CAJ | 학술논문

模2n 数乘运算(y=c×x 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 Wal sh 谱的循环谱值特性进行研究。该文对y=c×x 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Wal sh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Wal sh谱值为1时的输入输出组合的结构和计数。
모2n 수승운산(y=c×x mod 2n)시일개상용적밀마산법편마배절，재허다밀마산법중유엄범적응용，여Sosemanuk, RC6, MARS등。당상수c취기수시，해운산배절시일개구유교호적혼란확산성화량호실현효솔적비선성치환。해운산가간작일개향량치포이함수，목전몰유공개문헌대차배절적향량 Wal sh 보적순배보치특성진행연구。해문대y=c×x mod 2n(c시임의고정적기수)적향량Walsh보적순배보치특성진행연구，증명료불존재모2n수승운산적Wal sh보치위-1적수입수출조합，병급출료만족모2n수승운산적순배Wal sh보치위1시적수입수출조합적결구화계수。
Multiplied by constant on modulo 2n operation(y=c×x 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 Wal sh 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.