New bound of algebraic immunity of a class of Boolean function

Ye TIAN; Yu-qing ZHANG; Yu-pu HU; Gao-fei WU

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

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New bound of algebraic immunity of a class of Boolean function

Papers | 更新时间：2024-06-05

- New bound of algebraic immunity of a class of Boolean function
- Journal on Communications Vol. 37, Issue 10, Pages: 92-98(2016)
- 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：
- 基金信息：
  
  The National Natural Science Foundation of China(61572460);The National Natural Science Foundation of China(61272481);The National Key Research and Development Project(2016YFB0800703);The National Information Security Special Projects of National Development,The Reform Commission of China((2012)1424);China 111 Project(B16037)
- DOI：10.11959/j.issn.1000-436x.2016200
  CLC： TN918
- Online First：2016-10，
  
  Published：25 October 2016
- 稿件说明：
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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：

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.

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references

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