i use an offsite backup service

THe ones I've seen and used at default settings encrypt and upload content using the company's encryption key, but you can set your own encryption key which would render your files unreadable to anyone without it.

Carbonite i've tried and found to be really slow.

Also one thing to keep in mind, is that most of these services do not allow you to back up external drives, and if they do if the device hasn't been connected for 30 days the files would expire and be erased