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工程科学与技术:2013,45(6):1-7
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正形置换的一些新结论
(1.武汉数字工程研究所;2.武汉大学 计算机学院;3.武汉大学 空天信息安全与可信计算教育部重点实验室)
Some New Conclusions on Orthomorphisms
(1.Wuhan Digital Eng. Inst.;2.School of Computer,Wuhan Univ.;3.Key Lab. of Aerospace Info. Security and Trusted Computing of Ministry of Education,Wuhan Univ.)
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投稿时间:2013-06-15    修订日期:2013-09-18
中文摘要: 正形置换在对称密码的设计中占有重要的地位。为了对正形置换的构造计数和性质进行进一步的分析探讨,首先指出戴宗铎等关于线性正形置换结构的结论中存在的问题,并根据修改后的结论,得到了最大线性正形置换的结构形式,进而实现了最大线性正形置换的完全无重复构造,而原先的构造方法会产生重复的结果;通过分析正形置换的补置换和仿射正形置换的关系,得到了正形置换的个数为2的(n+1)次方的倍数,比原来为2的n次方的倍数的结论更进了一步;给出了一种代数免疫度的定义,证明了这样定义的代数免疫度是Carlet-Charpin-Zinoviev等价不变量,并得到非仿射正形置换与它的补置换的差分均匀度、非线性度、代数次数和代数免疫度均相等。
Abstract:Orthomorphism plays an important role in the design of symmetric cryptography. To analyze its construction, counting and properties further, a problem in a conclusion about linear orthomorphism was pointed out and corrected. Then, with the corrected conclusion, a non-redundant construction method to generate all maximal linear orthomorphisms was presented, while the previous method would produce repeatable results. The number of orthomorphism was proved to be a multiple of 2 to the power (n+1) based on the relationship between affine orthomorphism and complementary permutation. At last, a definition of algebraic immunity was proposed and proved to be CCZ-equivalence-invariant. The algebraic immunity of a non-affine orthomorphism was also proved to be equal to that of complementary permutation of this orthomorphism.Same is the case with some other cryptographic properties,such as difference uniformity, nonlinearity and algebraic degree.
文章编号:201300595     中图分类号:    文献标志码:
基金项目:国家自然科学基金资助项目(60673071;60970115;61003267;91018008;61003268);预研项目
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童言,张焕国,池志强,黄治华,张剑.正形置换的一些新结论[J].工程科学与技术,2013,45(6):1-7.
Tong Yan,Zhang Huanguo,Chi Huaqiang,Huang Zhihua,Zhang Jian.Some New Conclusions on Orthomorphisms[J].Advanced Engineering Sciences,2013,45(6):1-7.