We all know the OTP is unbreakable and we all love the OTP (judging by the amount of question on this site).
The strength of the OTP is not that it is unable to find a word without the key but you can find any word. Now obviously if we could create a cipher which output would be only letters and several keys would output several grammatically correct sentences (or what ever output you would expect to be a valid output). But is such a thing possible?
I find it odd the OTP is the only one with this characteristic. If we would take AES with a 128 bit key and encrypt hello world" with AES-CBC and key "Acknowledgement" (nvm the IV)
9e 6c d3 86 33 aa fa 09 59 b1 75 86 85 e1 5a ea
why wouldn't there be keys in the 128 bit space which could decrypt this to valid plain texts other than hello world.
With my above example if there are multiple valid decryptions for the given ciphertext then it won't be every single possibility which would make it weaker than the OTP since an attacker could sort the valid plain text on relevance. But when the valid plain texts are many (just not all possibilities) the chances of an attacker finding the right one are negligible.
lets disregard OTP for a second.
Is it possible to create a cipher with the following requirements: For each N keys and X valid plaintexts there is a X/N chance of the decryption of the ciphertext resulting in a valid plaintext. Where 1 key can be used to encrypt multiple plaintexts where the key is smaller than the overall lenght of all plaintexts without posing a weakness. (similar to a block cipher) and X/N is sufficiently large for it to be impossible to determine what the correct plain text is.
Key K = "secret"
Plaintext p = "hello"
Plaintext p2 = "noway"
Ciphertext c = "aqfum"
RandomKey N = "wrong"
Encrypt(p, k) = c;
Decrypt(c, N) = "array"
Decrypt(c, N2) = "pozdi"
Decrypt(c, N3) = "bonus"
Encrypt(p2, k) = C2 = "almost"
Scheme(C2, C) != K
Has anything ever been tried or am I wrong in assuming that this is possible with reuse of the key?
With cipher I mean an algorithm in the sense of something similar to a block cipher.