## 4 Proposed Scheme
### Identity, Route, and Location Privacy (IRL)
Recently, very nice random generation techniques have been specially designed for low power sensor networks, such as [30; 31]. These techniques could be used to generate random number for each packet. Also, overall computational overhead is dependent on the number of packets generated by the sensor nodes. Mostly, sensor nodes are event driven or query driven [32]. Therefore, amount of traffic is usually kept low as compared to traditional networks. Our proposed data privacy approach provides several benefits. Firstly, data secrecy is achieved in the presence of identity anonymity. This feature is not available in earlier proposed privacy schemes. Secondly, the base station will receive both the identity of the actual source node and message authentication. If the packet has been successfully decrypted with the shared secret key, it means that packet is received from genuine sensor node. ## 5 Analysis and Evaluation

### Security Resiliency Analysis

Suppose we have an adversary \(\mathcal{A}\) who strives to defeat our privacy protocols and guess the original source node. We will distinguish between two kinds of nodes. A source node is the original sender of a packet \(q\) and a forwarding node is the node that forwards a packet to another node until it reaches the destination. Hence the source node is also a forwarding node. The adversary's goal is to find out the source node. This analysis assumes that we are using IRL algorithm including our proposed data privacy mechanism. So if the adversary sees a packet, it will trivially know the identity of the last forwarding node (which could possibly be the sender node). We will deal with separate cases. Case 1 is when the adversary is close to the base station and can eavesdrop on any packet received by the base station. Case 2 deals with the case when the adversary can see any packet within the radio range of a particular node. Case 3 extends this into two or more nodes. An adversary will try to solve the following problem: Given a packet \(q\) and a subset of nodes \(N^{\prime}\), find out the sender node \(s\). In other words, the algorithm for the adversary takes two inputs and outputs a node \(s^{\prime}\); Namely \(\mathcal{A}(q,N^{\prime})=s^{\prime}\). If \(s^{\prime}=s\), the adversary succeeds in defeating our protocol. We have to find: \(\Pr[\mathcal{A}(q,N^{\prime})=s]\), which is the probability for an adversary to find out the sender node. Our assumption is that, from an adversarial perspective, all nodes are equally likely to be senders of a packet. This does not necessarily mean that the network traffic is uniformly distributed. Notice that if the adversary knows beforehand which nodes are more likely to send packets, then no privacy preserving method can prevent the adversary from guessing the most likely senders, since this constitutes the adversary's a priori knowledge. **Notations and definitions:** Denote a generic node by \(m\). The set of neighbors of \(m\) is denoted by \(N_{m}\), which also includes \(m\) itself. The number of forward and backward nodes of \(m\) is denoted by \(m_{f}\) and \(m_{b}\) respectively. If a node \(a\) is a backward node of \(m\), then we denote it as \(a\to m\). We say that a node \(a\) is in the backward set of node \(m\), if \(a\to a_{1}\to\ldots a_{r}\to m\), for some nodes \(a_{1},\ldots a_{r}\) where \(r\geq 0\). For compact notation we will denote this as \(a\to^{r}m\), if the IDs of the intermediate nodes are not significant. We will also use the notation \(\to^{r}m\) to denote a generic node, who is \(r\) links (hops) away from \(m\). Define the backward set \(C_{m}\) of \(m\) as \(C_{m}=\{a|a\to^{r}m,r\geq 0\}\), that is the set of all the possible nodes such that they have a forward link to \(m\). Denote the base station as \(B\). It will also be seen as another node. Let the total number of nodes in the network excluding the base station be \(N\).