Cryptology ePrint Archive: Report 2005/245

On the Algebraic Immunity of Symmetric Boolean Functions

An Braeken and Bart Preneel

Abstract: 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.

Category / Keywords: secret-key cryptography / algebraic immunity, symmetric functions, nonlinearity

Date: received 26 Jul 2005, last revised 1 Aug 2005

Contact author: An Braeken at esat kuleuven ac be

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Version: 20050801:143758 (All versions of this report)

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