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Security of SM4 Against (Related-Key) Differential Cryptanalysis

机译：SM4对（相关密钥）差异密码分析的安全性

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In this paper, we study the security of SM4 block cipher against (related-key) differential cryptanalysis by making use of the Mixed Integer Linear Programming (MILP) method. SM4 is the first commercial block cipher standard of China, which attracts lots of attentions in cryptography. To analyze the security of SM4 against differential attack, we exploit a highly automatic MILP method to determine the minimum number of active S-boxes for consecutive rounds of SM4. We try to dig out the underlying relationships in different rounds, and convert them to the constraints trickily to extend the MILP model, in order to cut off the invalid differential modes as many as possible. We obtain tighter lower bounds on the number of active S-boxes by solving the extended MILP model with optimizer Gurobi. Moreover, we consider the security of SM4 against related-key differential analysis. We construct the extended MILP model by adding more helpful constraints, and get the lower bounds on the number of active S-boxes, which proves the intuition of stronger differential security of SM4 in the related-key setting. Our results shows that there exists no differential characteristic with probability larger than 2~(-128) for 23 rounds of SM4 in the single-key setting and 19 rounds in the related-key setting.
机译：在本文中，我们使用混合整数线性规划（MILP）方法研究了SM4分组密码针对（相关密钥）差分密码分析的安全性。 SM4是中国第一个商业分组密码标准，在密码学领域引起了很多关注。为了分析SM4抵御差异攻击的安全性，我们利用一种高度自动化的MILP方法来确定SM4连续回合的活动S盒的最小数量。我们尝试在不同的回合中挖掘出潜在的关系，并将它们巧妙地转换为约束，以扩展MILP模型，以便尽可能多地消除无效的差分模式。通过使用优化程序Gurobi解决扩展的MILP模型，我们获得了更有效的S盒数量的下限。此外，我们考虑了SM4对相关键差异分析的安全性。我们通过添加更多有用的约束来构造扩展的MILP模型，并获得活动S-box数量的下限，这证明了在相关密钥设置中SM4的差分安全性更强的直觉。我们的结果表明，对于单键设置中的SM4 23轮和相关键设置中的19轮，不存在概率大于2〜（-128）的差分特征。

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