## 1 Introduction
### Related Work  
The main issue for secure communications in WSNs is how to set up secret keys between nodes, which is known as the key agreement. This task is a challenge due to resource constraints and the size of networks. Many proposed methods are based on random key pre-distribution [16, 17, 18]. The main idea is that any two sensor nodes have a probability for choosing the same key from the pre-distributed key pool. The weakness of these schemes is when sensor nodes are captured by an attacker. All encryption keys in the captured nodes will be revealed. In [19], the authors proposed an approach to resolve this issue. The proposed approach is to hash the keys in the key pool with a one-way hash function. Once a key is chosen by a sensor node, it will be hashed. If another sensor node chooses the same key afterwards, instead of using the same key as the previous sensor node, it will derive a new different key by hashingthe key value. This technique can reduce the amount of information revealed when a sensor node is captured for about 30% to 50% according to the authors of [19]. Another way to reduce the impact of compromised nodes in WSNs is to preserve the network connectivity. The authors in [20] propose an improved key distribution mechanism for large-scale networks that preserves the network connectivity when many sensors are compromised with a sufficient security level. Based on a three-tier hierarchical WSNs model, the authors propose three phases: the key predistribution phase, the inter-cluster pairwise establishment phase and the inter-cluster pairwise key establishment phase. Different secret information (polynomial shares) is pre-loaded in the first phase. Two bivariate symmetric polynomials are used to establish pairwise keys between cluster heads and their sensors in the second phase. In the last phase, each cluster head establishes a pairwise key with other cluster heads. Compared to the existing key pre-distribution schemes, this scheme can achieve better network resiliency against node capture attacks. However, the compromised nodes in these schemes can continue to use the shared secrets with neighbors without any revocation process. The neighbors of the compromised nodes should be alerted in order to ignore any further communications with the compromised nodes. Not all key distribution protocols for WSNs include a key renewal or revocation process. Most of those that do include one suppose that an IDS is implemented in each node and enables it to signal the presence of an intruder. In what follows, we summarize some of the key revocation and key renewal protocols for WSNs. One of the first key revocation protocols was proposed in [21, 22]. This proposition has been enhanced by the authors of [23], where they proposed a distributed collaborative key revocation mechanism that divides the network into regions. In each region, nodes collaborate to identify a malicious node. Once a malicious node is identified, the base station is informed, and it sends a broadcast message containing a list of keys to revoke. Unlike [21, 22], their contribution is able to revoke all of the keys with which the revoked node is involved and does not need to know the network topology before the deployment. The key revocation message sent by the base station is based on trivariate polynomial authentication and verified by each node according to the region to which it belongs. In [24], the authors propose a key distribution in a cluster-based network that is based on a probabilistic key establishment inside the cluster. In addition, they propose a voting mechanism that detects an intruder node of the network. Then, all of the keys shared with that node should be revoked. The revocation step is initiated by the cluster head. Cluster heads form path keys to reach the base station. The authors also discuss the revocation process for those keys. The key revocation is based on asymmetric cryptography for inside cluster revocation and symmetric encryptions for inter cluster revocation.