Low complexity of a class of normal bases over finite fields

被引：2
|
作者：
Liao, Qunying [2 ]
You, Lin [1 ]
机构：
[1] Hangzhou Dianzi Univ, Coll Commun Engn, Hangzhou 310018, Peoples R China
[2] Sichuan Normal Univ, Coll Math & Software Sci, Chengdu 610066, Peoples R China
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2011年 / 17卷 / 01期
基金：
浙江省自然科学基金; 美国国家科学基金会;
关键词：
Finite fields; Complexity; Trace mapping; Normal bases; Dual bases;
D O I：
10.1016/j.ffa.2010.09.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is well known that normal bases are useful for implementations of finite fields in various applications including coding theory, cryptography, signal processing, and so on. In particular, optimal normal bases are desirable. When no optimal normal basis exists, it is useful to have normal bases with low complexity. In this paper, we improve the upper bounds for the complexity of the trace normal bases over finite fields and prove that these upper bounds can be reached for some extension with small degree. In addition, we construct a class of normal bases with low complexity by this way. (C) 2010 Elsevier Inc. All rights reserved.
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页码：1 / 14
页数：14
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