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

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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(n2) time and O(n) space complexity.

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Authors and Affiliations

  1. Applied Statistics Unit, Indian Statistical Institute, 203 B T Road, Kolkata, 700 108, India

    Deepak Kumar Dalai, Subhamoy Maitra & Sumanta Sarkar

Authors
  1. Deepak Kumar Dalai
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  2. Subhamoy Maitra
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  3. Sumanta Sarkar
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Correspondence to Subhamoy Maitra.

Additional information

Communicated by A.J. Menezes

We use the term “Annihilator Immunity” instead of “Algebraic Immunity” referred in the recent papers [3–5, 9, 18, 19]. Please see Remark 1 for the details of this notational change

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Dalai, D.K., Maitra, S. & Sarkar, S. Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity. Des Codes Crypt 40, 41–58 (2006). https://doi.org/10.1007/s10623-005-6300-x

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  • DOI: https://doi.org/10.1007/s10623-005-6300-x

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