Impossible differential attacks on FOX

Some 4-round impossible differentials were found by means of meet-in-the-middle. By using impossible differential cryptanalysis methods and time-memory balanced technique, the results of previous attacks on FOX cipher were improved. The experiment results show that For FOX64, 5-round attack needs 239 chosen plaintexts and 268 encryptions, 6-round attack needs 256 chosen plaintexts and 2133 encryptions, 7-round needs 256 and 2213. For FOX128, 5-round attack needs 272 chosen plaintexts and 2134 encryptions. Therefore, 7-round FOX64/256 and 5-round FOX128/192/256 are not immune to impossible differential attack.