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[1]刘志高.拟Bent函数的代数免疫性[J].武汉工程大学学报,2014,(11):75-78.[doi:103969/jissn167428692014011014]
　LIU Zhi gao.Algebraic immunity of QuasiBent functions[J].Journal of Wuhan Institute of Technology,2014,(11):75-78.[doi:103969/jissn167428692014011014]
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《武汉工程大学学报》[ISSN:1674-2869/CN:42-1779/TQ]

卷:
期数:
2014年11期
页码:
75-78
栏目:
机电与信息工程
出版日期:
2014-11-30

文章信息/Info

Title:
Algebraic immunity of QuasiBent functions
文章编号:
16742869(2014)011007504
作者:
刘志高
马鞍山职业技术学院，安徽 马鞍山 243031
Author(s):
LIU Zhigao
Maanshan Technical College, Ma’anshan 243031, China
关键词:
布尔函数; 代数攻击; Walsh循环谱
Keywords:
Boolean functions; algebraic attacks; Walsh cyclic spectrum
分类号:
TN918.1, O158
DOI:
103969/jissn167428692014011014
文献标志码:
A
摘要:
基于布尔函数非线性度与代数免疫度之间的关系, 利用Walsh谱、组合数等工具得到了判定拟Bent函数存在低次零化子的一个充分条件, 它不需要利用Walsh循环谱或代数正规形来判定, 非常直观有效. 据此充分条件可知, 在变元个数确定的情况下, 拟Bent函数的阶数越高, 其存在低次零化子的可能性越大, 抵抗代数攻击的能力越弱. 反之, 在阶数确定的情况下, 拟Bent函数的变元个数越大, 其存在低次零化子的可能性越小, 抵抗代数攻击的能力越强.
Abstract:
Based on the relationship between the nonlinearity and the algebraic immunity of Boolean functions, a sufficient condition for judging the quasi bent function existing low degree annihilators is given by Walsh spectrum and combination tools, which need not to use the Walsh cyclic spectrum or algebraic normal form to judge, so it is very intuitive and effective. It concludes that the order of quasi bent functions is higher, the possibility of low degree annihilators is bigger and the ability to resist algebraic attack is weaker in the case of variable number under certain; on the other hand, the variable number of quasi bent functions is bigger, the possibility of low degree annihilators is smaller and the ability to resist algebraic attack is stronger in the case of the order numbers under certain conditions.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期：20141009基金项目：2014安徽省高校优秀青年人才支持计划资助作者简介：刘志高（1975），男，安徽郎溪人，副教授，硕士.研究方向：密码函数与信息安全.
更新日期/Last Update: 2014-12-11