An Braeken: Cryptographic Properties of Symmetric Boolean Functions

Symmetric Boolean functions have the property that that the function value is determined by the weight of the vector. Therefore, these functions are very interesting for hardware and software implementation. In this talk, we analyze the algebraic immunity of symmetric Boolean functions. This property is relevant for offering resistance against algebraic attacks. 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.