Constructions of Almost Optimal Resilient Boolean Functions on Large Even Number of Variables

Abstract

In this paper, a technique on constructing nonlinear resilient Boolean functions is described. By using several sets of disjoint spectra functions on a small number of variables, an almost optimal resilient function on a large even number of variables can be constructed. It is shown that given any m, one can construct infinitely many n-variable (n even), m-resilient functions with nonlinearity > 2 n−1 − 2 n/2 . A large class of highly nonlinear resilient functions which were not known are obtained. Then one method to optimize the degree of the constructed functions is proposed. Last, an improved version of the main construction is given.

Further results on constructions of generalized bent Boolean functions

“…Since bent functions have many applications in sequence design, cryptography and algebraic coding, they have been extensively studied during the last thirty years [2,3]. Over the past decades, based on bent functions, several constructions of highly nonlinear balanced functions were presented [4,5].…”

Construction of balanced Boolean functions with high nonlinearity, good local and global avalanche characteristics

“…Boolean functions are usually used for S-boxes design in block ciphers and utilized as nonlinear filters and combiners in stream ciphers [10,[14][15][16][17][18]. To resist various cryptanalytic attacks, they must satisfy several criteria.…”

On primary construction of Plateaued functions

“…As for the second construction and other constructions, they are also important to obtain Boolean functions approaching or achieving the best trade-off among the cryptographic properties. And these constructions can be seen in [8][9][10][11][12][13][14][15].…”