Is a one-time pad still breakable on a depth of 2+ if the plaintext is completely random?
I'm assuming this idea is wrong, mostly because it occurred to me, but let me walk you through my logic so you can concisely correct me:
- A one-time pad is unbreakable on a depth of 1 because a comprehensive brute-force attack will yield numerous reasonable plaintexts.
- Upon a depth of 2 or more (e.g., the same pad used with multiple
plaintext messages) it becomes breakable:
- Brute-forcing message $A$ may result in (say) 10 plaintexts
- Brute-forcing message $B_n$ may result in 10 plaintexts each
- The key that commonly results in valid plaintexts is probably the one-time pad used.
- If the plaintext is completely random, then this attack won't work, as there is no way to discriminate between "plaintext output" and incorrect outputs.
I was thinking of ways to pass encryption keys and IVs - which, if properly generated, should be very random data - between two systems. Let's presume they have a trusted channel by which they can exchange the one-time pad, but wish to use an untrusted channel for exchanging more voluminous data. They can use symmetric encryption to protect data across the untrusted channel if they have away to agree upon the keys used for the symmetric encryption. If a one-time pad could be used to securely exchange symmetric keys across that untrusted channel, then the sparse use of the trusted channel (exchanging the one-time password) could enable encryption across the untrusted channel.
Would this, instead of a one-time pad, be a shared secret? A key derivation function?
Some "please don't beat me up" caveats:
Yes, I realize this sounds like I'm breaking the "never invent a new cryptosystem" rule, and I realize the importance of that rule. Rather, I'm using this as a gedankenexperiment to understand encryption better, and/or as a way of identifying an existing model that describes what I'm suggesting.
Yes, I realize SSL is the appropriate model for what I'm suggesting - the certificate exchange and handshaking is the "trusted channel", enabling symmetric encryption of the general data over the "untrusted channel". I have reason to contemplate lighter-weight solutions.
I humbly appreciate any edification you can give me.