# Replacing the Rijndael S-Box?

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?

-
I assume your question has an implicit "holding other cryptographic properties constant", since an sbox of [1,2,...,255,0] has cycle type 256, but would make a fairly poor sbox. You may want to make this explicit. – Jack Lloyd Jul 13 '11 at 18:07