模2n 加和模2加混合运算的异或分支数

研究了扩散结构为二元域上非线性变换的异或分支数.给出了扩散结构为二元域上非线性变换的异或分支数的定义及其与分组密码抗差分攻击和线性分析能力的关系,证明了以模2n加和模2加的混合运算为扩散结构的异或分支数等于将模2n加换成模2加且将各变元系数模2后所得的二元域上线性变换的异或分支数,从而简化了此类非线性扩散结构异或分支数的计算问题.

On the XOR Branch Numbers of the Transformations About Modulo 2n Addition andModulo 2 Addition

This paper studies the xor branch numbers of diffusion structures, which uses the nonlinear transformations over the finite field GF(2). This paper gives the definition of the xor branch numbers of diffusion structures and the relations between it and the strength of a cipher against differential and linear cryptanalysis. Also, this paper has proven that the xor branch numbers of diffusion structures is about modulo 2ⁿ addition, and the modulo 2 addition is equal to that of the diffusion structure over the finite field GF(2), which 1 is substituted for the odd coefficient and 0 for the even coefficient and the modulo 2ⁿ addition for the modulo 2 addition. Consequently, this paper simplifies the computation problem of the xor branch numbers in this kind of nonlinear diffusion structure.