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利用代数方法,对SQUARE攻击的数学基础进行了研究.指出SQUARE区分器存在当且仅当n比特输出平衡字节和n比特输入活跃字节之间的多项式函数的次数2n-2,并给出了平衡字节通过S盒后仍为平衡字节的充要条件.在寻找SQUARE区分器时,采用代数方法有可能分析更多轮输出的性质.文中还研究了SQUARE攻击对不同结构密码的有效性问题,指出当一个Feistel密码的轮函数具有低代数次数时,SQUARE攻击有可能会失效,即对Feistel密码实施SQUARE攻击时,S盒的性质对攻击将产生一定的影响;在对SPN密码实施SQUARE攻击时,非线性S盒的性质不会对攻击产生影响.文章的最后研究了SQUARE攻击与其他密码分析方法之间的联系,指出一个算法抗插值攻击的一个必要条件是算法能抵抗SQUARE攻击.
The algebraic method is used to study the mathematical basis of SQUARE attack.It is pointed out that the SQUARE differentiator has 2n-2 if and only if the n-bit output polynomial function between balanced bytes and n-bit input active bytes is given by The necessary and sufficient conditions for the balanced bytes to balance the bytes after passing through the S-box. When looking for the SQUARE discriminator, it is possible to analyze the properties of more rounds by using the algebraic method. The paper also studies the validity of the SQUARE attack on different structured codes It is pointed out that the SQUARE attack may fail when the round function of a Feistel password has a low algebraic number. That is, the nature of the S-box will have an impact on the attack when a SQUARE attack is performed on the Feistel password. When implementing the SPN password SQUARE attack, the nature of non-linear S-box will not affect the attack.Finally, the paper studies the connection between SQUARE attack and other cryptanalysis methods, and points out that a necessary condition for an algorithm to resist the interpolation is that the algorithm can resist the SQUARE attack .