A New Higher Order Differential of FeW

FeW is a 64-bit block cipher proposed by Kumar et.al in 2014. It supports 80-,and 128-bit secret keys. The designer evaluated its security against typical attack, such as differential cryptanalysis, linear cryptanalysis, and so on. On the other hand, it has not been reported the security of FeW against higher order differential attack, which is one of the algebraic attacks. In this paper, we focused on a higher order differential of FeW. By computer experiment, we found a new 6-round saturation characteristic of FeW using 28-th order differential. Introducing two concepts for higher order differential which are control transform for the input and observation transform for the output, we also show a new 9-round saturation characteristic using 60-th order differential which is a 3-round extension of the 6-round one, and estimates the costs of attack exploiting the characteristic. As a result, we show that the 12-round FeW can be attacked with 2^62.3 blocks of chosen plaintext and times of data encryption. The 14-round FeW can be attacked with 2^63.2 blocks of chosen plaintext and 2^123.3 times of data encryption.