一类布尔函数的代数免疫度的下界

田叶; 张玉清; 胡予濮; 伍高飞

doi:10.11959/j.issn.1000-436x.2016200

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一类布尔函数的代数免疫度的下界

学术论文 | 更新时间：2024-06-05

- 一类布尔函数的代数免疫度的下界
- New bound of algebraic immunity of a class of Boolean function
- 通信学报 2016年37卷第10期页码：92-98
- 作者机构：
  
  1. 西安电子科技大学综合业务网理论及关键技术国家重点实验室，陕西西安 710071
  2. 中国科学院大学国家计算机网络入侵防范中心，北京 101408
- 作者简介：
  
  [ "田叶（1987-），女，山西平遥人，西安电子科技大学博士生，主要研究方向为布尔函数、序列密码的分析与构造。" ]
  [ "张玉清（1966-），男，陕西宝鸡人，博士，中国科学院大学教授、博士生导师，主要研究方向为网络与信息系统安全。" ]
  [ "胡予濮（1955-），男，河南濮阳人，西安电子科技大学教授、博士生导师，主要研究方向为序列密码与分组密码、网络安全协议的设计与分析。" ]
  [ "伍高飞（1987-），男，河南灵宝人，西安电子科技大学博士生，主要研究方向为序列设计和密码学。" ]
- 基金信息：
  
  国家自然科学基金资助项目(61572460);国家自然科学基金资助项目(61272481);国家重点研究计划基金资助项目(2016YFB0800703);国家发展改革委员会信息安全专项基金资助项目((2012)1424);国家111计划基金资助项目(B16037)
- DOI：10.11959/j.issn.1000-436x.2016200
  中图分类号： TN918
- 网络出版日期：2016-10，
  
  纸质出版日期：2016-10-25
- 稿件说明：
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田叶, 张玉清, 胡予濮, 等. 一类布尔函数的代数免疫度的下界[J]. 通信学报, 2016,37(10):92-98.

Ye TIAN, Yu-qing ZHANG, Yu-pu HU, et al. New bound of algebraic immunity of a class of Boolean function[J]. Journal on communications, 2016, 37(10): 92-98.
田叶, 张玉清, 胡予濮, 等. 一类布尔函数的代数免疫度的下界[J]. 通信学报, 2016,37(10):92-98. DOI： 10.11959/j.issn.1000-436x.2016200.

Ye TIAN, Yu-qing ZHANG, Yu-pu HU, et al. New bound of algebraic immunity of a class of Boolean function[J]. Journal on communications, 2016, 37(10): 92-98. DOI： 10.11959/j.issn.1000-436x.2016200.

摘要

代数免疫度是衡量布尔函数抵抗代数攻击的重要指标。最近，Mesnager等研究了布尔函数的零化子与函数所对应循环码最小距离之间的联系，代数免疫度的下界可以由对应的循环码的最小距离得到。解决了Mesnager提出的一个公开问题，给出了一类特定函数的零化子次数的下界，并得到一类布尔函数的代数免疫度的下界。

Abstract

Algebraic immunity quantified the resistance of a Boolean function to the algebraic attack.Recently

Mesnager

et al showed that there were direct linked between the annihilators used in algebraic attacks and the coding theory.They showed that the lower bound of the algebraic immunity of Boolean functions could been derived from the minimum distance of the associated cyclic codes.An open problem proposed by Mesnager is settled with a detailed proof.Also

a lower bound of algebraic immunity of a class of Boolean functions will be introduced.

关键词

Keywords

references

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