How does a changing key length affects the ciphertext, not only in case of AES,

Question

How does a changing key length affects the ciphertext, not only in case of AES, but in general? I know that the key spaces become much larger and the number of rounds in case of AES changes, but is security really that much enhanced that if I choose 256 bits as key length it is sort of unbreakable?

Something else what I'm thinking about currently, any idea if it is possible to get any details about key length or algorithm of an observed ciphertext? For example when measuring the entropy (or anything else) is there any difference e.g. between AES and DES?

Explanation / Answer

A longer key length means a greater search space for someone trying to brute force the key. There are 2128 times more 256-bit keys than 128-bit keys. So, all other things being equal, a brute force search for a 256-bit key could be impractical by a factor of billions in a case where a brute force search for a 128-bit key might be practical.

However, all other things are rarely equal. And they are unequal for AES. 256-bit AES has key schedule vulnerabilities that 128-bit AES does not have. As a result, many (including myself) believe that there is no reason to think 256-bit AES is any stronger than 128-bit AES.

I should also point out that AES uses the same block size regardless of key length. However, AES uses more rounds with larger keys. 10 for 128-bit keys, 14 for 256-bit keys. Generally, more rounds would be expected to make an algorithm stronger, and this is believed to be the case for AES.

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