Higher Order Differential Attacks on Reduced-Round MISTY1

MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it has been recommended for Japanese e-Government ciphers by the CRYPTREC project. This paper shows that higher order differential attacks can be successful against 6-round and 7-round versions of MISTY1 with FL functions. The attack on 6-round MISTY1 can recover a partial subkey with a data complexity of 253.7 and a computational complexity of 253.7, which is the smallest computational complexity for an attack on 6-round MISTY1. The attack on 7-round MISTY1 can recover a partial subkey with a data complexity of 254.1 and a computational complexity of 2120.7, which signifies the first successful attack on 7-round MISTY1 without limiting conditions such as a weak key.