Constructions of 1‐Resilient Boolean Functions with High Nonlinearity and Good Algebraic Degree | Zendy

Ge Hui | Zendy; Sun Yujuan | Zendy; Zhuo Zepeng | Zendy

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Constructions of 1‐Resilient Boolean Functions with High Nonlinearity and Good Algebraic Degree

Author(s) -

Ge Hui,

Sun Yujuan,

Zhuo Zepeng

Publication year - 2020

Publication title -

chinese journal of electronics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.267

H-Index - 25

eISSN - 2075-5597

pISSN - 1022-4653

DOI - 10.1049/cje.2020.05.011

Subject(s) - boolean function , linear subspace , class (philosophy) , nonlinear system , degree (music) , mathematics , bent molecular geometry , algebraic number , bent function , discrete mathematics , pure mathematics , computer science , mathematical analysis , physics , quantum mechanics , acoustics , chemistry , organic chemistry , artificial intelligence

Three of the most essential criteria for cryptographically strong Boolean functions are resiliency, high nonlinearity and high algebraic degree. We give a technique for constructing 1‐resilient Boolean functions with high nonlinearity via modifying PS ‐ class bent functions. The main technique is to extend the support of bent functions in PS ‐ class by additionally defining two different plateaued functions on two suitably chosen subspaces. A large class of highly nonlinear 1‐resilient functions which were not known earlier are obtained.

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