Improved Impossible Differential Attacks on Large-Block Rijndael

In this paper, we present more powerful 6-round impossible differentials for large-block Rijndael-224 and Rijndael-256 than the ones used by Zhang et al. in ISC 2008. Using those, we can improve the previous impossible differential cryptanalysis of both 9-round Rijndael-224 and Rijndael-256. The improvement can lead to 10-round attack on Rijndael-256 as well. With 2198.1 chosen plaintexts, an attack is demonstrated on 9-round Rijndael-224 with 2 195.2 encryptions and 2140.4 bytes memory. Increasing the data complexity to 2216 plaintexts, the time complexity can be reduced to 2130 encryptions and the memory requirements to 2 93.6 bytes. For 9-round Rijndael-256, we provide an attack requiring 2229.3 chosen plaintexts, 2194 encryptions, and 2 139.6 bytes memory. Alternatively, with 2245.3 plaintexts, an attack with a reduced time of 2127.1 encryptions and a memory complexity of 290.9 bytes can be mounted. With 2244.2 chosen plaintexts, we can attack 10-round Rijndael-256 with 2253.9 encryptions and 2186.8 bytes of memory.