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Highly nonlinear 0–1 balanced boolean functions satisfying strict avalanche criterion (extended abstract)

  • Jennifer Seberry
  • Xian-Mo Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 718)

Abstract

Nonlinearity, 0–1 balancedness and strict avalanche criterion (SAC) are important criteria for cryptographic functions. Bent functions have maximum nonlinearity and satisfy SAC however they are not 0–1 balanced and hence cannot be directly used in many cryptosystems where 0–1 balancedness is needed. In this paper we construct

  1. (i)

    0–1 balanced boolean functions on V2k+1 (k≥1) having nonlinearity 22k−2k and satisfying SAC,

     
  2. (ii)

    0–1 balanced boolean functions on V2k (k≥2) having nonlinearity 22k−1−2k and satisfying SAC.

     

We demonstrate that the above nonlinearities are very high not only for the 0–1 balanced functions satisfying SAC but also for all 0–1 balanced functions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Jennifer Seberry
    • 1
  • Xian-Mo Zhang
    • 1
  1. 1.Department of Computer ScienceThe University of WollongongWollongongAustralia

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