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异或线性分支数是衡量分组密码扩散结构的扩散性能的一个重要指标,它对分组密码抵抗线性密码分析的能力有重要的影响.二元域上的非线性变换也常用作分组密码的扩散结构,本文给出了此类扩散结构的异或线性分支数的一个定义及其与分组密码抗线性逼近攻击能力的关系,证明了以模2n剩余类环上的线性变换为扩散结构的异或线性分支数等于将其奇系数换成1、偶系数换成0且将模2n加换成模2加所得的二元域上线性变换的异或线性分支数,从而将这类扩散结构的异或线性分支数归结为二元域上线性变换的异或线性分支数.
The number of XOR linear bifurcation is an important index to measure the diffusion performance of the block cipher diffusion structure and it has an important influence on the ability of block cipher to resist the linear cryptanalysis.The nonlinear transformation on the binary field is also used as the diffusion structure of the block cipher In this paper, we give a definition of XOR branch of such a diffusion structure and its relation to the ability of the block cipher against linear approximation attack, and prove that the XOR of the diffusion structure is linear or linear The number of branches equals the number of exclusive or linear branches of the linear transformation on the binary field obtained by changing its odd coefficient to 1, the even coefficient to 0 and the modulo 2n to the modulo 2 plus, so that the exclusive OR of such diffusion structures The number of linear braches is reduced to the number of exclusive OR linear bins of a linear transformation on a binary field.