《置换多项式及其应用》

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 classes1

1．Starting from complete residue classes3

2．Characterization and construction of permutation polynomials10

3．Dickson polynomials14

4．Permutation spectra21

Chapter 2．Some applications of permutation polynomials29

1．A brief introduction to cryptographic system31

2．Dickson polynomials and RSA system34

3．Permutational rational functions and RSA system38

Chapter 3．Permutation polynomials over finite fields47

1．Characterization of permutation polynomials49

2．Construction of permutation polynomials55

3．Groups of permutation polynomials64

4．Exceptional polynomials68

5．Complete mappings74

Appendix, Algebraic foundations85

1．Elementary number theory87

2．Groups, rings and fields97

3．Finite fields97

4．polynomials100

References105

Author Index111