How to root Samsung Galaxy S2 GT-I9100 on Jelly Bean Android 4.1.2

This method, according to my research, is the safest and easiest method to root your Galaxy S2 running stock Android 4.1.2 Jelly Bean.

Step 1:
Download the following files.

• recovery-clockwork-touch-5.8.1.5-galaxys2.zip
• CWM-SuperSU-v0.97

Step 2

• Put recovery-clockwork-touch-5.8.1.5-galaxys2.zip in the external_sd of your device.
• Put CWM-SuperSU-v0.97 in the sdcard (inbuilt) of your device.
• Power off your phone.

Step 3

• Boot into Recovery Mode by holding Volume Up+Home Button+Power Button till you see the Android dude and then the list of options.
• Now using the Volume Down button scroll down to 'apply update from external storage'  and then press the Power button to select that option.
• Select recovery-clockwork-touch-5.8.1.5-galaxys2.zip and let it finish installing.
• Wait for CWM Recovery to appear. From here on you will be able to use the touch screen so don't press the volume keys to scroll.
• Select 'install zip from sdcard' and look for CWM-SuperSU-v0.97 on your sdcard and install it.
• Reboot phone.
• Congratulations, your phone is now rooted!!

Step 4 (Additional steps to ensure smooth running after rooting)

• Open Google Play Store.
• Find BusyBox (free) and install it. Open the app and install BusyBox.
• All Done!