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Paper: On the Algebraic Immunity of Symmetric Boolean Functions

Authors:
An Braeken
Bart Preneel
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URL: http://eprint.iacr.org/2005/245
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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.
BibTeX
@misc{eprint-2005-12579,
  title={On the Algebraic Immunity of Symmetric Boolean Functions},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / algebraic immunity, symmetric functions, nonlinearity},
  url={http://eprint.iacr.org/2005/245},
  note={ An.Braeken@esat.kuleuven.ac.be 12996 received 26 Jul 2005, last revised 1 Aug 2005},
  author={An Braeken and Bart Preneel},
  year=2005
}