Results on Algebraic Immunity for Cryptographically Significant Boolean Functions

  • Deepak Kumar Dalai
  • Kishan Chand Gupta
  • Subhamoy Maitra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3348)

Abstract

Recently algebraic attack has received a lot of attention in cryptographic literature. It has been observed that a Boolean function f, interpreted as a multivariate polynomial over GF(2), should not have low degree multiples when used as a cryptographic primitive. In this paper we show that high nonlinearity is a necessary condition to resist algebraic attack and explain how the Walsh spectra values are related to the algebraic immunity (resistance against algebraic attack) of a Boolean function. Next we present enumeration results on linearly independent annihilators. We also study certain classes of highly nonlinear resilient Boolean functions for their algebraic immunity.

Keywords

Algebraic Attacks Annihilators Boolean Functions Nonlinearity Walsh Spectra 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Deepak Kumar Dalai
    • 1
  • Kishan Chand Gupta
    • 1
  • Subhamoy Maitra
    • 1
  1. 1.Applied Statistics UnitIndian Statistical InstituteCalcuttaIndia

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