## 2 Related Work  
Very few works have been done for node authentication protocols in multi-hop WSNs. Most of the existing authentication protocols proposed for WSNs neglect the multi-hop factor. In [12], [PERSON] _et al._ propose a protocol where the base station broadcast authentication elements for in-range sensor nodes to be able to authenticate new arriving nodes. In fact, they consider that any previously authenticated node can authenticate new nodes using identity-based signature (IBS) algorithm, Elliptic Curve Cryptography (ECC) and a digital signature algorithm (DSA). They provide an informal security analysis and have not implemented their protocols. In [13, 14], the authors propose an authentication mechanism for users and consider that sensor nodes inside the WSN are trusted nodes. In [14], [PERSON] _et al._ show the weakness of some protocols proposed in [13], due to lack of authentication. Then they propose a stronger authentication protocol usingECC that ensures mutual authentication and protection against attacks from other users, which was not included in [13]. They also provide a manual security analysis of their solution and only a theoretical complexity evaluation of their protocols. Recently in [15], [PERSON] _et al._ propose an authentication model that aims at reducing overhead for the re-authentication of sensor nodes using symmetric and public key cryptography. It is based on a ticket encrypted using a common secret key between neighbouring fixed nodes. This ticket is sent to a mobile node during the first authentication phase. This ticket is only useful when the mobile node decides to re-authenticate with this neighbour fixed node. In addition, the protocol only works well when the fixed node is in direct range with the base station, and the initial authentication phase suffers from internal attacks. Sinks in the network can easily take the place of each other when they are not in communication range with the base station. The authors only give a quick informal security analysis of their solutions and they have not deployed their solutions on real motes. In [16], [PERSON] _et al._ propose an authentication technique using ECC and ElGamal digital signature scheme for message authentication. The authors do not perform any security analysis of their solution. Moreover, the proposition is evaluated on a computer using MATLAB simulator, which makes it difficult to estimate compared with a real testbed implementation, since digital signatures and public key cryptographic primitives are very resource consuming operations. In [17], [PERSON] _et al._ propose a node authentication protocol for hierarchical WSNs. The hierarchical topology is limited to a base station, cluster heads and sensor nodes. The cluster heads can reach the sensors of their clusters directly, and can also reach the base station directly. The authentication is based on hash chain functions and symmetric encryption. The proposed protocol is not resilient to insider attacks as cluster heads are trusted to forward join requests to base station. In addition, the coverage of the network is limited due to the limited number of hops in a hierarchical topology. Many contributions have been made in the key establishment and symmetric key distribution in WSNs using symmetric cryptography and hash functions. Some of them are based on a probabilistic pre-distribution that guarantees that any two nodes in the network are able to share a key with a certain probability, and others are deterministic but cause more storage overhead [18]. They do not evaluate on real motes their solutions and the security analysis is only informal. One of the most known symmetric key systems that were proposed for wireless sensor networks is SPINS (Security Protocols for Sensor Networks) [19], which uses a simplified version of TESLA (Timed, Efficient, Streaming, Loss-tolerant Authentication) protocol [20].