模2n数乘运算的向量Walsh谱1值点分布特性
doi: 10.3724/SP.J.1146.2012.01746
Walsh Distribution of Multiplied by Constant Operation on Modulo 2n
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摘要: 模2n数乘运算(y=cx mod 2n)是一个常用的密码算法编码环节，在许多密码算法中有广泛的应用，如Sosemanuk, RC6, MARS等。当常数c取奇数时，该运算环节是一个具有较好的混乱扩散性和良好实现效率的非线性置换。该运算可看作一个向量值布尔函数，目前没有公开文献对此环节的向量Walsh谱的循环谱值特性进行研究。该文对y=cx mod 2n(c是任意固定的奇数)的向量Walsh谱的循环谱值特性进行研究，证明了不存在模2n数乘运算的Walsh谱值为-1的输入输出组合，并给出了满足模2n数乘运算的循环Walsh谱值为1时的输入输出组合的结构和计数。Abstract: Multiplied by constant on modulo 2n operation(y=cx mod 2n), is widely used in the ciphers like Sosemanuk, RC6, MARS, and so on. This operation is recognized as a permutation with considerable diffusion, confusion and fine realization efficiency, where the constant c is odd. The operation can be viewed as a vector Boolean function, which vector Walsh spectrum character is not analyzed in published paper. In this paper, the property of the vector Walsh spectrum distribution of the operation is studied, the structure and counting formulas of input and output linear masks and the constant are given for the first time, where the Walsh spectrum of the operation is to be 1. It is proved that there is not input and output linear masks which Walsh spectrum is to be -1.
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