Initial results on the rotation symmetric bent-negabent functions

Sumanta Sarkar; Thomas Cusick

doi:10.1109/IWSDA.2015.7458419

Initial results on the rotation symmetric bent-negabent functions

Sumanta Sarkar
, Thomas Cusick

Mathematics

Indian Statistical Institute

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

For the first time in the literature, we investigate the negabent Boolean functions in the class of rotation symmetric Boolean functions. We derive a matrix to analyze the negabent property of rotation symmetric negabent Boolean functions. The dimension of this matrix is much smaller than the nega-Hadamard matrix. We show that for even n ≤ 8, there is no rotation symmetric negabent function which is also bent. Taking the cue from this numerical results, we prove that there is no rotation symmetric Boolean function of degree 2 which is both bent and negabent.

Original language	English
Title of host publication	7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	80-84
Number of pages	5
ISBN (Electronic)	9781467383080
DOIs	https://doi.org/10.1109/IWSDA.2015.7458419
State	Published - Apr 22 2016
Event	7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015 - Bengaluru, India Duration: Sep 13 2015 → Sep 18 2015

Publication series

Name	7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015

Conference

Conference	7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015
Country/Territory	India
City	Bengaluru
Period	09/13/15 → 09/18/15

Keywords

bent function
nega-Hadamard matrix
nega-Hadamard transform
negabent function
Rotation symmetric Boolean function

Access to Document

10.1109/IWSDA.2015.7458419

Cite this

Sarkar, S., & Cusick, T. (2016). Initial results on the rotation symmetric bent-negabent functions. In 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015 (pp. 80-84). Article 7458419 (7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/IWSDA.2015.7458419

@inproceedings{913ee1ca3f4f42808ce0ed32492dcaaa,

title = "Initial results on the rotation symmetric bent-negabent functions",

abstract = "For the first time in the literature, we investigate the negabent Boolean functions in the class of rotation symmetric Boolean functions. We derive a matrix to analyze the negabent property of rotation symmetric negabent Boolean functions. The dimension of this matrix is much smaller than the nega-Hadamard matrix. We show that for even n ≤ 8, there is no rotation symmetric negabent function which is also bent. Taking the cue from this numerical results, we prove that there is no rotation symmetric Boolean function of degree 2 which is both bent and negabent.",

keywords = "bent function, nega-Hadamard matrix, nega-Hadamard transform, negabent function, Rotation symmetric Boolean function",

author = "Sumanta Sarkar and Thomas Cusick",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.; 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015 ; Conference date: 13-09-2015 Through 18-09-2015",

year = "2016",

month = apr,

day = "22",

doi = "10.1109/IWSDA.2015.7458419",

language = "English",

series = "7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "80--84",

booktitle = "7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015",

address = "United States",

}

Sarkar, S & Cusick, T 2016, Initial results on the rotation symmetric bent-negabent functions. in 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015., 7458419, 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015, Institute of Electrical and Electronics Engineers Inc., pp. 80-84, 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015, Bengaluru, India, 09/13/15. https://doi.org/10.1109/IWSDA.2015.7458419

Initial results on the rotation symmetric bent-negabent functions. / Sarkar, Sumanta; Cusick, Thomas.
7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015. Institute of Electrical and Electronics Engineers Inc., 2016. p. 80-84 7458419 (7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Initial results on the rotation symmetric bent-negabent functions

AU - Sarkar, Sumanta

AU - Cusick, Thomas

PY - 2016/4/22

Y1 - 2016/4/22

N2 - For the first time in the literature, we investigate the negabent Boolean functions in the class of rotation symmetric Boolean functions. We derive a matrix to analyze the negabent property of rotation symmetric negabent Boolean functions. The dimension of this matrix is much smaller than the nega-Hadamard matrix. We show that for even n ≤ 8, there is no rotation symmetric negabent function which is also bent. Taking the cue from this numerical results, we prove that there is no rotation symmetric Boolean function of degree 2 which is both bent and negabent.

AB - For the first time in the literature, we investigate the negabent Boolean functions in the class of rotation symmetric Boolean functions. We derive a matrix to analyze the negabent property of rotation symmetric negabent Boolean functions. The dimension of this matrix is much smaller than the nega-Hadamard matrix. We show that for even n ≤ 8, there is no rotation symmetric negabent function which is also bent. Taking the cue from this numerical results, we prove that there is no rotation symmetric Boolean function of degree 2 which is both bent and negabent.

KW - bent function

KW - nega-Hadamard matrix

KW - nega-Hadamard transform

KW - negabent function

KW - Rotation symmetric Boolean function

UR - https://www.scopus.com/pages/publications/84978474647

U2 - 10.1109/IWSDA.2015.7458419

DO - 10.1109/IWSDA.2015.7458419

M3 - Conference contribution

AN - SCOPUS:84978474647

T3 - 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015

SP - 80

EP - 84

BT - 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015

Y2 - 13 September 2015 through 18 September 2015

ER -

Sarkar S, Cusick T. Initial results on the rotation symmetric bent-negabent functions. In 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015. Institute of Electrical and Electronics Engineers Inc. 2016. p. 80-84. 7458419. (7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015). doi: 10.1109/IWSDA.2015.7458419

Initial results on the rotation symmetric bent-negabent functions

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this