置换多项式及其应用PDF电子书下载

一 剩余类环的置换多项式 1

1．从完全剩余系谈起 3

2．置换多项式的判别与构造 10

3．迪克逊多项式 14

4．置换谱 21

二 置焕多项式的应用举例 29

1．密码系统简介 31

2．迪克逊多项式与RSA系统 34

3．置换有理函数与RSA系统 38

4．置换多项式与一致分布 41

三 有限域上的置换多项式 47

1．置换多项式的判别 49

2．置换多项式的构造 55

3．置换多项式的群 64

4．例外多项式 63

5．完备映射 74

附录 代数基础 85

1．初等数论 87

2．群，环，域 92

3．有限域 97

4．多项式 100

参考文献 105

外国人名索引 111

Chapter 1．Permutation polynomials over the residue classes 1

1．Starting from complete residue classes 3

2．Characterization and construction of permutation polynomials 10

3．Dickson polynomials 14

4．Permutation spectra 21

Chapter 2．Some applications of permutation polynomials 29

1．A brief introduction to cryptographic system 31

2．Dickson polynomials and RSA system 34

3．Permutational rational functions and RSA system 38

Chapter 3．Permutation polynomials over finite fields 47

1．Characterization of permutation polynomials 49

2．Construction of permutation polynomials 55

3．Groups of permutation polynomials 64

4．Exceptional polynomials 68

5．Complete mappings 74

Appendix, Algebraic foundations 85

1．Elementary number theory 87

2．Groups, rings and fields 97

3．Finite fields 97

4．polynomials 100

References 105

Author Index 111