The authentication failure wifi is very common on mobile devices, this error is because you are not connecting to wifi, you aveces the wifi is authenticating and never connects and is due to the same thing and the problem can happen for many reasons and for that reason we will explain below the reasons and solutions, since the solution depends on the problem due.
This error is very common in cell phones and Android tablets and also in the blackberry phones.
In some cases it is easy to solve the authentication error, in others it may be a bit more difficult, much it depends on the cause of the problem and the knowledge that you as a user have. Here I present the causes and solutions.
Sometimes you think and even you sure you're typing in the correct password, but not, in most cases can happen for that reason. To ensure what is your wifi password enter the settings of your modem or router for confirmation of this information and then try to connect again.
The network name is saved with incorrect credentials
When you connect or you try to connect to a Wi-Fi network, it remains stored on the phone, I recommend you try to delete the network that is saved and try to connect again, to delete the network from the list of wireless networks saved will ask the password again.
The security guy is not compatible with your mobile phone
Some phones have compatibility problems with some types of authentication, as is the WPA2-PSK. I recommend changing the type of authentication to your Wi-Fi to WPA-PSK as this is much more compatible devices.
The modem is inhibited
When this happens the connection is also on the other devices that are connected to that network, to solve the problem I recommend restarting the modem and if it persists reset.
You do not have Internet access
When you try to connect to a connection, some phones also check if there is an Internet connection, if there is not we often throws that error.
You can read this article if you continue with any problems with Wi-Fi, there I explain the most common problems with Wi-Fi and solutions. Also if you have any questions please leave it in the comments, I will try to help as much as possible. Luck.