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.