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Subject: Computer Science
Title:
on the nonexistence of bent functions
Author: Zhang Yin ; Liu Meicheng ; Lin Dongdai
Keyword: Boolean function ; bent function ; nonlinearity ; d-upper Boolean function
Source: INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
Issued Date: 2011
Volume: 22, Issue:6, Pages:1431-1438
Indexed Type: SCI
Department: Zhang Yin; Liu Meicheng; Lin Dongdai Chinese Acad Sci Inst Software State Key Lab Informat Secur Beijing 100190 Peoples R China. Zhang Yin; Liu Meicheng Chinese Acad Sci Grad Univ Beijing 100049 Peoples R China.
Sponsorship: National 973 Program of China2011CB302400; National Natural Science Foundation of China60970152; Institute of SoftwareYOCX285056; CAS
Abstract: In this paper, we study the nonexistence of bent functions in the class of Boolean functions without monomials of degree less than d in their algebraic normal forms (ANF). We prove that n-variable Boolean functions in such class are not bent when there are not more than n + d - 3 monomials in their ANFs. We also show that an n-variable Boolean function is not bent if it has no monomial of degree less than inverted right perpendicular3n/8 + 3/4inverted left perpendicular in its ANF.
English Abstract: In this paper, we study the nonexistence of bent functions in the class of Boolean functions without monomials of degree less than d in their algebraic normal forms (ANF). We prove that n-variable Boolean functions in such class are not bent when there are not more than n + d - 3 monomials in their ANFs. We also show that an n-variable Boolean function is not bent if it has no monomial of degree less than inverted right perpendicular3n/8 + 3/4inverted left perpendicular in its ANF.
Language: 英语
WOS ID: WOS:000294809400013
Citation statistics:
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/16078
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Zhang Yin,Liu Meicheng,Lin Dongdai. on the nonexistence of bent functions[J]. INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE,2011-01-01,22(6):1431-1438.
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