the same time. Having variable withhold time (\(\tau_{w}\)) is useful for privacy and for reducing the average network delay. The delivery time (\(\tau_{d}\)) presuming that the message is always sent at the end of the interval \(I_{i}\) is:  
\[\tau_{d}=\tau_{w}+\tau_{trans}+\tau_{proc} \tag{35}\]  
where: \(\tau_{d}\) is delivery time, \(\tau_{trans}\) is transmission time, \(\tau_{proc}\) is processing time.