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The question is pretty clear. I’m wondering if it uses a hashing algorithm, or it is simply an encryption. If it is a hash, then what algorithm is used (md5, sha1, etc)? Also, does the router compare the password in plain text for validation or a hash?
In WPA-PSK, the WPA passphrase and SSID are used to derive the 256 AES key used to encrypt the wireless traffic. The key derivation function is PBKDF2, defined in RFC 2898. If the passphrase for the SSID is correct the encryption will work so that the client can successfully communicate with the AP. Otherwise, the communication will fail. That’s how the AP knows the passphrase is correct (the traffic isn’t gibberish).