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 242 and 2239.54 one-round encryptions, respectively, and the memory required is 244 bytes. For 6-round FOX128, the data complexity and the time complexity is 275 and 2209.55 one-round encryptions, respectively, and the memory required is 277 bytes.

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