improved integral attacks on rijndael

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. Based 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 Rijndael-256, all the other results are the best cryptanalytic results on Rijndael with large blocks so far.