Cryptology ePrint Archive: Report 2009/357

Impossible Differential Cryptanalysis of FOX

Zhongming Wu and Xuejia Lai and Bo Zhu and Yiyuan Luo

Abstract: 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.

Category / Keywords: secret-key cryptography / FOX, Lai-Massey Scheme, Impossible differential cryptanalysis, complexity.

Date: received 18 Jul 2009, last revised 21 Jul 2009

Contact author: patwu1985 at gmail com

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Version: 20090722:010624 (All versions of this report)

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