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.
引用
收藏
页码：1 / 14
页数：14
相关论文
共 50 条
  • [21] Finding normal bases over finite fields with prescribed trace self-orthogonal relations
    Zhang, Xiyong
    Feng, Rongquan
    Liao, Qunying
    Gao, Xuhong
    FINITE FIELDS AND THEIR APPLICATIONS, 2014, 28 : 1 - 21
  • [22] On the number of k-normal elements over finite fields
    Saygi, Zulfukar
    Tilenbaev, Ernist
    Urtis, Cetin
    TURKISH JOURNAL OF MATHEMATICS, 2019, 43 (02) : 795 - 812
  • [23] Improving Complexity Bounds for the Computation of Puiseux Series over Finite Fields
    Poteaux, Adrien
    Rybowicz, Marc
    PROCEEDINGS OF THE 2015 ACM ON INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION (ISSAC'15), 2015, : 299 - 306
  • [24] Primitive normal values of rational functions over finite fields
    Sharma, Avnish K.
    Rani, Mamta
    Tiwari, Sharwan K.
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2023, 22 (07)
  • [25] On a class of permutation trinomials over finite fields
    Temur, Burcu Gulmez
    Ozkaya, Buket
    TURKISH JOURNAL OF MATHEMATICS, 2024, 48 (04) : 778 - 792
  • [26] Linear Complexity Cubic Sequences over Finite Fields
    Edemskiy, Vladimir
    Sokolovskiy, Nikita
    PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICS AND COMPUTERS IN SCIENCES AND IN INDUSTRY (MCSI 2016), 2016, : 57 - 60
  • [27] Arithmetic in the Finite Fields Using Optimal Normal and Polynomial Bases in Combination
    Gashkov, Sergej
    Frolov, Alexander
    Lukin, Sergej
    Sukhanova, Olga
    THEORY AND ENGINEERING OF COMPLEX SYSTEMS AND DEPENDABILITY, 2015, 365 : 153 - 162
  • [28] ON THE DETERMINISTIC COMPLEXITY OF FACTORING POLYNOMIALS OVER FINITE-FIELDS
    SHOUP, V
    INFORMATION PROCESSING LETTERS, 1990, 33 (05) : 261 - 267
  • [29] The complexity of elliptic normal bases
    Panario, Daniel
    Sall, Mohamadou
    Wang, Qiang
    FINITE FIELDS AND THEIR APPLICATIONS, 2025, 103
  • [30] A Class of Quadratic Matrix Equations over Finite Fields
    Chen, Yin
    Zhang, Xinxin
    ALGEBRA COLLOQUIUM, 2023, 30 (01) : 169 - 180
12345