A peculiar higher order differential of CLEFIA

CLEFIA is a 128-bit block cipher proposed by Shirai et al. in 2007. In this paper, we focused on a higher order differential of CLEFIA. It has been reported that CLEFIA has 6-round saturation characteristics using 32-nd order differential. This paper introduces two new concepts for higher order differential (HOD) which are control transform for the input and observation transform for the output. With these concepts, we found a new 6-round HOD characteristic using 8-th order differential. By close examination of byte-value, we found the reason for this HOD. If we use the new HOD characteristic, instead of 32-nd order differential for the attack to 7-round CLEFIA, we can reduce to data and computational complexity around 2
^-23
, 2
^-15
of the conventional one, respectively.