Fast evaluation, weights and nonlinearity of rotation-symmetric functions

Thomas W. Cusick; Pantelimon Stǎnicǎ

doi:10.1016/S0012-365X(02)00354-0

Fast evaluation, weights and nonlinearity of rotation-symmetric functions

Thomas W. Cusick
, Pantelimon Stǎnicǎ

Mathematics

Auburn University

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

81 Scopus citations

Abstract

We study the nonlinearity and the weight of the rotation-symmetric (RotS) functions defined by Pieprzyk and Qu. We give exact results for the nonlinearity and weight of 2-degree RotS functions with the help of the semi-bent functions and we give the generating function for the weight of the 3-degree RotS function. Based on the numerical examples and our observations we state a conjecture on the nonlinearity and weight of the 3-degree RotS function.

Original language	English
Pages (from-to)	X289-301
Journal	Discrete Mathematics
Volume	258
Issue number	1-3
DOIs	https://doi.org/10.1016/S0012-365X(02)00354-0
State	Published - Dec 6 2002

Keywords

Bent
Boolean functions
Hash functions
Nonlinearity
Semi-bent

Access to Document

10.1016/S0012-365X(02)00354-0

Cite this

@article{59093aedda6b48368526419d1ee72abc,

title = "Fast evaluation, weights and nonlinearity of rotation-symmetric functions",

abstract = "We study the nonlinearity and the weight of the rotation-symmetric (RotS) functions defined by Pieprzyk and Qu. We give exact results for the nonlinearity and weight of 2-degree RotS functions with the help of the semi-bent functions and we give the generating function for the weight of the 3-degree RotS function. Based on the numerical examples and our observations we state a conjecture on the nonlinearity and weight of the 3-degree RotS function.",

keywords = "Bent, Boolean functions, Hash functions, Nonlinearity, Semi-bent",

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

year = "2002",

month = dec,

day = "6",

doi = "10.1016/S0012-365X(02)00354-0",

language = "English",

volume = "258",

pages = "X289--301",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier B.V.",

number = "1-3",

}

TY - JOUR

T1 - Fast evaluation, weights and nonlinearity of rotation-symmetric functions

AU - Cusick, Thomas W.

AU - Stǎnicǎ, Pantelimon

PY - 2002/12/6

Y1 - 2002/12/6

N2 - We study the nonlinearity and the weight of the rotation-symmetric (RotS) functions defined by Pieprzyk and Qu. We give exact results for the nonlinearity and weight of 2-degree RotS functions with the help of the semi-bent functions and we give the generating function for the weight of the 3-degree RotS function. Based on the numerical examples and our observations we state a conjecture on the nonlinearity and weight of the 3-degree RotS function.

AB - We study the nonlinearity and the weight of the rotation-symmetric (RotS) functions defined by Pieprzyk and Qu. We give exact results for the nonlinearity and weight of 2-degree RotS functions with the help of the semi-bent functions and we give the generating function for the weight of the 3-degree RotS function. Based on the numerical examples and our observations we state a conjecture on the nonlinearity and weight of the 3-degree RotS function.

KW - Bent

KW - Boolean functions

KW - Hash functions

KW - Nonlinearity

KW - Semi-bent

UR - https://www.scopus.com/pages/publications/0037032959

U2 - 10.1016/S0012-365X(02)00354-0

DO - 10.1016/S0012-365X(02)00354-0

M3 - Article

AN - SCOPUS:0037032959

SN - 0012-365X

VL - 258

SP - X289-301

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -

Fast evaluation, weights and nonlinearity of rotation-symmetric functions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this