Integral Cryptanalysis of Reduced Round FOX64

FOX family block ciphers are based on Lai-Massey scheme. Firstly, the evaluation is performed on the ability of the reduced round FOX64 to resist zero-correlation linear cryptanalysis, and some 4-round zero- correlation linear distinguishers are presented. Then, by using the relation between the integral distinguishers and zero-correlation distinguishers, the 4-round integral distinguishers of FOX64 are found. Finally, the 4-round integral distinguishers are used to attack 5, 6, 7 and 8 rounds FOX64 with the time complexity of 252.7, 2116.7, 2180.7 and 2244.7 encryptions respectively, and the data complexity is 250 chosen plaintexts. This is the first paper pointing out that 8-round FOX64/256 is vulnerable against the statistical attack.