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密码算法的非线性组件决定了整个算法的安全强度.通过混合不同群上的运算来构造非线性组件是设计密码算法时经常使用的手段.为了衡量F_(2~n)上的三元加法运算与F2上的三元加法运算的混合使用对密码算法安全性的影响,本文分析了三元模2~n加运算与模2加运算的相容程度,给出了在减差分意义下三元模2~n加与三元模2加整体逼近的噪声函数概率分布及其取值平方和的计算公式.结果显示减差分整体逼近的噪声函数的概率分布取值是均匀的,且整体逼近的相容概率为2~(1-n).
The non-linear component of the cryptographic algorithm determines the security strength of the whole algorithm.It is often used in the design of the cryptographic algorithm to construct the non-linear component by mixing the operations on different groups.In order to measure the ternary addition on F_ (2 ~ n) And F2 ternary addition on the security of the cryptographic algorithm, this paper analyzes the degree of compatibility of 2 ~ n additions and modulo-2 additions of ternary modules, and gives the ternary The calculation formulas of the probability distribution and the square sum of the noise functions of the modulo 2 ~ n plus ternary modulo 2 plus the whole approximation show that the probability distribution of the noise function approximated by the reduced difference is uniform and the whole approximation The probability of compatibility is 2 ~ (1-n).