On a conjecture for balanced symmetric Boolean functions

Thomas W. Cusick; Yuan Li; Pantelimon Stǎnicǎ

doi:10.1515/JMC.2009.017

On a conjecture for balanced symmetric Boolean functions

Thomas W. Cusick
, Yuan Li
, Pantelimon Stǎnicǎ

Mathematics

Winston-Salem State University
Naval Postgraduate School

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We give some results towards the conjecture that X(2 ^t; 2 ^t+ℓ-1) are the only nonlinear balanced elementary symmetric polynomials over GF(2), where t and ℓ are any positive integers and X(d; n) = Σ 1≤i ₁<i ₂<⋯<i _d≤n xi1xi2⋯ xid.

Original language	English
Pages (from-to)	273-290
Number of pages	18
Journal	Journal of Mathematical Cryptology
Volume	3
Issue number	4
DOIs	https://doi.org/10.1515/JMC.2009.017
State	Published - Dec 2009

Keywords

Balancedness
Boolean functions
Cryptography
Symmetry

Access to Document

10.1515/JMC.2009.017

Cite this

@article{d3dbec0cc841406996f6d6de8d643421,

title = "On a conjecture for balanced symmetric Boolean functions",

abstract = "We give some results towards the conjecture that X(2 t; 2 t+ℓ-1) are the only nonlinear balanced elementary symmetric polynomials over GF(2), where t and ℓ are any positive integers and X(d; n) = Σ 1≤i 12<⋯d≤n xi1xi2⋯ xid.",

keywords = "Balancedness, Boolean functions, Cryptography, Symmetry",

author = "Cusick, \{Thomas W.\} and Yuan Li and Pantelimon Stǎnicǎ",

year = "2009",

month = dec,

doi = "10.1515/JMC.2009.017",

language = "English",

volume = "3",

pages = "273--290",

journal = "Journal of Mathematical Cryptology",

issn = "1862-2976",

publisher = "Walter de Gruyter GmbH",

number = "4",

}

TY - JOUR

T1 - On a conjecture for balanced symmetric Boolean functions

AU - Cusick, Thomas W.

AU - Li, Yuan

AU - Stǎnicǎ, Pantelimon

PY - 2009/12

Y1 - 2009/12

N2 - We give some results towards the conjecture that X(2 t; 2 t+ℓ-1) are the only nonlinear balanced elementary symmetric polynomials over GF(2), where t and ℓ are any positive integers and X(d; n) = Σ 1≤i 12<⋯d≤n xi1xi2⋯ xid.

AB - We give some results towards the conjecture that X(2 t; 2 t+ℓ-1) are the only nonlinear balanced elementary symmetric polynomials over GF(2), where t and ℓ are any positive integers and X(d; n) = Σ 1≤i 12<⋯d≤n xi1xi2⋯ xid.

KW - Balancedness

KW - Boolean functions

KW - Cryptography

KW - Symmetry

UR - https://www.scopus.com/pages/publications/84863337786

U2 - 10.1515/JMC.2009.017

DO - 10.1515/JMC.2009.017

M3 - Article

AN - SCOPUS:84863337786

SN - 1862-2976

VL - 3

SP - 273

EP - 290

JO - Journal of Mathematical Cryptology

JF - Journal of Mathematical Cryptology

IS - 4

ER -

On a conjecture for balanced symmetric Boolean functions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this