On the Algebraic Immunity of Symmetric Boolean Functions

An Braeken; Bart Preneel

Paper 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.

Metadata

Available format(s): PDF PS
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: algebraic immunity symmetric functions nonlinearity
Contact author(s): An Braeken @ esat kuleuven ac be
History: 2005-08-01: revised; 2005-07-30: received; See all versions
Short URL: https://ia.cr/2005/245
License: CC BY

BibTeX

@misc{cryptoeprint:2005/245,
      author = {An Braeken and Bart Preneel},
      title = {On the Algebraic Immunity of Symmetric Boolean Functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2005/245},
      year = {2005},
      url = {https://eprint.iacr.org/2005/245}
}