Secondary constructions of highly nonlinear Boolean functions and disjoint spectra plateaued functions

Construction of resilient Boolean functions with high nonlinearity and good algebraic degree

“…Let Y = (y 9 , , y 1 ) 2 F 9 2 , and X = (x 9 , , x 1 ) 2 F 9 2 . Let h 1 (y 3 , y 2 , y 1 , x 9 , , x 1 ) be a (12,1,8,2008) function and h 2 (y 1 , x 9 , , x 1 ) be a (10, 1, 8, 492) function. By Construction 1, the function f 2 B 18 can be constructed as follows:…”

“…Boolean functions play a significant role in the design of certain stream cipher schemes such as nonlinear combiners and filtering generators . To resist known attacks, a filtering function used in the aforementioned schemes must satisfy several criteria.…”

Characterization of Basic 5-Value Spectrum Functions Through Walsh-Hadamard Transform

“…Another well-studied class of Boolean functions f : F n 2 → F 2 having the range of their WHT equal to {0, ±2 r } (for r > n/2 ) is known as plateaued functions [29]. Their various design methods have been addressed in several papers [6], [8], [10], [17], [18], [26], [27]. Due to their simple characterization in the spectral domain an alternative design approach was proposed recently in [13], [14].…”

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] .…”