Designs, Codes and Cryptography

, Volume 40, Issue 1, pp 41–58

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

  • Deepak Kumar Dalai
  • Subhamoy Maitra
  • Sumanta Sarkar
Article

DOI: 10.1007/s10623-005-6300-x

Cite this article as:
Dalai, D.K., Maitra, S. & Sarkar, S. Des Codes Crypt (2006) 40: 41. doi:10.1007/s10623-005-6300-x

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.

Keywords

Algebraic attack Algebraic degree Algebraic immunity Annihilator Annihilator immunity Balancedness Boolean functions Krawtchouk polynomials Nonlinearity Symmetric Boolean functions 

AMS Classification

94A60 06E30 

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Deepak Kumar Dalai
    • 1
  • Subhamoy Maitra
    • 1
  • Sumanta Sarkar
    • 1
  1. 1.Applied Statistics UnitIndian Statistical InstituteKolkataIndia