Counting all bent functions in dimension eight 99270589265934370305785861242880

Philippe Langevin; Gregor Leander

doi:10.1007/s10623-010-9455-z

Counting all bent functions in dimension eight 99270589265934370305785861242880

Philippe Langevin
, Gregor Leander

Université de Toulon

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

Based on the classification of the homogeneous Boolean functions of degree 4 in 8 variables we present the strategy that we used to count the number of all bent functions in dimension 8. There are $$99270589265934370305785861242880 \approx 2^{106}$$such functions in total. Furthermore, we show that most of the bent functions in dimension 8 are nonequivalent to Maiorana–McFarland and partial spread functions.

Original language	English
Journal	Designs, Codes and Cryptography
Volume	59
Issue number	1-3
Pages (from-to)	193-205
ISSN	0925-1022
DOIs	https://doi.org/10.1007/s10623-010-9455-z
Publication status	Published - 2011

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title = "Counting all bent functions in dimension eight 99270589265934370305785861242880",

abstract = "Based on the classification of the homogeneous Boolean functions of degree 4 in 8 variables we present the strategy that we used to count the number of all bent functions in dimension 8. There are \$\$99270589265934370305785861242880 \textbackslash{}approx 2\textasciicircum{}\{106\}\$\$such functions in total. Furthermore, we show that most of the bent functions in dimension 8 are nonequivalent to Maiorana–McFarland and partial spread functions.",

author = "Philippe Langevin and Gregor Leander",

year = "2011",

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journal = "Designs, Codes and Cryptography",

issn = "0925-1022",

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AU - Langevin, Philippe

AU - Leander, Gregor

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AB - Based on the classification of the homogeneous Boolean functions of degree 4 in 8 variables we present the strategy that we used to count the number of all bent functions in dimension 8. There are $$99270589265934370305785861242880 \approx 2^{106}$$such functions in total. Furthermore, we show that most of the bent functions in dimension 8 are nonequivalent to Maiorana–McFarland and partial spread functions.

U2 - 10.1007/s10623-010-9455-z

DO - 10.1007/s10623-010-9455-z

M3 - Journal article

SN - 0925-1022

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JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

IS - 1-3

ER -

Counting all bent functions in dimension eight 99270589265934370305785861242880

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