首页|Further study on constructing bent functions outside the completed Maiorana–McFarland class

Further study on constructing bent functions outside the completed Maiorana–McFarland class

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  • NSTL
  • Inst Engineering Technology-Iet
In the mid-sixties, Rothaus introduced the notion of bent function and later presented a secondary construction of bent functions (building new bent functions from already defined ones), called Rothaus' construction. In Zhang et al. 2017 ('Constructing bent functions outside the Maiorana-Mcfarland class using a general form of Rothaus,' IEEE Transactions on Information Theory, 2017, vol. 63, no. 8, pp. 5336-5349.') provided two constructions of bent functions using a general form of Rothaus and showed that the obtained classes lie outside the completed Maiorana-McFarland (MM) class. In this study, the authors propose two similar methods for constructing bent functions outside the completed MM class but with significantly simplified sufficient conditions compared to those in Zhang et al. 2017. These simplified conditions do not induce any serious restrictions on the choice of permutations used in the construction apart from a simple requirement on their algebraic degree and the request that the component functions of one permutation do not admit linear structures. This enables us to generate a huge class of bent functions lying outside the completed MM class. Even more importantly, they prove that the new classes of bent functions are affine inequivalent to the bent functions in Zhang et al. 2017.

Boolean functionsbent functioncompleted Maiorana-McFarland classRothaus constructionsufficient conditionsalgebraic degreecomponent functionslinear structurescompleted partial spread classBoolean functions

Liu, Shishi、Zhang, Fengrong、Pasalic, Enes、Xia, Shixiong、Zhuo, Zepeng

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China Univ Min & Technol, Sch Comp Sci & Technol, Xuzhou 221116, Jiangsu, Peoples R China|State Key Lab Cryptol, POB 5159, Beijing, Peoples R China|CUMT, Minist Educ, Mine Digitizat Engn Res Ctr, Xuzhou 221116, Jiangsu, Peoples R China

Univ Primorska, FAMNIT & IAM, Koper, Slovenia

China Univ Min & Technol, Sch Comp Sci & Technol, Xuzhou 221116, Jiangsu, Peoples R China|CUMT, Minist Educ, Mine Digitizat Engn Res Ctr, Xuzhou 221116, Jiangsu, Peoples R China

Huaibei Normal Univ, Sch Math Sci, Huaibei, Anhui 235000, Peoples R China

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2020

10.1049/iet-ifs.2018.5425

IET information security

IET information security

ISSN：1751-8709
年,卷(期)：2020.14(6)
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