An Improvement of Correlation Analysis for Vectorial Boolean Functions

  • Youssef HarmouchEmail author
  • Rachid El Kouch
  • Hussain Ben-Azza
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11627)


This paper investigates the correlation of n-bit to m-bit vectorial Boolean functions denoted by F. At Crypto 2000, Zhang and Chan showed that the maximum of linear approximations for F with Boolean functions g have a higher bias than those based on the usual correlation attack. The correlation for this linear approximation has been named the maximum correlation and has been shown to be a useful tool for correlation attack resistance. In this work, we deal with two issues. Firstly, we show that combining F with any g does not always increase the bias as stated by several works. To justify such results, we demonstrate the exact correlation link between F, g and the combination of F by g. Secondly, we provide the exact condition in which the correlation coefficients for this approximation are maximum.


Correlation attack Vectorial boolean function Bias Maximum correlator Stream cipher 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Youssef Harmouch
    • 1
    Email author
  • Rachid El Kouch
    • 1
  • Hussain Ben-Azza
    • 2
  1. 1.Department of Mathematics, Computing and NetworksNational Institute of Posts and TelecommunicationsRabatMorocco
  2. 2.Moulay Ismail University, ENSAM-MeknèsMeknesMorocco

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