## 1 Introduction
### Related Work
The authors do not specify the cryptographic algorithms used for symmetric or asymmetric primitives. In [25], the authors propose a key distribution based on key chains where each key is obtained by applying a hash function on the next key in the chain. These key chains are either exchanged through a secure channel or installed in nodes before deployment. Authenticating the keys is done by verifying the hash result. A central node is used as a key service entity that manages the key revocation process. This entity shares a secret key with every node in the network. The authors do not explain how this secret key is shared, nor how this secret is renewed. In [26], the authors propose a key revocation scheme based on public key cryptography that demands periodical certificate broadcast. They propose the use of hash function chains instead of digital signatures in order to conserve the limited resources of nodes. It is based on the exchanges that take place after deployment on a secure channel, which means that the verification process of the proposed protocol supposes the existence of a secure channel that helps them to define the shared information between neighbors. The authors also propose using a voting mechanism in order to avoid malicious revocations. Only revocations that reach a certain threshold in a neighborhood are validated. Protocols based on key chains cannot easily update the chains, for their key renewal is based solely on the hashing function and the root value of the chain. Moreover, chains should be long enough to last for the life duration of the network. In [27], the revocation method is centralized and based on preventing nodes from updating session keys and, thus, preventing them from being able to exchange messages with other nodes in the network. All communications are encrypted with a session key and a message authentication code (MAC). Symmetric session keys are renewed using a function that takes the previous session key as a parameter in addition to a pairwise key. The authors assume that the base station can reach all nodes in the topology. In [28], the same key revocation scheme is used and applied on a hierarchical network topology with three levels. In this method, keys are only revoked upon periodic renewal at the end of each session. This can be a handicap when the session is very long. In [29], the authors proposed a periodic key renewal based on fragmentation of the key generation function. This method supposes that nodes will assemble the fragments sent by the base station. The process of assembling the function is not authenticated and might be easily falsified, for it uses only one key, which is a shared key between all of the nodes of the network; thus, any compromised node is able to interfere in the process. In [30], the authors propose a cluster reorganization in order to avoid renewing keys. By updating the cluster head, a new pairwise key is established between the base station and the cluster head. This key established is made without exchanging the key materials between the two entities. The shared key is a simple exclusive-or of all of the keys of the nodes of the cluster. This supposes that the number of keys is limited to the number of potential cluster heads, which is a limited number compared to the life time of the network. In addition, the initial pairwise key agreement between neighboring nodes lacks authentication. Any neighboring node is able to establish a key with its neighbor. In [31], the authors propose a key renewal mechanism that is managed by a special entity called the command node. The network is organized into clusters with one cluster head node that is used for key revocation. This cluster head receives the list of new keys for renewal and sends them to the other cluster gateways, which, in turn, send them to the sensor nodes. The authors use the shared key with the command node to update keys and do not propose a mechanism for updating this shared key. Table 1 summarizes the comparison between the related work schemes and our proposition.