Random-Walk Based Techniques

Ozturk et al. [115] use the random walk as a technique to provide SLP. In the phantom routing scheme (PRS), there are two phases: (i) the random walk phase which is a pure or directed random walk, meant to deliver the message to a

Figure 2.3: Illustration of phantom routing scheme

phantom source after travellinghwalkhops, and (ii) a subsequent flooding meant

to deliver messages to the sink (see Figure 2.3). Ozturk et al. discuss the pure random walk in the phantom routing in detail and claim that the phantom node

is within 20% ofhwalkfrom the real source afterhwalkhops (see Figure 2.4a).

Then Ozturk et al. propose the directed random walk that avoids random walks cancelling each other out (see Figure 2.4b). Both sector-based directed random walk and hop-based directed random walk could guarantee phantom sources far away from the true source. Instead of using flooding for the second phase, Ozturk et al. also use single path routing algorithms, such as shortest path routing. The combination of the random walk together with single path routing is often referred to as the phantom single-path routing scheme (PSRS). Both PRS and PSRS has received a lot of attention in the literature. On the other hand, this class of solutions is known to have weaknesses [89, 124, 138], ascribing poor SLP performance to the directed random walk reusing the routing path and exposing direction information. Zhang [156] introduces an improved algorithm of a sector-based directed random walk called self-adjusting directed random walk (SADRW). Instead of dividing neighbours into two sets in the phantom routing,

(a) Pure Random Walk (b) Directed Random Walk

Figure 2.4: Illustration of pure random walk and directed random walk

in SADRW neighbours are divided into four different sets. Nodes randomly pick a neighbour out of one of the four directional sets and send messages to it. If an intermediate node receives the message and cannot forward it to the same direction, then it chooses a new direction to forward the message to until the

message travels a total ofhwalkhops. SADRW solves the weakness of a phantom

walk that may unexpectedly terminate beforehwalkhops, hence increasing the

SLP level.

Wang et al. [140] introduce phantom routing with a locational angle (PRLA). In PRLA, the random walk is based on the inclination angle between a node and its neighbours towards the sink. PRLA works as follows. In the deployment stage, every node calculates the inclination angle between itself and its neighbours. Then, every node uses the inclination angle to calculate the forward probability of each of its neighbours. The higher the inclination angle of a neighbour, the higher the forward probability of that neighbour will be. The source sends messages to neighbours by using the forward probability of the neighbours. After

the message travelshwalkhops or the last node is not able to forward the message

with the same inclination angle, the message is forwarded to the sink using a single path routing strategy.

Yao and Wen [151] provide another improvement by introducing the directed random walk (DROW). In DROW, every node has the knowledge of its own hop-distance to the sink and the hop-distance of its neighbours to the sink. Each node chooses the neighbours with a lower hop-distance towards the sink than its parent’s. When sending messages, the node randomly chooses one of its parents as the next destination. Authors claim several advantages applying to DROW

such as routing diversity, long safety period1 _{and energy efficiency. However,}

Deng et al. [32] show that DROW does not defend against a time correlation attack. Wang and Hsiang [139] mention that the direction information retrieved from the packet headers helps the adversary to find the source of messages.

Xi et al. [144] introduce the greedy random walk (GROW). In the GROW, one random walk starts from the sink and goes to a randomly chosen receptor- node. The other random walk starts from the source and meets the first random walk at the receptor-node. Then the receptor-node uses the path established by the random walk from the sink to the receptor-node to route the packet from the source to the sink. In addition, the authors use a different approach, by recording neighbours in a bloom filter which informs the choice of the next node to be used in the random walk. However, there is still scope to improve nodes that are allocated to take part in the directed random walk. Yao and Wen [151] point out that the random walk used in the GROW is inefficient at creating a safe distance between the receptor-node and the source. Wang et al. [140] state that the latency is unstable due to the usage of two random walks. Other weakness can be found from [89, 122, 124].

An algorithm called randomly selected intermediary node (RRIN) is intro- duced by Li et al. [88] as an improvement over PRS. Unlike PRS, RRIN does not leak any directional information via its messages. A source node sends a message to a chosen intermediate node, and the intermediate node sends the message to the sink. The choice of the intermediate node must meet the following criteria: the location of the intermediary node must be at least a minimum distance away

from the source and be normally distributed within the rest of the network. The authors claim that RRIN has the same latency and power consumption as PRS, but a higher safety period. Then Li et al. propose a second version of choosing intermediate nodes. Each node in the WSN has an equal probability to be the intermediate node of any given source node. The second version of RRIN consumes much more energy [89] and has a higher delay than PRS, but it does provide an even better safety period.

There are other algorithms using random walk techniques to address the SLP issue such as the random routing scheme (RRS) [96], location privacy support scheme (LPSS) [76] and network mixing ring (NMR) [87]. As random walk is one of the early techniques used to provide SLP, they could only defend against a local adversary. In fact, some solutions in the literature have discussed weaknesses, which shows that the random walk is not always effective. Therefore, algorithms need to be developed to guard against a powerful adversary with a global view.