Question

I need to encrypt a plaintext message, using a 256-bit secret key.

The ciphertext may be of any length (not equal to the plaintext length)

Is there an encryption method that can give me extra security when I allow the ciphertext to be longer?

For example: Encoding a 256-bit plaintext into a 8192-bits ciphertext would be more secure than encoding it into a 256-bit ciphertext.

Answer 1

Theoretically speaking, there’s no way to get any extra advantage from encrypting the plaintext into a longer ciphertext. If I naively try to break your encryption by trying all possible decryption keys, then the length of the ciphertext doesn’t matter since I’m still doing a brute-force search over the same key space. In practice, this might help because it would slow down my attempts to reverse your encryption, but you gain no extra security by having the longer ciphertext.

The reason for this is that the difficulty of breaking a cipher (without attacking the cipher itself) rests in trying to explore the entire space of keys to decrypt. If your ciphertext is longer but is still decryptable using a 256-bit key, then the space I have to search isn’t any bigger than what I started with.

Now, if you make the ciphertext longer by somehow introducing a larger key space (for example, by picking four random keys and encrypting different pieces of the message with each key), then you would indeed gain extra security because the space of keys I have to search when trying to decrypt the message is now substantially larger.