Improved Integral Attacks on Rijndael with Large Blocks

In this paper, we present some improved integral attacks on Rijndael whose block sizes are larger than 128 bits. We will introduce some 4-round distinguishers for Rijndael with large blocks proposed by Marine Minier (AFRICACRYPT 2009), and propose a new 4th-order 4-round distinguisher for Rijndael-192. Basing on these distinguishers, together with the partial sum technique proposed by Niels Ferguson (FSE 2000), we can apply integral attacks up to 8-round Rijndael-160, 9-round Rijndael-192, and 9-round Rijndael-224. Compared to the square attack proposed by Samuel Galice (AFRICACRYPT 2008), we give different attacks on Rijndael-256 to 8 and 9 rounds. Except the attack on Rijndael256, all the other results are the best cryptanalytic results on Rijndael with large blocks so far.