Multiple Impossible Differential Cryptanalysis On Reduced Fox

FOX is a family of block ciphers published in 2004 and is famous for its provable security to cryptanalysis. In this paper, we present multiple 4-round impossible differentials and several new results of impossible differential attacks on 5,6,7-round FOX64 and 5-round FOX128 with the multiple differentials and the new early abort technique which shall reduce the data complexity and the time complexity respectively. In terms of the data complexity and the time complexity, our results are better than any of the previously known attacks.