What happens when you try?

 

Do you have the official Samsung 4.3 ROM? Since 4.3, Samsung installs KNOX, some security software embedded into the rom which you can't seem to remove and it prevents superuser access which means it stops you from rooting your phone. I had the same problem when I upgraded from 4.1.2 to 4.3. I don't remember how I got around it but I think I used ODIN and tried to flash the official 4.1.2 ROM back onto the phone using ODIN. In ODIN, check BOOTLOADER UPDATE and start flashing the rom. It may take several attempts.

 

Exactly. Flash 4.1.2 using ODIN. Root it again. Then flash the ROM you desire.

 

Wow wow wait. No offence man but a lot of people are bricking their phone trying to downgrade from samsung 4.3!

 

DO NOT do this. The problem is with the asserts, you are getting a status 7 error because 4.3 ROM's don't recognize the new bootloader. Following advice that involves "I don't remember..." and "I think..." can be a good way to gain a fancy new paperweight, especially when Knox is involved. And no, Knox does not stop rooting, the latest SuperSU .zip file is all that is needed, once custom recovery is installed, in order to gain root. From the OP, it sounds like gaining root is not the issue anyway, the issue is that the new MK3 bootloader is not listed in the old updater-script assert checks which are included on any custom AOSP ROM based on 4.3 prior to the official update.

To the thread author: this is a good example of why being much more specific in the OP would save a lot of trouble, instead of a vague "Please help" message. Specifics allow other users the chance to offer valid advice instead of playing Twenty Questions and risking harmful answers.

 

very well said, and to the OP, go to Android, Windows Phone, and Windows Mobile Development News, Information, and Howtos - XDA Developers , go to forums and go check out the Verizon Samsung S3 threads, there you will find everything you need.