International Association for Cryptologic Research

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Paper: Spectral Analysis of High Order Correlation Immune Functions

Authors:
Yuriy Tarannikov
Denis Kirienko
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URL: http://eprint.iacr.org/2000/050
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Abstract: We use the recent results on the spectral structure of correlation immune and resilient Boolean functions for the investigations of high order correlation immune functions. At first, we give simple proofs of some theorems where only long proofs were known. Next, we introduce the matrix of nonzero Walsh coefficients and establish important properties of this matrix. We use these properties to prove the nonexistence of some high order correlation immune functions. Finally, we establish the order of magnitude for the number of (n-4)th order correlation immune functions of n variables.
BibTeX
@misc{eprint-2000-11394,
  title={Spectral Analysis of High Order Correlation Immune Functions},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / Boolean function, correlation immunity, resiliency, Walsh Transform},
  url={http://eprint.iacr.org/2000/050},
  note={ yutaran@mech.math.msu.su 11247 received 6 Oct 2000, revised 17 Oct 2000},
  author={Yuriy Tarannikov and Denis Kirienko},
  year=2000
}