Open AccessConstructing Odd‐Variable Rotation Symmetric Boolean Functions with Optimal Algebraic Immunity and High Nonlinearity
Author(s) -
Zhao Qinglan,
Han Gang,
Zheng Dong,
Li Xiangxue
Publication year - 2019
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.2018.01.009
Subject(s) - boolean function , mathematics , rotation (mathematics) , nonlinear system , algebraic number , variable (mathematics) , pure mathematics , discrete mathematics , mathematical analysis , physics , geometry , quantum mechanics
Rotation symmetric Boolean functions (RSBFs) have attracted widespread attention due to their good cryptographic properties. We present a new construction of RSBFs with optimal algebraic immunity on odd number of variables. The nonlinearity of the new function is much higher than other best known RSBFs with optimal algebraic immunity. The algebraic degree of the constructed n‐variable RSBF can achieve the upper bound n ‐1 when n /2 is odd or when n /2 is a power of 2 for n ‐11. In addition, the constructed function can possess almost perfect immunity to fast algebraic attacks for n =11, 13, 15