有限域上低差分函数的构造与分析

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1、分类号O29学号14020002UDC密级公开理学硕士学位论文有限域上低差分函数的构造与分析硕士生姓名邓雅芝学科专业数学研究方向编码密码理论及其应用指导教师屈龙江教授国防科学技术大学研究生院二〇一六年十二月ConstructionandanalysisoffunctionswithlowdifferentialuniformityoverfinitefieldsCandidate:DengYazhiAdvisor:ProfessorQuLongjiangAdissertationSubmittedinpartialfulfillmentof

2、therequirementsforthedegreeofMasterofScienceinMathematicsGraduateSchoolofNationalUniversityofDefenseTechnologyChangsha,Hunan,P.R.ChinaDecember8,2016国防科学技术大学研究生院硕士学位论文目录摘要.......................................................................................................

3、.................iABSTRACT...............................................................................................................iii第一章绪论............................................................................................................11.1研究背景............

4、.......................................................................................11.2国内外相关问题的研究现状...................................................................31.2.1偶特征域上低差分函数的研究现状............................................31.2.2奇特征域上低差分函数的研究现状.................

5、...........................41.3论文的组织与安排...................................................................................6第二章基本概念....................................................................................................72.1布尔函数和向量值函数.............................

6、..............................................72.2密码函数的安全性指标...........................................................................82.2.1平衡性............................................................................................82.2.2代数次数...........................

7、.............................................................82.2.3差分均匀度....................................................................................92.2.4非线性度........................................................................................92.2.5EA等价和CCZ等价...

8、.................................................................102.3一些有用的引理和结论.........