This paper proposes an ID-Based authentication method for the Extensible Authentication Protocol (EAP), as an alternative to methods relying on PKI (Public Key Infrastructure), to provide nodes with private and public keys. It proposes to derive the public key from the node's identity directly. As such, there is no need for deployment of CA (Certification Authority) and the burdensome management of certificates is removed. The presented authentication method is resistant to the Key Escrow Attack. In addition, the results from implementation tests are given and prove how efficient the ID-Based cryptography might be for use in wireless networks.