Several services provide file backup over the Internet. Two of them avoid copying entire files with only small changes. I will call this fractional backup. Several claim to transmit only ciphered versions outside your machine. I think that none provide ciphered fractional backup. Here is a scheme to do just that.

Here are some backup services.

To back up a file at a remote site in encrypted form and also avoid re-transmission the whole file when large portions remain the same, we may use an algorithm such as the following.

We call the site with the plain text of the file P, and the site that keeps the ciphered version C. At P we create a tree version of the file. This is much smaller than the file but requires reading the entire file except to the extent that the file system can reliably report changes.

C stores the tree of secure hashes and the ciphered leaves. It can coordinate a tree walk with P to find changed leaves. The cipher text of those leaves can then be sent to C.

It may be risky to store even hashes of the cipher text at C as this could aid in guessing the text. Computing those hashes with a custom initial vector alleviates this problem. C need not know that IV.