有限域上的不可约多项式RSA体制

Irreducible Polynomials about RSA Type Public Key Cryptosystem over Finite Fields

摘要: 有限域是计算科学和数字通讯领域基础的数学工具之一，同时也是现代数学的主要分支之一。有限域的一般理论主要是从Gauss和Galois的工作开始，但最近几十年，随着离散数学的成长与发展，很多专家开始慢慢注重有限域理论的研究和应用。同时，多项式理论，特别是不可约多项式的性质对剖析各种伪随机序列的性能有着异常的性能，因此对于有限域上的不可约多项式的研究一直受到数学界、编码与密码领域的广泛关注。尤其是在信息化的时代，人们开始越来越重视自身的信息安全。本文对基于有限域上的不可约多项式对RSA公钥密码体制的三种模拟进行比较，发现PK-RSA模拟安全性更高。

Abstract: Finite field is one of the most basic mathematical tools of computer science and digital communi-cation field, as well as one of the important branches of modern mathematics. The general theory of finite field mainly starts from the Gauss and Galois, but in recent decades, with the development of discrete mathematics, many mathematicians engaged in applied research and paid attention to the research and application of theory of limited. At the same time, the polynomial theory, especially the properties of irreducible polynomials to analyze various performances of pseudorandom sequence, has a special performance, so the studies of the irreducible polynomials over finite field have been widespreadly concerned in mathematical, coding and cryptology research. This paper found that the PK-RSA simulated security is higher by comparing the irreducible polynomials over finite field to the system of three RSAs.