Balanced Boolean Functions with (more than) Maximum Algebraic Immunity

Deepak Kumar Dalai; Subhamoy Maitra

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 Attacks Annihilators Boolean Functions Fast Algebraic Attacks.
Contact author(s): deepak_r @ isical ac in
History: 2006-11-21: received
Short URL: https://ia.cr/2006/434
License: 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},
      url = {https://eprint.iacr.org/2006/434}
}