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Paper: Plateaued Rotation Symmetric Boolean Functions on Odd Number of Variables

Authors:
Alexander Maximov
Martin Hell
Subhamoy Maitra
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URL: http://eprint.iacr.org/2004/144
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Abstract: The class of Rotation Symmetric Boolean Functions (RSBFs) has received serious attention recently in searching functions of cryptographic significance. These functions are invariant under circular translation of indices. In this paper we study such functions on odd number of variables and interesting combinatorial properties related to Walsh spectra of such functions are revealed. In particular we concentrate on plateaued functions (functions with three valued Walsh spectra) in this class and derive necessary conditions for existence of balanced rotation symmetric plateaued functions. As application of our result we show the non existence of 9-variable, 3-resilient RSBF with nonlinearity 240 that has been posed as an open question in FSE 2004. Further we show how one can make efficient search in the space of RSBFs based on our theoretical results and as example we complete the search for unbalanced 9-variable, 3rd order correlation immune plateaued RSBFs with nonlinearity 240.
BibTeX
@misc{eprint-2004-12116,
  title={Plateaued Rotation Symmetric Boolean Functions on Odd Number of Variables},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / boolean functions},
  url={http://eprint.iacr.org/2004/144},
  note={ subho@isical.ac.in 12594 received 21 Jun 2004, last revised 25 Jun 2004},
  author={Alexander Maximov and Martin Hell and Subhamoy Maitra},
  year=2004
}