You don't have to apply the CBC mode to complete files. If it is secure for a 1 MB file, I don't see why it would be insecure for 100 parts of a 100 MB file.
If you manage to merge small files into the same blocks, you even gain some privacy because the server can't even tell the number of files anymore.
[1] also has a discussion of the trade-offs of the different modes of operation for whole disk encryption. That seems related here because nobody wants to rewrite the whole disk after changing the first byte.
Comments
You don't have to apply the CBC mode to complete files. If it is secure for a 1 MB file, I don't see why it would be insecure for 100 parts of a 100 MB file.
If you manage to merge small files into the same blocks, you even gain some privacy because the server can't even tell the number of files anymore.
[1] also has a discussion of the trade-offs of the different modes of operation for whole disk encryption. That seems related here because nobody wants to rewrite the whole disk after changing the first byte.
1: https://en.wikipedia.org/wiki/Disk_encryption_theory
I understand now. that is a clever idea; I like it a lot.