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Paper: Classification of Highly Nonlinear Boolean Power Functions with a Randomised Algorithm for Checking Normality

Authors:
An Braeken
Christopher Wolf
Bart Preneel
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URL: http://eprint.iacr.org/2004/214
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Abstract: A Boolean function is called normal if it is constant on flats of certain dimensions. This property is relevant for the construction and analysis of cryptosystems. This paper presents an asymmetric Monte Carlo algorithm to determine whether a given Boolean function is normal. Our algorithm is far faster than the best known (deterministic) algorithm of Daum et al. In a first phase, it checks for flats of low dimension whether the given Boolean function is constant on them and combines such flats to flats of higher dimension in a second phase. This way, the algorithm is much faster than exhaustive search. Moreover, the algorithm benefits from randomising the first phase. In addition, by evaluating several flats implicitly in parallel, the time-complexity of the algorithm decreases further. As an application, we determine the level of normality for several, highly nonlinear Boolean power functions.
BibTeX
@misc{eprint-2004-12186,
  title={Classification of Highly Nonlinear Boolean Power Functions with a Randomised Algorithm for Checking Normality},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / boolean functions, normality, power-functions, Monte Carlo},
  url={http://eprint.iacr.org/2004/214},
  note={ Christopher.Wolf@Esat.KULeuven.ac.be 12888 received 30 Aug 2004, last revised 15 Apr 2005},
  author={An Braeken and Christopher Wolf and Bart Preneel},
  year=2004
}