Symmetric Boolean functions depending on an odd number of variables with maximum algebraic immunity

To resist algebraic attacks, Boolean functions should possess high algebraic immunity. In 2003, Courtois and Meier showed that the algebraic immunity of an n-variable Boolean function is upper bounded by ┌n/2┐. And then several papers studied how to find symmetric Boolean functions with maximum algebraic immunity. In this correspondence, we prove that for each odd n, there is exactly one trivially balanced n-variable symmetric Boolean function achieving the maximum algebraic immunity.