Constructing Odd‐Variable Rotation Symmetric Boolean Functions with Optimal Algebraic Immunity and High Nonlinearity

The GAC Property of a Class of 1‐Resilient Functions with High Nonlinearity

“…Confusion refers to making the relation between the ciphertext and the plaintext as complex as possible for the attackers and diffusion is the spreading out of the influence of one or several arbitrary bits of the plaintext over the output bits. These two properties are usually achieved by the nonlinear Boolean functions through various cryptographic criteria, including: balancedness, high nonlinearity [2][3][4][5][6] , optimal algebraic immunity [7,8] , good autocorrelation properties [9,10] , and proper order of resiliency [11][12][13] . Furthermore, confusion is related to the Walsh spectrum and diffusion is related to the autocorrelation spectrum of the Boolean function.…”

Constructing Odd-Variable Rotation Symmetric Boolean Functions With Optimal AI and Higher Nonlinearity

“…However, fast algebraic immunity is not discussed in these functions [20]- [22]. In 2019, a new odd-variable RSBF with optimal AI and good behavior for resisting fast algebraic attacks (FAAs) was proposed by Zhao et al [23], which have higher nonlinearity…”

New Secondary Constructions of Generalized Bent Functions

“…The latter is also called secondary construction (using known bent functions to built new bent functions), which contains "Rothaus construction [5,6] , direct sum and indirect sum [7,8] ". It is an efficient way to generate more bent functions and thus has received sustained attentions by the researchers in the last decades [9][10][11][12][13][14] .…”