We propose in this paper, two ID-Based authentication methods for the Extensible Authentication Protocol (EAP), as an alternative to methods relying on Public Key Infrastructure (PKI), to provide nodes with private and public keys. ID-Based Cryptography (IBC) proposes to derive the public key from the node's identity directly. As such, there is no need for deployment of a Certification Authority (CA) and the burdensome management of certificates is removed. IBC relies on a Private Key Generator (PKG) for the computation of stations private keys. Our first presented authentication method corresponds to a situation where the PKG is trustful. As such, the PKG generates the private keys of all the network stations. However, our second contribution presents an authentication method which is resistant to the Key Escrow Attack. That is, we make each station generate its own ID-Based private key. In addition, results from implementation tests are given and prove how efficient IBC might be for use in wireless networks