On the Algebraic Immunity of Symmetric Boolean Functions

In this paper, we analyse the algebraic immunity of symmetric Boolean functions. We identify a set of lowest degree annihilators for symmetric functions and propose an efficient algorithm for computing the algebraic immunity of a symmetric function. The existence of several symmetric functions with maximum algebraic immunity is proven. In this way, a new class of function which have good implementation properties and maximum algebraic immunity is found. We also investigate the existence of symmetric functions with high nonlinearity and reasonable order of algebraic immunity. Finally, we give suggestions how to use symmetric functions in a stream cipher. 1 Introdution Symmetric functions have the property that the function value is determined by the weight of the vector. Therefore, a symmetric function in n variables can be defined by a vector of length n+1 which represents the function values of the different weights of the vectors. For this reason, symmetric functions are very inter...

• Type: Conference
• Year: 2005
• Where: INDOCRYPT
• Authors: An Braeken, Bart Preneel
• Keywords: Algebraic Immunity, INDOCRYPT 2005, Maximum Algebraic Immunity, Symmetric Function