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Three of the most essential criteria for cryptographically strong Boolean functions are balancedness, high nonlinearity and high algebraic degree. In this paper, we give two methods for constructing balanced Boolean functions with high nonlinearity via modifying Maiorana–McFarland type bent functions. The algebraic immunity of the constructed functions is also considered. [ABSTRACT FROM AUTHOR]

This paper studies the construction of resilient Boolean functions in odd variables with strictly almost optimal (SAO) nonlinearity. Based on High-Meets-Low technique, we present a new construction to obtain Boolean functions with higher resiliency order and currently best known nonlinearity. It is shown that this method can achieve a better tradeoff between resiliency and nonlinearity than those of the previous research results. [ABSTRACT FROM AUTHOR]