Creating backups of an encrypted drive

For a while now, I am running Linux (Fedora) – on a FDE volume – after having switched from Mac OS X. One thing that I enjoyed on Mac OS X was the automatic and seamless backup tool called Time Machine. I had set up a Time-Machine-capable AFP-share on my FreeNAS box that I would backup to and could get my data back if the need would arise. If the drive failed, I could just re-install Mac OS X from a DVD or USB stick and recover the backup from the NAS and I would have the same machine like before.

Since I am running Linux now, I was looking for a comparable solution where I can backup my drive to the NAS as some form of incremental backup of course. Ideally it would not just backup my home folder but create an image that I can flash to a new drive, if the old one breaks, so I can get my system back up running faster and retain all settings, applications, etc.

Now the challenge is how to do this since the drive is encrypted and the system running. My idea was to run a daily backup that would copy the parts of the image that changed as some sort of incremental image, when the system is shutting down (i.e. after locking the volume) at the end of the day. Yes, I know hourly backups would be better but I am thinking I can create those using different measures while the system is running. So far, I am mainly looking for a solution that would allow me to keep an up-to-date image for an easy reset in case of a drive failure.

Zbackup is a good solution for you. It's command line based but it will do incrementals and encrypted backups. It's not image backup in the disk image sense but it will do a full restore merging the most recent incrementals into one restore

But will it restore all files of my system, not just the home directory? And how is restoring going to work? Will I need to boot a live Linux and create an encrypted container on the "new" drive and then restore the data onto that?

Depends how you configure it. This is file level backup so you will most certainly need to format, encrypt then restore to encrypted disk to DR the system. Zbackup encrypts the individual files so that they can be stored on unencrypted mediums. You could also use Crashplan

I was looking more into something that can incrementally backup the encrypted volume, so I don't have to worry about encrypting the backups and have a quick and simple solution.

Well that depends on how you define simple. Zbackup is incredibly simple and you just put it in cron. It handles the encryption/decryption on the fly.