Impossible Differential Cryptanalysis of the FBC Block Cipher

The FBC block cipher is an award-winning algorithm of the recent Cryptographic Algorithm Design Competition in China. It employs a generalised Feistel structure and has three versions FBC128-128, FBC128-256 and FBC256, which have a 128-bit block size with a 128- or 256-bit user key and a 256-bit block size with a 256-bit user key, respectively. The best previously published cryptanalysis results on FBC are Zhang et al.’s impossible differential attack on 13-round FBC128-128 and Ren et al.’s boomerang attack on 13-round FBC128-256. In this paper, we observe that when conducting impossible differential cryptanalysis of FBC, both inactive and active nibble differences on plaintext and ciphertext as well as a few intermediate states may be exploited for some refined sorting conditions on plaintexts and ciphertexts to filter out preliminary satisfying plaintext/ciphertext pairs efficiently. Taking advantage of this observation, we use Zhang et al.’s 9-round impossible differentials of FBC128 to make key-recovery attacks on 14-round FBC128-128 and 15-round FBC128-256, and similarly we exploit 13-round impossible differentials on FBC256 and make a key-recovery attack on 19-round FBC256. Our results are better than any previously published cryptanalytic results on FBC in terms of the numbers of attacked rounds.