See whether this helps..
-->>
http://xdaforums.com/showthread.php?t=2646904
Same info here:
http://xdaforums.com/showthread.php?t=2648538
(See second part below, for locked BL)
(strictly speaking, this is not "rooting" the stock rom, rather a means of having a rooted stock 4.3 rom, without unlocking the BL).
#I've managed to get it done... For this, I had to downgrade to 4.1.2 (
http://xdaforums.com/showpost.php?p=50356952&postcount=8), root 4.1.2 (
http://xdaforums.com/showthread.php?t=2405933), and install CWM (
http://xdaforums.com/showthread.php?t=2352920), then followed the instructions (to get root 4.3) in above links. Had to erase all data in the process.
*[backed up the TA partition while rooted at 4.1.2, just in case it might be needed later.. (
http://xdaforums.com/showthread.php?t=2292598)]
My phone model: c5303
#For backing up data WITHOUT root, I used the app "Backup & restore" which comes with stock rom (under 'Tools'). However, it didn't restore my game data properly. Alternatively, can try backup and restore with ADB (
http://stackoverflow.com/questions/19225467/backing-up-android-device-using-adb), but I couldn't try it's restore function yet, so not sure whether it works. If you've backed up the data while at 4.1.2 rooted (initially) with titanium backup, there's not much of a dilemma I suppose..
Dunno whether this provides any solution to your problem, but glad if this helps anyone. Just sharing my experience..