Correlation matrices

  • Joan Daemen
  • René Govaerts
  • Joos Vandewalle
Session 5: Block Ciphers-Linear Cryptanalysis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1008)


In this paper we introduce the correlation matrix of a Boolean mapping, a useful concept in demonstrating and proving properties of Boolean functions and mappings. It is argued that correlation matrices are the “natural” representation for the proper understanding and description of the mechanisms of linear cryptanalysis [4]. It is also shown that the difference propagation probabilities and the table consisting of the squared elements of the correlation matrix are linked by a scaled Walsh-Hadamard transform.

Key words

Boolean Mappings Linear Cryptanalysis Correlation Matrices 


  1. 1.
    S. W. Golomb, Shift Register Sequences, Holden-Day Inc., San Francisco, 1967.Google Scholar
  2. 2.
    G.Z. Xiao, J.L. Massey, A Spectral Characterization of Correlation-Immune Functions, IEEE Trans. Inform. Theory, Vol. 34, No. 3, 1988, pp. 569–571Google Scholar
  3. 3.
    E. Biham and A. Shamir, Differential Cryptanalysis of of the Data Encryption Standard, Springer-Verlag, 1993.Google Scholar
  4. 4.
    M. Matsui, Linear Cryptanalysis Method for DES Cipher, Advances in Cryptology — Proceedings of Eurocrypt '93, LNCS 765, T. Helleseth, Ed., Springer-Verlag, 1993, pp. 386–397.Google Scholar
  5. 5.
    B. Preneel, Analysis and Design of Cryptographic Hash Functions, Doct. Dissertation K.U.Leuven, January 1993.Google Scholar
  6. 6.
    J. Daemen, Cipher and Hash Function Design. Strategies Based on Linear and Differential Cryptanalysis, Doct. Dissertation K.U.Leuven, March 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Joan Daemen
    • 1
  • René Govaerts
    • 1
  • Joos Vandewalle
    • 1
  1. 1.ESAT-COSICKatholieke Universiteit LeuvenHeverleeBelgium

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