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Pre-share Key, or PSK, refers to a commonly used method with Wi-Fi Protected Access (WPA) security, which requires the owner of the network to come up with a "passphrase" that must then be given to anybody who wants to access the network. This passphrase could be a random string of characters or an actual understandable phrase, although random characters is highly recommended for security reasons.
This Pre-share Key (PSK) is saved by most operating systems that have WiFi support built-in so that the computer can automatically connect to the network after disconnection without needing to use the passphrase again.
The PSK must also be stored on the Wireless Access Point (WAP) or router hardware. Attacks against weak passphrases could be successful if the passphrase is not strong. To get around this problem, manufacturers often include their own software that generates a strong passphrase which can be shared to machines through an in-between medium (USB key for example). This can improve security as a program is not very likely to randomly generate a key that would be part of a dictionary used in a brute force attack.
More Information: Wi-Fi Protected Access (WPA)
WPA2 brought the the Advanced Encryption Standard (AES) block cipher to the standard, greatly increasing the security strength of wireless networks using the technology. As of 2008, WPA2 does not have any major security concerns associated with it. WPA's use of TKIP however has revealed some weaknesses. Martin Beck and Erik Tews, two graduate students in Germany, reported some weaknesses with TKIP that could be used to compromise some communications, but not to compromise the network's security fully.
WPA2's use of AES shields it from such vulnerabilities for the time being.
More information: Wi-Fi Protected Access (WPA)