摘要
有限域上的正规基在有限域的算法快速实现以及编码和密码应用等方面有着重要作用.本文从理论和应用两方面综述了有限域上正规基,包括正规基元、本原正规基元、对偶正规基、自对偶正规基的基本性质;以及正规基表示下的快速算法、低复杂度正规基的构造等等.
Normal bases are important in efficient implementation of finite field arithmetic for many applications in coding theory and cryptography. This paper gives a survey on various topics of normal bases including basic properties of normal elements, primitive normal bases, dual and self-dual normal bases, fast arithmetic under normal bases, and constructions for low complexity normal bases.
出处
《数学进展》
CSCD
北大核心
2013年第5期577-586,共10页
Advances in Mathematics（China）
基金
Supported by NSFC(No.10990011)
the Ph.D.Program Foundation of Ministry of Educationof China(No.20095134120001)
Sichuan Provincial Advance Research Program for Excellent Youth Leadersof Disciplines in Science of China(No.2011JQ0037)
关键词
有限域
正规基
对偶基
复杂度
快速算法
finite field
normal basis
dual basis
complexity
fast arithmetic
