Symmetric Boolean functions depending on an odd number of variables with maximum algebraic immunity
Na Li, Wen‐Feng Qi · IEEE Transactions on Information Theory · 2006
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 /spl lceil/n/2/spl rceil/. 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.