Open AccessConstructions 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) - degree (music) , boolean function , algebraic number , mathematics , nonlinear system , pure mathematics , discrete mathematics , physics , mathematical analysis , quantum mechanics , acoustics
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.