Finding optimal related-key differential characteristics for a given cipher is a problem that hardly scales. For the first time, we study this problem against the 25 instances of the block cipher Rijndael, which are the little brothers of the AES. To achieve this, we adapt and improve an existing approach for the AES which is based on Constraint Programming.
The attacks presented here overpass all the previous cryptanalytic results of Rijndael. Among all our results, we obtain a 12-round (out of 13 rounds) related-key differential attack for Rijndael with a block size equal to 128 bits and a key size equal to 224 bits. We also obtain an 11-round related-key differential characteristic distinguisher for Rijndael with a block size equal to 160 bits and a key size equal to 256 bits leading to an attack on 12 rounds (out of 14 rounds).