I don't feel that the claim is even correct, that the size of the output is proportional to the largest size. I mean, assume that the largest size is 1024 bytes

I don't feel that the claim is even correct, that the size of the output is proportional to the largest size. I mean, assume that the largest size is 1024 bytes. Then take two files that are gigabyte each into 1024 byte chunks. Make a function that encrypts each chunk into the appropriate chunk in the second file. I don't think this is possible to do without being on the order of a gigabyte (the number of documents being encrypted). If it behaves like a one-time pad, where f(d1, k) = d2, and you can find a d' such that f(d', k) = d3, then it means that d' is likely to be gibberish and I don't understand what this is doing.