How to tell if a encrypted (LUKS) device is already open

Your approach looks good. Some remarks though:

• If you want to encrypt rootfs, you'll need to use initrd (to have some minimal unencrypted system that will process the encrypted partitions).

  If the USB device is removable, both initrd and kernel can be stored on the USB to heighten tamper resistance (supposing you make sure the USB won't get into unauthorized hands) - which is usually why one encrypts rootfs. Once both kernel and initrd are on a removable media, you can ensure that nobody changes the kernel (or initrd) from the running system by simply removing the media.

  This is of course not an option if you want to have it inside of a server, but then again the question stands whether it makes sense to have such a device at all and not to use a small partition on one of the hard-drives. If for example all drives in the machine are in RAID, one would probably want to put rootfs on the USB as well. An interesting alternative to an internally connected USB flash device could be a CompactFlash card attached to ATA interface through an adapter, by the way.

  Some distributions offer prepared solutions for encrypted root, some don't - but mostly it's question of putting a couple of lines into initrd script before it tries to mount the "real" root (see for example man pages for pivot_root, usually in sections 2 (syscall) and 8 (bonary), if you're not familiar with the process).

• remember to backup the keys and passphrases in case your USB drive dies. LUKS follows rather one-sided approach when it comes to damaging its header - once a single sector of its header (key-slot to be more precise) dies, you are unable to mount it. This is to make sure that erasing the header isn't effectively thwarted by block reallocation performed by the device itself (because that's what flash-memory based devices do a lot) - the key is spread over the whole key slot and one needs all of the data to reconstruct it - there is no redundancy. See Clemens Fruwirth's website for deeper discussion.

  That said, maybe a simple encrypted device on the USB would be enough (check section PLAIN MODE in man cryptsetup). Or a file encrypted with e.g. openssl enc. The former might actually be an option even for the encrypted partitions themselves.

cryptsetup handles image files just as well as block devices, if that was your question. So if you make a dd image (which will be freaking huge) it will work. And if it didn't, you could just create the loop device yourself.

Best practice (if you want to keep the backup encrypted) is to encrypt the backup disk also, then open both containers, then run any backup solution of your choice as you would with unencrypted filesystems. It won't be the fastest method as it'd decrypt data from the source disk and then re-encrypt it for the backup disk. On the other hand it allows for incremental backup solutions, so it should still beat the dd-image-creation on average.

If you want to stick to dd, the only way to make something faster than dd would be a partimage of sorts which takes LUKS header and offset into account, so it would only store the encrypted data that is actually in use by the filesystem.

If the source disk is a SSD and you allow TRIM inside LUKS, and the SSD shows trimmed regions as zeroes, you get this behaviour for free with dd conv=sparse. It's still not something I'd recommend, though.