Is there a simple proof that shows AES is not a uniform permutation on any $n$-bit string? Since I'm just starting with crypto, I'd like to see a simple yet elegant proof for the said property. ...
The Rijndael S-Box design generates a permutation cycle of type $2+27+59+81+87$. What effect would replacing that permutation with a cycle of type $256$ have on the security of AES?