论文部分内容阅读
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。
Each of the maps on a finite field can be represented as a polynomial function, while the permutation polynomials (functions) on a finite field are a one-to-one mapping of the finite fields to themselves. Therefore, the permutation polynomial on a finite field has always been an important research topic, and the research on this subject has at least 140 years of history. Since 70s of last century, due to the need of cryptography research, the research on permutation polynomials in finite fields has drawn much attention from maths and engineering technicians. In this paper, we present some new permutation polynomials over finite fields, and prove that the two types of permutation polynomials give reciprocal mapping on the finite fields, so that a key exchange protocol can be constructed.