## 3 Model and Assumptions
### Adversary Model  
In this section, we describe the characteristics of the adversary who intends to inject replicas into the sensor network. We adopt the adversary classification model of [PERSON] _et al._[14, 15] and identify the particular class of adversaries that our protocol **Disccard** defends against. [PERSON] _et al._[14, 15] classified adversaries based on their abilities along two attributes.  
1. Mobility: The adversary was classified as being either localized or ubiquitous based on his mobility. A localized adversary was limited to injecting replicas within a particular convex sub-area of the sensor field while a ubiquitous adversary had the freedom to traverse the entire network field in his effort to identify, compromise and inject duplicate nodes. In some sense, this captures the degree of physical monitoring or surveillance present in the sensor field. If the sensor network is highly unattended, then perhaps this allows the adversary to freely traverse the entire field without fear of detection. It is of course in the adversary's best interest to operate in a stealthy manner and attempt to avoid detection, since detection could trigger automated protocols, such as SWATT [34], to sweep the network and remove compromised nodes.
2. Intelligence: The adversary was classified as being either oblivious or smart based on his or her intelligence to identify potential target nodes to compromise. The smart adversary chooses to compromise sensor nodes that yield the most benefit, _i.e._, that maximizes the chances of his or her injected replicas to go undetected, while the oblivious adversary merely compromises a random sensor node oblivious of the processes used in the detection algorithm.  
As we will show, our scheme defends against the most powerful adversary according to the above classification model: the smart/ubiquitous adversary. Given our network setup and the classification of nodes as being in the home zone (safe) and being outside the home zone (unsafe), we can succinctly describe all possible actions of such an adversary as described here. We use the term source to refer to the original sensor node chosen by the adversary for compromise and subsequent duplication. The possible adversarial choices for the source node are to either choose a node from inside the home zone (IHZ) or outside the home zone (OHZ) from any territory. After compromising the source node, duplicate nodes can now be deployed either in their corresponding home zones (IHZ) or elsewhere (OHZ). The third possibility to consider is what the adversary does with the original source node. The original sensor node can either be removed from the network (REM) or left intact in its initial deployment point (inserted (INS)). The notation \"INS\" stands for the duplicate nodes being \"inserted\" into the network with the original node not being removed. Finally, we are only interested in studying those scenarios when there are at least two nodes with the same identity in the network (in each of the eight cases). In other words, we are not trying to identify compromised nodes, but only to detect the duplicate nodes in the network. Therefore, we assume that the adversary, after his duplication efforts, has at least two copies of the same node identity in the sensor network at distinct locations. Indeed, if there are more replicas, **Disccard** will only detect them faster. In our simulation experiments, we analyze (conservatively) the performance of **Disccard** in the presence of exactly two duplicates to best understand the costs and other performance characteristics.