## 2 Related Work
[PERSON] _et al._ test several symmetric encryption functions and MAC (Message Authentication Code) for their protocols using an extremely limited sensor network platform. They show that data transmission takes 71% of the time. In SPINS, the base station plays an essential role in the key establishment process. It is a lightweight cryptography protocol but has limited scalability and depends heavily on the base station. [PERSON] _et al._ in [21] propose a multi-hop key establishment between nodes called Micro-PKI, using ECC and MAC. Their method is based on the pre-distribution of the public key of the base station. Using this public key, every node is able to create a secret key with any other node of the network. They evaluate the energy consumption of their solution and perform an informal security analysis. The authentication process in this proposal is only dependent on the public key of the base station; if a node has this key,it is considered authenticated. This makes the procurement of this public key very critical for the whole security architecture. In [22] [PERSON] _et al._ propose PIKE (Peer Intermediaries for Key Establishment), one of the most famous key establishment protocols that is not dependent on a central trusted node. According to PIKE, symmetric keys are pre-deployed in the nodes in such a way to guarantee that any two nodes in the network have at least one node in common with which each one of the two nodes has a secret key with it. Therefore, these two nodes are able to establish a secret key by using the trusted channel established with the common node. They provide a simulation evaluation of the protocol and estimate the energy and memory cost of several schemes. They also give an informal security analysis of the protocol against node compromise. PIKE suffers from high memory storage to make sure that nodes are able to find at least one node in common to establish a new key. CARPY and CARPY+ are proposed in [23]. They are based on the symmetric keys of Blom [24] with a perturbation function that makes it more difficult for an attacker to guess the pairwise keys. In their paper they discuss the five criteria proposed in [25] and claim that CARPY+ satisfies all of them. These criteria are:  
* _Resilience to the Adversary's Intervention_ during the key establishment phase,
* _Directed and Guaranteed Key Establishment_ for any couple of nodes in the network,
* _Resilience to Network Configurations_, _i.e._, nodes should be able to establish keys in any kind of network topology,
* _Efficiency_ of the key establishment process in terms of memory storage, communication overhead and complexity,
* _Resilience to Dynamic Node Deployment_, which allows nodes to be added at any time to the network and establish keys on demand. The authors give a detailed security analysis including a security model to prove manually the resistance against a given number of compromised nodes. They have implemented their solutions on TelosB compatible more to evaluate their performances. The main weakness of this scheme is the lack of a re-keying process. The pre-shared matrices will only help to create one pairwise key for every couple of nodes. Comparing these protocols to determine which is the most suitable requires to possession of all different implementations on one platform. However, most of the implementations, if exist at all, are very platform-dependent, thus an implementation on one platform might not give reproducible results on another platform and might not even operate on incompatible platforms. For this reason, in this paper, we will not compare execution results between protocols. On the other hand, Table 1 summarizes a comparison between the related work schemes and our proposition. The comparison is based on some repudiated criteria in the WSNs area. As the table shows, [PERSON] _et al._'s scheme [23] is the closest to our schemes.