1-Resilient Boolean Function with Optimal Algebraic Immunity

In this paper, We propose a class of 2k-variable Boolean functions, which have optimal algebraic degree, high nonlinearity, and are 1-resilient. These functions have optimal algebraic immunity when k > 2 and u = -2^l; 0 = 2 and u = 2^l; 0 = 2, otherwise u

A general conjecture similar to T-D conjecture and its applications in constructing Boolean functions with optimal algebraic immunity

In this paper, we propose two classes of 2k-variable Boolean functions, which have optimal algebraic immunity under the assumption that a general combinatorial conjecture is correct. These functions also have high algebraic degree and high nonlinearity. One class contain more bent functions, and the other class are balanced