有限域上每一个到其自身的映射都可以用多项式函数形式表示,而有限域上的置换多项式(函数)是有限域到其自身的一个一一映射。因此,有限域上的置换多项式一直是一个重要的研究课题,关于这一课题的研究至少有140年的历史。上世纪70年代以来,由于密码学研究的需要,有限域上置换多项式的研究更是受到数学界和工程技术人员的广泛关注。本文给出了有限域上几个新的置换多项式,证明了两类置换多项式在有限域上给出的是互逆映射,从而由此可以构造一个密钥交换协议。

Any function which maps from a finite field to itself can be represented as a polynomial,and a permutation polynomial is in fact a one-to-one map from a finite field to itself.Hence the research on permutation polynomials has been an important subject for at least 140 years,especially from 70s of the last century for the necessary of the study of cryptography.In this paper,two kinds of permutation polynomials are provided,and the reversibility of the these polynomials is proved.Therefore,one can construct a security key exchange protocol from these functions.