Paper 2007/290

Construction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity on Odd Number of Variables

Sumanta Sarkar and Subhamoy Maitra

Abstract

In this paper we present a theoretical construction of Rotation Symmetric Boolean Functions (RSBFs) on odd number of variables with maximum possible \ai and further these functions are not symmetric. Our RSBFs are of better nonlinearity than the existing theoretical constructions with maximum possible \ai. To get very good nonlinearity, which is important for practical cryptographic design, we generalize our construction to a construction cum search technique in the RSBF class. We find 7, 9, 11 variable RSBFs with maximum possible \ai having nonlinearities 56, 240, 984 respectively with very small amount of search after our basic construction.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Algebraic ImmunityBoolean FunctionNonlinearityNonsingular MatrixRotational SymmetryWalsh Spectrum.
Contact author(s)
subho @ isical ac in
History
2007-08-07: received
Short URL
https://ia.cr/2007/290
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2007/290,
      author = {Sumanta Sarkar and Subhamoy Maitra},
      title = {Construction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity on Odd Number of Variables},
      howpublished = {Cryptology ePrint Archive, Paper 2007/290},
      year = {2007},
      note = {\url{https://eprint.iacr.org/2007/290}},
      url = {https://eprint.iacr.org/2007/290}
}
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