Paper 2006/434

Balanced Boolean Functions with (more than) Maximum Algebraic Immunity

Deepak Kumar Dalai and Subhamoy Maitra

Abstract

In this correspondence, construction of balanced Boolean functions with maximum possible algebraic (annihilator) immunity (AI) is studied with an additional property which is necessary to resist fast algebraic attack. The additional property considered here is, given an $n$-variable ($n$ even) balanced function $f$ with maximum possible AI $\frac{n}{2}$, and given two $n$-variable Boolean functions $g, h$ such that $fg = h$, if $\deg(h) = \frac{n}{2}$, then $\deg(g)$ must be greater than or equal to $\frac{n}{2}$. Our results can also be used to present theoretical construction of resilient Boolean functions having maximum possible AI.

Metadata
Available format(s)
PDF PS
Category
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Algebraic AttacksAnnihilatorsBoolean FunctionsFast Algebraic Attacks.
Contact author(s)
deepak_r @ isical ac in
History
2006-11-21: received
Short URL
https://ia.cr/2006/434
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2006/434,
      author = {Deepak Kumar Dalai and Subhamoy Maitra},
      title = {Balanced Boolean Functions with (more than) Maximum Algebraic Immunity},
      howpublished = {Cryptology ePrint Archive, Paper 2006/434},
      year = {2006},
      note = {\url{https://eprint.iacr.org/2006/434}},
      url = {https://eprint.iacr.org/2006/434}
}
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