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On Relationships among Avalanche, Nonlinearity, and Correlation Immunity

  • Yuliang Zheng
  • Xian-Mo Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1976)

Abstract

We establish, for the first time, an explicit and simple lower bound on the nonlinearity N f of a Boolean function f of n variables satisfying the avalanche criterion of degree p, namely, Nf≥ 2n-1 . 2n-1-1/2p. We also show that the lower bound is tight, and identify all the functions whose nonlinearity attains the lower bound. As a further contribution of this paper, we prove that except for very few cases, the sum of the degree of avalanche and the order of correlation immunity of a Boolean function of n variables is atmost n-2. These new results further highlight the significance of the fact that while avalanche property is in harmony with nonlinearity, it goes against correlation immunity.

Key Words

Avalanche Criterion Boolean Functions Correlation Immunity Nonlinearity Propagation Criterion 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Yuliang Zheng
    • 1
  • Xian-Mo Zhang
    • 2
  1. 1.Monash UniversityMelbourneAustralia
  2. 2.The University of WollongongWollongongAustralia

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