Why is it that most messages seem to be expanded?

Question

Whenever I have seen a more secure version of a message, the message seems to be expanded by some factor. One example is RSA encryption, but whenever a message does not appear to be expanded it is very easy to crack. Such as the Caesar Shift Cipher, or a Substitution Cipher, or even the Vingere Cipher. Is there a reason that expanded messages are much more difficult to crack?

Answer 1

Is there a reason that expanded messages are much more difficult to crack?

When looking purely at encryption, message expansion does not really tell you anything about the difficulty to crack it.

Message expansion is often a feature of asymmetric cryptosystems. Those are not inherently more difficult to crack than symmetric systems. Block ciphers also expand the length slightly in some modes, but other equally secure modes do not expand the message length.

Weak classical ciphers often act on single symbols, so they will not expand the message, but e.g. stream ciphers can likewise act on single symbols and remain secure.

However, there are a couple of caveats:

• Semantically secure encryption requires some kind of an IV if you reuse the key for multiple messages. This can expand the message if it is added as part of the ciphertext, but it does not need to be - many protocols handle the IV implicitly.

• Authenticated encryption must expand the ciphertext at least somewhat. And authentication is usually necessary to prevent attacks that would be possible even with otherwise secure encryption. So in that sense message expansion is often necessary.