多输出旋转对称函数的密码学性质

Cryptological properties of multi-output rotation symmetric functions

提出了多输出旋转对称函数的概念。首先给出了多输出旋转对称函数的广义一阶Walsh线性谱特征和广义自相关函数特征;然后通过构造关联矩阵,利用多输出旋转对称函数的广义一阶Walsh循环谱,给出了多输出旋转对称函数满足平衡性、相关免疫性等密码学性质的充分必要条件,特别利用矩阵的取值特点,给出了函数满足一阶相关免疫性的等价判别条件;最后讨论了奇数变元多输出旋转对称函数广义一阶Walsh循环谱的性质,并给出了一种通过计算一部分循环谱值来寻找奇数变元多输出Plateaued旋转对称函数的方法,相对于算出全部的循环谱值减少了约1/2的计算量,提高了效率。

The notion of multi-output rotation symmetric functions was introduced.Firstly, the properties of generalized Walsh spectrum and the generalized autocorrelation functions were presented.Then by constructing matrixes, some necessary and sufficient conditions were given for this class of functions to satisfying cryptological properties of balancedness, correlation immunity and so on.Especially, it presented a necessary and sufficient condition to fulfilling 1st order correlation immunity.At last, when n was odd number, the matrixes of n variables multi-output Plateaued rotation symmetric functions had special properties, so a method was introduced to find the odd number variables multi-output Plateated rotation symmetric functions.And this method only need calculate part of the generalized Walsh cycle spectrum, and the calculation could be reduced by almost half of the amount.