My experience with this error message is that it really depends on the received signal(s) and possibly having several network with the same SSID and the channel in use.
I have indeed 3 Wifi access points in my house. All are configured with the same password and encryption: WPA2 (AES). They also all have the same SSID and same channel. My purpose is to get a very good signal anywhere without having to take care of picking the best network myself (This is actually just a best practice).
But at some locations in my house, where I get either a poor signal or two signals of quite the same strength, I get the infamous "Authentication Error Occurred" message with my Galaxy SII (Android 4.1.2). I get this message whatever access point I am trying to connect from those locations (if several accessible).
First, it's important to notice that at the very same locations, my Sony Vaio laptop can connect without any issue. Reason why I also conclude it's an Android/S3 issue and not a router/access point issue. I can also at the very same time connect using my tablet with Android 4.0.4 (a Nabi 2).
Next, moving away from those locations (only a few meters), I can successfully connect quite immediately (I simply have to disable and re-enable the Wifi on my Galaxy SII). But in such cases, although I moved from only a few meters, I am now at a location where I get one signal much stronger than the others.
My access points are "DEVOLO DLAN 200 Wireless N". They only support WPA(TKIP) or WPA2(AES). So I tried to reconfigure them to use WPA(TKIP), as suggested here, but it didn't solve the issue.
I also tried to use shorter password (min is 8 chars) without success. But I admit I didn't try to connect using WPS (which is supported by my DEVELO).
I also tried to completely disabled the encryption for testing purpose, but as I am not mad I did enable the MAC filtering (which I don't use usually). In that mode, the connections succeed really more often, but not always. I still get from time to time the message mentioned above. And there is at least one location where I can never connect with my Galaxy SII although I can with my laptop: my bed
During my tests, I am monitoring the wireless signals using "Wifi Analyzer", to be sure that the signal keeps "stable". So, this is not presumed to be the issue either. And anyway, I do the same test simultaneously (I.e.: I enable the Wifi and wait for a connection) with my Galaxy SII Android 4.1.2 and my Nabi 2 Android 4.0.4. At some locations, only the Nabi 2 get the connection. But if I disable the Wifi, move from a few meters and re-enable it on both devices, then, I get the connection also on the Galaxy. When located on my bed, I can repeat the test 10 times with the very same outcomes.
Did I finally solve this issue... Maybe... I have switched from channel 6 to channel 13 on all my access points and I can now connect flawlessly from all the locations where I was experiencing issues. That being said, there are possibly some other locations where I will experience the problem. But for sure, changing the frequency has an impact on the reception!
As far as choosing the right channel is concerned, here in Europe, it's well known that frequency 2450 GHz is the one used by microwave ovens. So, those could possibly disturb the Wifi channel 9 and 10. But if your does, change it immediately ! Radiation that escapes from a microwave oven while it is in use may not exceed 5 mW (per cm2 at a distance of 5 cm). So, if your experience Wifi issues when using your oven, the leakage radiation is probably exceeding that limit. It happens as some of my colleagues have already experienced.
Next, I just discovered that frequency from 2400 to 2450 MHz (channel 1 to 8) are used by "ham radio" who are therefore maybe impacting the use of our Wifi (especially as they go up to 120 watts while Wifi is usually around ~18-30 mWatts). Check within your neighborhood if anyone has such a hobby. This could likely be the case if you experience issues only during certain period of the day (e.G.: the evening) or during the weekend.
Channels 1, 5, 9 and 13 are known to be used by some wireless transmitter and camera (at least here in Europe). As I don't have such device, and taking into account this info about the frequency used by "ham radio", I decided to use 9 or 13.
O.