Abstract: Focusing on the problem whether there are new security flaws of several kinds of high-level cryptographic S-boxes, an algorithm for solving the nonlinear invariant function of S-boxes was proposed, which is mainly based on the algebraic relationship between the input and output of the cryptographic S-boxes. Using the proposed algorithm, several kinds of S-boxes were tested and it was found that several of them had the same nonlinear invariant function. In addition, if these S-boxes were used to non-linear parts of the block cipher Midori-64, a new variant algorithm would be obtained. The security analysis was carried out by non-linear invariant attack. The analytical results show that the Midori-64 variant is faced with serious secure vulnerability. In other words, there exist 2⁶⁴ weak keys when nonlinear invariant attack is applied to the Midori-64 variant, meanwhile data, time and storage complexity can be neglected, consequently some high-level cryptographic S-boxes have security flaws.

Key words: S-box, nonlinear invariant function, Midori-64 algorithm, nonlinear invariant attack, weak key

摘要： 针对几类高强度密码S盒是否存在新的安全性漏洞问题，提出了一种求解S盒非线性不变函数的算法。该算法主要基于密码S盒输入和输出的代数关系来设计。利用该算法对这几类密码S盒进行测试，发现其中几类存在相同的非线性不变函数；此外，如果将这些S盒使用于分组密码Midori-64的非线性部件上，将会得到一个新的变体算法。利用非线性不变攻击对其进行安全性分析，结果表明：该Midori-64变体算法存在严重的安全漏洞，即在非线性不变攻击下，存在2⁶⁴个弱密钥，并且攻击所需的数据、时间及存储复杂度可忽略不计，因此这几类高强度密码S盒存在新的安全缺陷。

关键词: S盒, 非线性不变函数, Midori-64算法, 非线性不变攻击, 弱密钥