Abstract:In 2009, based on a combinatorial conjecture, Tu and Deng constructed a class of Boolean functions in even variables with optimal algebraic immunity, optimal algebraic degree and good nonlinearity. This class of functions is called the Tu-Deng function. Based on the same conjecture, they also proposed a class of resilient functions in even variables with suboptimal algebraic immunity, optimal algebraic degree and good nonlinearity. By studying the cryptographic properties of the concatenation of two Boolean functions derived from the Tu-Deng function, based on Tu-Deng's conjecture, a class of resilient Boolean functions in odd variables is proposed. This class of functions has suboptimal algebraic immunity, optimal algebraic degree and good nonlinearity.