Paper 2000/050

Spectral Analysis of High Order Correlation Immune Functions

Yuriy Tarannikov and Denis Kirienko

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.

Metadata
Available format(s)
PS
Category
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Boolean functioncorrelation immunityresiliencyWalsh Transform
Contact author(s)
yutaran @ mech math msu su
History
2000-10-17: revised
2000-10-06: received
See all versions
Short URL
https://ia.cr/2000/050
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2000/050,
      author = {Yuriy Tarannikov and Denis Kirienko},
      title = {Spectral Analysis of High Order Correlation Immune Functions},
      howpublished = {Cryptology ePrint Archive, Paper 2000/050},
      year = {2000},
      note = {\url{https://eprint.iacr.org/2000/050}},
      url = {https://eprint.iacr.org/2000/050}
}
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