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 1resilient. These functions have optimal algebraic immunity when k > 2 and u = −2, 0 ≤ l < k. Based on a general combinatorial conjecture, algebraic immunity of these functions is optimal when k > 2 and u = 2, 0 ≤ l < k. If the general combinatorial conjecture and a new assumption are both true, algebraic immunity of our functions is also optimal when k > 2, u 6= ±2, 0 ≤ l < k.