Security Analysis of the GF-NLFSR Structure and Four-Cell Block Cipher

The overall structure is one of the most important properties of block ciphers. At present, the most common structures include Feistel structure, SP structure, MISTY structure, L-M structure and Generalized Feistel structure. In [29], Choy et al. proposed a new structure called GF-NLFSR (Generalized Feistel-NonLinear Feedback Shift Register), and designed a new block cipher called Four-Cell which is based on the 4-cell GF-NLFSR. In this paper, we first study properties of the ncell GF-NLFSR structure, and prove that for an n-cell GF-NLFSR, there exists an (n +n− 2) rounds impossible differential. Then we present an impossible differential attack on the full 25-round Four-Cell using this kind of 18-round impossible differential distinguisher together with differential cryptanalysis technique. The data complexity of our attack is 2 and the time complexity is less than 2 encryptions. In addition, we expect the attack to be more efficient when the relations between different round subkeys can be exploited by taking the key schedule algorithm into consideration.