一 剩余类环的置换多项式

1．从完全剩余系谈起

2．置换多项式的判别与构造

3．迪克逊多项式

4．置换谱

二 置焕多项式的应用举例

1．密码系统简介

2．迪克逊多项式与RSA系统

3．置换有理函数与RSA系统

4．置换多项式与一致分布

三 有限域上的置换多项式

1．置换多项式的判别

2．置换多项式的构造

3．置换多项式的群

4．例外多项式

5．完备映射

附录 代数基础

1．初等数论

2．群，环，域

3．有限域

4．多项式

参考文献

外国人名索引

Chapter 1．Permutation polynomials over the residue classes

1．Starting from complete residue classes

2．Characterization and construction of permutation polynomials

3．Dickson polynomials

4．Permutation spectra

Chapter 2．Some applications of permutation polynomials

1．A brief introduction to cryptographic system

2．Dickson polynomials and RSA system

3．Permutational rational functions and RSA system

Chapter 3．Permutation polynomials over finite fields

1．Characterization of permutation polynomials

2．Construction of permutation polynomials

3．Groups of permutation polynomials

4．Exceptional polynomials

5．Complete mappings

Appendix, Algebraic foundations

1．Elementary number theory

2．Groups, rings and fields

3．Finite fields

4．polynomials

References

Author Index