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Paper: Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity

Authors:
Deepak Kumar Dalai
Subhamoy Maitra
Sumanta Sarkar
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URL: http://eprint.iacr.org/2005/229
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Abstract: So far there is no systematic attempt to construct Boolean functions with maximum annihilator immunity. In this paper we present a construction keeping in mind the basic theory of annihilator immunity. This construction provides functions with the maximum possible annihilator immunity and the weight, nonlinearity and algebraic degree of the functions can be properly calculated under certain cases. The basic construction is that of symmetric Boolean functions and applying linear transformation on the input variables of these functions,one can get a large class of non-symmetric functions too. Moreover, we also study several other modifications on the basic symmetric functions to identify interesting non symmetric functions with maximum annihilator immunity. In the process we also present an algorithm to compute the Walsh spectra of a symmetric Boolean function with $O(n^2)$ time and $O(n)$ space complexity.
BibTeX
@misc{eprint-2005-12564,
  title={Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / Algebraic Attack, Algebraic Degree, Algebraic Immunity,},
  url={http://eprint.iacr.org/2005/229},
  note={ subho@isical.ac.in 12979 received 15 Jul 2005, last revised 15 Jul 2005},
  author={Deepak Kumar Dalai and Subhamoy Maitra and Sumanta Sarkar},
  year=2005
}