Improved Results of Impossible Differential Cryptanalysis on Reduced FOX.

FOX is a family of block ciphers published in 2004 and several attacks on reduced FOX have been published, and the best known attacks are on 7-round FOX64 and 5-round FOX128. In this paper, we present impossible differential attacks on 8-round FOX64 and 6-round FOX128 with various techniques such as the multiple differentials, the state-test technique, the quick sort method and the early abort technique. For 8-round FOX64, the data complexity and the time complexity is 2(42) and 2(239.54) one-round encryptions, respectively, and the memory required is 2(44) bytes. For 6-round FOX128, the data complexity and the time complexity is 2(75) and 2(209.55) one-round encryptions, respectively, and the memory required is 2(77) bytes.