I have a Verizon Galaxy S 3. I also have a corporate policy that forces encryption of devices. This is a big problem when I want to try a new rom on my phone. If the partition “/data” cannot be mounted and overwritten, as it cannot be with an encrypted file system, you cannot overwrite that partition and run a custom ROM. Which is the whole reason I choose Android.
The TL;DR version
You have to ODIN on a Full ROM, such as VRALHD, that will overwrite the entire file system. Create a backup and pull your SIM first. Flashing from Recovery from your SD card won’t work because the /data partition needs to be totally annihilated.
Follow the detailed directions at this link to get the USB drivers installed and the phone Rooted, and a Rooted VRALHD rom installed:
USE ODIN. If you use Odin rather than flashing from an image on your external SD, the device will be re-partitioned and the encryption will be wiped out. Otherwise, the encryption will stay.
1. After following those directions, you should be rooted with a ClockWorkMod recovery installed on a stock-like ICS rooted ROM.
2. Next, unlock the bootloader. You can’t flash any rom with the stock verizon bootloader. That would result in the infamous “System Software not authorized by Verizon Wireless” error. Go to the Google Play store and download EZ-Unlock.
3. Install AirDroid, and use that to copy the rom of your choice to your external SD Card.
4. Next, install a better recovery controller. ClockWorkMod 18.104.22.168 is better than CWM Touch 5.8. Go to the Google Play Store and download EZ-Recovery. Make sure to select CWM 6 instead of the the CWM Touch version. Reboot into recovery.
5. Flash with any rom you choose. I use Cyanogen Mod 10. You can even go back to Stock at this point if you like.