filevaulthddtime-machine
My MacBook is running Mac OS X Mavericks with FileVault HDD encryption. I use Time Machine to backup this drive to an unencrypted USB HDD.
Will this backup be encrypted? Or does Time Machine decrypt files from my internal HDD and save them in an unencrypted form on the USB HDD?
No, the backups will not be encrypted automatically, but it's very easy to enable for directly attached disks. Just check "Encrypt Backup Disk" in the Time Machine disk selection settings.
If you're backing up to another Mac, you can use Disk Utility on that Mac to erase non-boot drives and put an encrypted partition on them:
No - OS X older than Lion cannot read or comprehend/mount/use a Core Storage volume such as used with FileVault 2.
Someone could reverse engineer the protocol and write drivers for older OS or different OS, but I haven't even seen a start towards that effort in any open source project.
Best Answer
No - Time Machine will not preserve the encryption of the source disk since it reads the files in an unencrypted manner just like any other process once you log in to the Mac.
You would need to ensure that all Time Machine destinations are also encrypted to properly secure your data both on the main computer as well as have it encrypted on the Time Machine volumes. This is as easy as ticking a checkbox on the Time Machine preference pane in system preferences.
On macOS 10.12 Time Machine will throw a helpful notification if you do in fact select an unencrypted destination for encrypted OS.