You download it on your phone not your PC. Its an app. Its not a Trojan, it uses an exploit (hack) to gain root. Just like all root exploits. Thousands of people use it to root their phones. It will root any phone with a kernel made before like June of this year. So if you haven't had an update since then it will work. Or just do it manually with Odin. Use Odin to install Twrp, use Twrp to install supersu, done. Follow the same instructions as all other s3's on this site. You can follow the one in the virgin mobile rooting for noobs. Just use the Twrp tar I linked earlier instead of philz. But same Odin and same SuperSU. Either method. Both are fine and easy.
here is the thread. Just skip down to where it says Root mk5. And don't use that philz file, use the Twrp one I linked before. Everything else is exactly the same. And don't worry about it says mk5, or about Knox, or it says 4.3. It works. Its how you root all s3's (except Verizon)