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拉丁方变换是一类非常重要的变换,在密码算法设计、组合设计等领域具有广泛的应用,目前对密码性质好的拉丁方阵的构造方法研究较少。通过研究基于可逆方阵的多输出Bent函数的构造方法,提出了一种利用本原多项式来构造非线性度高的拉丁方阵的算法,并对这类拉丁方阵的密码性质进行了分析和测试,结果表明这类拉丁方阵具有较高的非线性度和较高的代数次数,能够用于实际应用中密码算法的设计。
Latin Square Transformation is a very important transformation. It has a wide range of applications in the field of cryptographic algorithm design and combined design. At present, there are few researches on the construction method of Latin Square with good cryptographic properties. By studying the construction method of multi-output Bent function based on reversible matrix, a new method of constructing Latin square with high non-linearity by using primitive polynomial is proposed and the cryptographic properties of Latin square matrix are analyzed. The results show that this type of Latin square has high nonlinearity and high algebraic frequency, which can be used in the design of cryptographic algorithms in practice.