Let's say we have a message m of small size. I am looking for a system $S$ so that $S(m)$ is arbitrarily large, we can easily compute the inverse $I(S(m)) = m$, and any modification to $S(m)$ makes it impossible to recover any part of the initial message $m$.
Let's say my initial message is $m$ = "Hello world!" (12 characters long), and I want $S(m) = c$ to be larger (let's say, 1000 characters long, so 8000 bits). Let's say that $c'$ is the same as $c$, but with at least one error (one bit changed). I know $I(c) = m$. I want $I(c') \neq m$, so that it is impossible to obtain $m$ from $I(c')$.
Initially, I thought I could do this with some kind of symmetric private key encryption, with padding on the message and the "private" key public (anyone should be able to get $m$ from $c$; but no one should be able to get $m$ from $c'$). I tried AES in CBC mode, with padding to increase the original message's length, but it didn't do what I wanted. Introducing an error in $c$ would see this error propagate to the latter blocks, but not the preceding blocks, and so the original message $m$ was often still legible.
Is there a system that could achieve the specific behavior that I'm looking for?
Thanks in advance!