Paper 2009/357

Impossible Differential Cryptanalysis of FOX

Zhongming Wu, Xuejia Lai, Bo Zhu, and Yiyuan Luo


Block ciphers are the very foundation of computer and information security. FOX, also known as IDEA NXT, is a family of block ciphers published in 2004 and is famous for its provable security to cryptanalysis. In this paper, we apply impossible differential cryptanalysis on FOX cipher. We find a 4-round impossible difference, by using which adversaries can attack 5, 6 and 7-round FOX64 with $2^{71}$, $2^{135}$ and $2^{199}$ one-round encryptions respectively. Compared to the previous best attack with $2^{109.4}$, $2^{173.4}$ and $2^{237.4}$ full-round encryptions to 5, 6 and 7-round FOX64, the method in this paper is the best attack to FOX cipher. This attack can also be applied to 5-round FOX128 with $2^{135}$ one-round encryptions.

Available format(s)
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
FOXLai-Massey SchemeImpossible differential cryptanalysiscomplexity.
Contact author(s)
patwu1985 @ gmail com
2009-07-22: revised
2009-07-21: received
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      author = {Zhongming Wu and Xuejia Lai and Bo Zhu and Yiyuan Luo},
      title = {Impossible Differential Cryptanalysis of FOX},
      howpublished = {Cryptology ePrint Archive, Paper 2009/357},
      year = {2009},
      note = {\url{}},
      url = {}
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