International Conference on Cryptology in India

INDOCRYPT 2004: Progress in Cryptology - INDOCRYPT 2004 pp 92-106

Results on Algebraic Immunity for Cryptographically Significant Boolean Functions

  • Deepak Kumar Dalai
  • Kishan Chand Gupta
  • Subhamoy Maitra
Conference paper

DOI: 10.1007/978-3-540-30556-9_9

Volume 3348 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Dalai D.K., Gupta K.C., Maitra S. (2004) Results on Algebraic Immunity for Cryptographically Significant Boolean Functions. In: Canteaut A., Viswanathan K. (eds) Progress in Cryptology - INDOCRYPT 2004. INDOCRYPT 2004. Lecture Notes in Computer Science, vol 3348. Springer, Berlin, Heidelberg

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