一类非线性度较高的拉丁方阵

A Class of Latin Square with Higher Nonlinearity

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,as an important transformation, is widely used in some applications,including crypto-graphic algorithm design and combinational design. At present, less study is done on the methods to con-struct Latin squares with good cryptographic properties. By studying the construction method of vectorial bent function based on invertible square and with primitive polynomial, a method to construct Latin squares with high nonlinearity is proposed. Meanwhile these Latin squares are analyzed and the primary cryptographic properties tested,including nonlinearity and algebraic degree. The experiment results show that the Latin square is of good nonlinearity and high algebraic degree,and could be used to design cryptographic algorithm with many applications.