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I have found a way to make "SafeRoot" root the galaxy S3 GT-I9300 on the latest android 4.3 jelly bean like any other devices.

Requirements :

• I9300_Root_Kernel file
• I9300_MK6_Kernel file
• Odin3
• Installed Samsung Kies or Samsung mobile USB driver
• Saferoot file

Instructions :

1. All the process WONT wipe your data, but back it up just incase this process corrupt your data.
2. Flash Root_Kernel.tar.md5 file by odin3 in PDA or AP section.
3. Make sure Re-Partition is NOT selected.
   
4. Root your device using SafeRoot method by following this guide : [No Warranty Void] Safe Root Android 4.3 for Galaxy S3/S4 Note 2
5. Flash back the current kernel of your firmware MK6 until Samsung update it by Odin3

Notes:

• Download and install manually busybox if the tool is failed to install it.
• Use this guide at your own risk
• This process and kernel files ONLY for the international version GT-I9300 and ONLY for Android 4.3 jelly bean.
• Normally this process will continue to work until Samsung starts to push Android 4.4 kitkat to the S3 (DONT use it on 4.4 kitkat, it will brick your device).
• You will not be able to receive OTA update, but you can update your device at any time by Kies or Odin3. 
• This process is tested by me and worked on all the latest Android 4.3 jelly bean firmwares.
• To unroot your device --> Open SuperSU app / Settings / Full UnRoot.

Downloads :

• Odin3 v3.04 HERE, v3.07 HERE, v3.09 HERE
• Latest Samsung Mobile Driver HERE
• Latest Samsung Kies HERE
• Latest Samsung Kies 3 HERE
• I9300_Root_Kernel HERE
• I9300_MK6_Kernel  HERE 
• I9300_NB1_Kernel HERE thanks to "afham"
• SafeRoot files HERE 

This rooting method is working for a wide range of Android device (not only Samsung), it can also root devices which are running Android 4.2

• Samsung galaxy device or other
• USB cable
• Windows or Mac PC
• Rooting tool

• Download and install USB driver of your device
• Download and unzip Saferoot tool
• Put your device in "USB debugging" mode (Settings > Developer options)
• Backup your data just in case of this process corrupt your data

• Open "run.bat" or "install.bat"
• Connect your device to PC via USB cable
• Accept when your device display "Allow USB debugging" message
• Follow the instructions 
• After finishing root process, go to play store and update SuperSU

YT video link : https://www.youtube.com/watch?v=GiZ7D2zjJdANotes :

• This tool can root more android devices and it is harmless if it fails to root your device.
• This process wont delete any data, but backup your important data just in case this process corrupt your files.
• Rooting by using this method will not change the binary or KNOX counter. 
• The status of the system will be changed to custom.
• If you would like to restore system status to official, flash stock Rom.
• I am not responsible for any damage to your device (use this AT YOUR OWN RISK).
• Credit goes to "k1mu" who modify root exploit to work on 4.3 with SELinux enforcing
• Xda thread

Tested and worked for :
- SCH-I545 Verizon Galaxy S4  ME7,MJ7,MK2
- SGH-I337 ATT Galaxy S4  MK2, MK6
- SGH-I337M Canadian Galaxy S4
- SGH-M919 T-Mobile Galaxy S4  MK2
- GT-I9505 LTE Galaxy S4  MH6, MKE, MKF, MJ5
- GT-I9500 3G Galaxy S4  MK1
- SPH-L720 Sprint Galaxy S4
- SCH-I435 Verizon Galaxy S4 Mini  MK5
- GT-I9192 Galaxy S4 Mini  MK4
- SPH-L520 Sprint Galaxy S4 Mini
- SCH-I535 Verizon Galaxy S3 - MK2, MJ3
- SGH-I747 AT&T Galaxy S3
- SGH-1747M Canadian/Bell Galaxy S3
- SGT-T999 AT&T Galaxy S3
- SGH-T999L T-Mobile Galaxy S3 4.3
- SGH-T999V Wind Galaxy S3 4.3
- GT-I9300 Galaxy S3  4.2 & 4.3
- SPH-L710 Sprint Galaxy S3
- SCH-R530C Cricket Galaxy S3
- SCH-R530U US Cellular Galaxy S3
- SCH-R530X Alltell Galaxy S3  MK4
- SCH-L710 CSpire Galaxy S3
- SCH-I605 Verizon Galaxy Note 2  4.3
- GT-N7100 Galaxy Note 2 MKA
- SGH-I317M Telus Galaxy Note 2
- GT-P5513 Galaxy Tab 2
- Razr HD 9.30.1
- Razr M 98.18.94,98.30.1
- Kindle Fire HD
- Verizon HTC One
- .....

Downloads :

• Latest Samsung Mobile Driver HERE
• Latest Samsung Kies HERE
• Latest Samsung Kies 3 HERE
• Saferoot.zip on xda thread or my rewritten script HERE