## 1 Introduction  
Nowadays, the Internet of Things (IoT) is a reality: more and more devices are used to monitor our environment and to interconnect such embedded objects. IoT relies on wireless sensor networks (WSNs) for ensuring connectivity between nodes on the lower level of the network architecture. In such a context, some sensitive applications often require cryptographic mechanisms in order to achieve security. For instance, most of the military applications of WSNs require a high level of security [1]. Thus, it is important to design secure communication mechanisms between nodes of the network. These mechanisms can be achieved thanks to modern cryptographic primitives. Once we have established a secure communication channel in the network, several situations might occur; a node can run out of battery, even get destroyed, or just leave the network, or a new node can join the network. In addition, an intruder could capture a node and get all of its secret data (including secret cryptographic keys). An attacker could also try to join the network and be part of the authenticated nodes of the network. There exist several intrusion detection systems (IDS) in the literature [2,3] in order to detect such malicious behavior. In general, an IDS either searches for signs of malicious activity in the network, or monitors the internal behavior of one node. Several works use signature-based or anomaly-based detection techniques. Using the results of IDS, the next step is to revoke identified malicious nodes and to renew the cryptographic keys used by the nodes of the network.  
Moreover, in WSNs, it is widely admitted that asymmetric encryption primitives based on exponentiation, like, for instance, RSA [4] or Elgamal [5], cannot be used since sensor nodes have limited resources (battery and computation power). However, there exist several lightweight cryptographic primitives that are adapted for WSN, e.g., [6,7]. Such lightweight primitives guarantee a low level of security, which remains a real obstacle for their deployment. For instance, using an improved differential fault analysis, the authors in [8] claim that they can break a lightweight block cipher for WSNs called LBlock using a personal computer within one hour. It is clearly not surprising that lightweight encryption can be attacked in a few hours with a computer that has more computation power than a node. Recently, a promising work [9] provided a solution to avoid such an attack by using code polymorphism. This method improves security at several levels in electronic devices.  
In this context, it is therefore crucial to have efficient key revocation and renewal mechanisms in WSNs. The goal of this work is to propose secure and efficient protocols for key revocation and renewal in WSNs. In the literature, many key revocation protocols have been proposed for WSNs. In [10], the authors made a survey and a taxonomy of the most relevant key management protocols proposed for WSNs. Key revocation is closely related to key distribution. Key revocation protocols can be classified into centralized and distributed protocols. In centralized mode, a central entity decides to revoke certain keys or nodes in the network. In distributed mode, a local voting procedure takes place to revoke keys or nodes. The latter might be faster and requires less messages to send, but it is generally more complex to implement. We propose several centralized secure key revocation and renewal protocols. Note that we cover the revocation/renewal of both symmetric and asymmetric keys. Indeed, according to the security level requirements, one or both cryptographic methods should be used. Therefore, it is crucial to be able to renew both types of keys, asymmetric keys and symmetric keys.