| 摘要: |
| 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,从而简此类非线性扩散结构异或分支数的计算问题. |
| 关键词: 分组密码 非线性扩散结构 异或分支数 混合运算 可证明安全性 |
| DOI：10.3724/SP.J.1001.2011.03837 |
| 分类号: |
| 基金项目:河南省杰出青年科学基金(0312001800) |
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| On the XOR Branch Numbers of the Transformations About Modulo 2n Addition andModulo 2 Addition |
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CHANG Ya-Qin, JIN Chen-Hui
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College of Electronic Technology, PLA Information Engineering University, Zhengzhou 450004, China
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| Abstract: |
| 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. |
| Key words: block cipher nonlinear diffusion structure xor branch number mixed operator provable security |
