wireless authentication- WEP and WPA Authentication

There are 2 types of methods used for authentication in wireless LAN client on an access point.

Open system
Shared key authentication

Open system do not have any security mechanism. It is a request to make a connection to the network.
Unlike Open system, shared key authentication has the wireless client hash a string of challenge text with the WEP key to authenticate to the network. WEP is used to encrypt the data on WLAN. WEP uses an RC4 64-bit or 128-bit encryption key to encrypt the layer 2 data payload. This WEP key comprises a 40-bit or 104-bit user-defined key combined with a 24-bit Initialization Vector (IV), making the WEP key either 64- or 128-bit.
The process by which RC4 uses IVs is the real weakness of WEP: It allows a hacker to crack the WEP key. The method, knows as the FMS attack, uses encrypted output bytes to determine the most probable key bytes. Hacker can also crack WEP using bruteforce attack.

WPA is safer than WEP which employs the Temporal Key Integrity Protocol (TKIP). There are 2 types of WPA, WPA Personal and WPA Enterprise.
WPA Personal uses an ASCII passphrase for authentication while WPA Enterprise uses
a RADIUS server to authenticate users. WPA Enterprise is a more secure robust security option
but relies on the creation and more complex setup of a RADIUS server. TKIP rotates the data encryption key to prevent the vulnerabilities of WEP and, consequently, cracking attacks. WPA2 is similar to 802.11i and uses the Advanced Encryption Standard (AES) to encrypt the data payload. AES is considered an uncrackable encryption algorithm. WPA2 also allows for the use of TKIP during a transitional period called mixed mode security. This transitional mode means both TKIP and AES can be used to encrypt data. AES requires a faster processor, which means low-end devices like PDAs may only support TKIP. WPA Personal and WPA2 Personal use a passphrase to authentication WLAN clients. WPA Enterprise and WPA2 Enterprise authenticate WLAN users via a RADIUS server using the 802.1X/Extensible Authentication Protocol (EAP) standards.

Reference Sybex CEH official