Firstly, 2013 version isn't the issue here, but I'll respond any way...
I was also using KIS 2013 with Windows 8.1 (Upgraded* to 8.1 with KIS 2013 still installed). Then I was getting BSOD which I read may have been KIS 2013 being incompatible with 8.1, so I upgraded to 2014 version (Turns out cause was another program).
As posted above KIS 2014 was causing slow browsing (hence my post here), and you CAN'T install 2013 back on Windows 8.1 (Incompatible, does not allow installation - even if you change compatibility mode).
So yeah.. not that hard to understand. I've moved on and doubt I'll be touching Kaspersky any time soon.
*More of an "upgrade" than "update", seeing how you can't use system restore to go back.