FOX are a family of block ciphers presented recently

which are based upon some results on proven security and have high performances on various platforms.In this paper

we construct some distinguishers between 3-round FOX and a random permutation of the blocks space.By using collision-searching techniques and integral attack

the distinguishers are used to attack on 4

5

6 and 7 rounds of FOX64.The four subkeys of 4-round FOX64 can be recovered with 2

9

chosen plaintexts and 2

45.4

encryptions.The five subkeys of 5-round FOX64 can be recovered with 2

9

chosen plaintexts and 2

109.4

encryptions.The six subkeys of 6-round FOX64 can be recovered with 2

9

chosen plaintexts and 2

173.4

encryptions.The seven subkeys of 7-round FOX64 can be recovered with 2

9

chosen plaintexts and 2

237.4

encryptions.Therefore

4-round FOX64/64

5-round FOX64/128

6-round FOX64/192 and 7-round FOX64/256 are not immune to Collision-Integral attack.