Attacking Seven Rounds of Rijndael under 192-bit and 256-bit Keys

The authors of Rijndael [3] describe the \Square attack" as the best known attack against the block cipher Rijndael. If the key size is 128 bit, the attack is faster than exhaustive search for up to six rounds. We extend the Square attack on Rijndael variants with larger keys of 192 bit and 256 bit. Our attacks exploit minor weaknesses of the Rijndael key schedule and are faster than exhaustive search for up to seven rounds of Rijndael.