Remote incremental backups for the paranoid?

I have some servers which I'd like to backup to remote (i.e., off-site) locations. Since I'd like to perform backups no less than daily, I need these to be incremental.

Now for the hard part: I'm paranoid. As FreeBSD Security Officer, it's my job to be paranoid -- so I'd like to ensure that even if someone gains total control of the remote system which I'm using to store the backups, they will not be able to
* See the contents of the files I'm backing up,
* See the names of the files I'm backing up,
* Work out how large the files are that I'm backing up, or
* Know which regions of a file have changed between incremental backups.

Put another way, aside from knowing how much I'm backing up (which is unavoidable unless I waste bandwidth and disk space) and how much that material is changing (unavoidable unless I waste bandwidth during incremental backups), I don't want the 0wner of the backup server to be able to figure out anything about what I have on my servers.

Any suggestions? Even if my complete security requirements can't be met, I'd be interested to hear about any software which comes close.

 

 

 

 

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