I know there are three method for wifi security. What are the relative strengths of the password encryption in WEP, WPA and WPA2 PSK?
The schemes you mention are protocols for securing 802.11x traffic over wireless networks. They don't mandate how the AP password is encrypted or hashed during storage. However, the security of the protocol does rely on making the key secure.
- WEP relies on a broken RC4 implementation and has severe flaws in various aspects of its protocol which make breaking WEP near-trivial. Anyone with a laptop and a $20 wifi antenna can send special de-auth packets, which cause legitimate clients to re-authenticate to the AP. The attacker can then capture the initialization vectors from these re-authentication packets and use them to crack the WEP key in minutes. Due to the severity of the break, WEP is now considered deprecated. See this question for more details on WEP security.
- WPA improves upon this, by combining RC4 with TKIP, which helps defend against the IV-based attacks found in WEP. It also improves upon the old handshake mechanism, to make it more resistant to de-auth attacks. Whilst this makes a large improvement, vulnerabilities were found in the way that the protocol worked, allowing an attacker to break TKIP keys in about 15-20 minutes. You can read more about the attack at this other question.
- WPA2 closes holes in WPA, and introduces an enhanced version of TKIP, as well as CCMP. The standard also bring support for AES, which provides even further security benefits. At current there are no known generic attacks against WPA2.
Updated answer: Now even WPA2 is broken
The KRACK Attack can breaks WPA2 WiFi protocol.
Router, access point, WiFi client need to be patched.
Old answer here:
The short answer is that WPA2 is the only secure protocol.
But it's secure only if WPS (WiFi Protected Setup) on the access point is disabled.
WPS is broken, an access point with WPS enabled is crackable, no matter what kind of WiFi protocol it uses.
For more info: How to crack a WPS enabled WiFi network
Sadly, WPS is enabled by default on the majority of WiFi Router and Access Point...
The first thing I do on any router I put my hand on, is disabling WPS.