A New 10-Variable Cubic Bent Function Outside the Completed Maiorana-McFarland Class

Yanjun LI; Haibin KAN; Jie PENG; Chik How TAN; Baixiang LIU

doi:10.1587/transfun.2021EAL2003

A New 10-Variable Cubic Bent Function Outside the Completed Maiorana-McFarland Class

Yanjun LI, Haibin KAN, Jie PENG, Chik How TAN, Baixiang LIU

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In this letter, we present a construction of bent functions which generalizes a work of Zhang et al. in 2016. Based on that, we obtain a cubic bent function in 10 variables and prove that, it has no affine derivative and does not belong to the completed Maiorana-McFarland class, which is opposite to all 6/8-variable cubic bent functions as they are inside the completed Maiorana-McFarland class. This is the first time a theoretical proof is given to show that the cubic bent functions in 10 variables can be outside the completed Maiorana-McFarland class. Before that, only a sporadic example with such properties was known by computer search. We also show that our function is EA-inequivalent to that sporadic one.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.9 pp.1353-1356

Publication Date: 2021/09/01

Publicized: 2021/02/22

Online ISSN: 1745-1337

DOI: 10.1587/transfun.2021EAL2003

Type of Manuscript: LETTER

Category: Cryptography and Information Security

Authors

Yanjun LI
  Anhui University of Finance and Economics
Haibin KAN
  Fudan University
Jie PENG
  Shanghai Normal University
Chik How TAN
  National University of Singapore
Baixiang LIU
  Fudan University

Keyword

affine derivative, bent functions, the completed Maiorana-McFarland class

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Yanjun LI, Haibin KAN, Jie PENG, Chik How TAN, Baixiang LIU, "A New 10-Variable Cubic Bent Function Outside the Completed Maiorana-McFarland Class" in IEICE TRANSACTIONS on Fundamentals, vol. E104-A, no. 9, pp. 1353-1356, September 2021, doi: 10.1587/transfun.2021EAL2003.
Abstract: In this letter, we present a construction of bent functions which generalizes a work of Zhang et al. in 2016. Based on that, we obtain a cubic bent function in 10 variables and prove that, it has no affine derivative and does not belong to the completed Maiorana-McFarland class, which is opposite to all 6/8-variable cubic bent functions as they are inside the completed Maiorana-McFarland class. This is the first time a theoretical proof is given to show that the cubic bent functions in 10 variables can be outside the completed Maiorana-McFarland class. Before that, only a sporadic example with such properties was known by computer search. We also show that our function is EA-inequivalent to that sporadic one.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAL2003/_p

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@ARTICLE{e104-a_9_1353,
author={Yanjun LI, Haibin KAN, Jie PENG, Chik How TAN, Baixiang LIU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A New 10-Variable Cubic Bent Function Outside the Completed Maiorana-McFarland Class},
year={2021},
volume={E104-A},
number={9},
pages={1353-1356},
abstract={In this letter, we present a construction of bent functions which generalizes a work of Zhang et al. in 2016. Based on that, we obtain a cubic bent function in 10 variables and prove that, it has no affine derivative and does not belong to the completed Maiorana-McFarland class, which is opposite to all 6/8-variable cubic bent functions as they are inside the completed Maiorana-McFarland class. This is the first time a theoretical proof is given to show that the cubic bent functions in 10 variables can be outside the completed Maiorana-McFarland class. Before that, only a sporadic example with such properties was known by computer search. We also show that our function is EA-inequivalent to that sporadic one.},
keywords={},
doi={10.1587/transfun.2021EAL2003},
ISSN={1745-1337},
month={September},}

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TY - JOUR
TI - A New 10-Variable Cubic Bent Function Outside the Completed Maiorana-McFarland Class
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1353
EP - 1356
AU - Yanjun LI
AU - Haibin KAN
AU - Jie PENG
AU - Chik How TAN
AU - Baixiang LIU
PY - 2021
DO - 10.1587/transfun.2021EAL2003
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2021
AB - In this letter, we present a construction of bent functions which generalizes a work of Zhang et al. in 2016. Based on that, we obtain a cubic bent function in 10 variables and prove that, it has no affine derivative and does not belong to the completed Maiorana-McFarland class, which is opposite to all 6/8-variable cubic bent functions as they are inside the completed Maiorana-McFarland class. This is the first time a theoretical proof is given to show that the cubic bent functions in 10 variables can be outside the completed Maiorana-McFarland class. Before that, only a sporadic example with such properties was known by computer search. We also show that our function is EA-inequivalent to that sporadic one.
ER -