A note on the construction and upper bounds of correlation-immune functions

  • Markus Schneider
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1355)


In this paper, an algorithm for the construction of correlation-immune functions is given. It will be shown that the proposed algorithm provides a method to construct every mth order correlationimmune function. Besides correlation-immunity, also other properties of Boolean functions, like Hamming weight, can be taken into account. The complexity analysis of the proposed algorithm leads to a new upper bound for the number of specified correlation-immune functions and correlation-immune functions in general, depending on the number of input variables n and the order of correlation-immunity.


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  1. [CCCS 91]
    P. Camion, C. Carlet, P. Charpin, N. Sendrier: ‘On Correlation-immune Functions', Advances in Cryptology: Crypto '91, Proceedings, Lecture Notes on Computer Science 576, 1991, p. 86–100Google Scholar
  2. [GuMa 88]
    X. Guo-Zhen, J. Massey: ‘A Spectral Characterization of CorrelationImmune Combining Functions', IEEE Transactions on Information Theory, Vol. 34, No.3, May 1988, p. 569–571CrossRefGoogle Scholar
  3. [SeZh 93]
    J. Seberry, X. Zhang, Y. Zheng: ‘On Constructions and Nonlinearity of Correlation Immune Functions', Advances in Cryptology: Eurocrypt '93, Proceedings, Lecture Notes on Computer Science 765, 1993, p. 181–199Google Scholar
  4. [Sieg 84]
    T. Siegenthaler: ‘Correlation-Immunity of Nonlinear Combining Functions of Cryptographic Applications', IEEE Transactions on Information Theory, Vol. IT-30, No.5, Sep. 1984, p. 776–780CrossRefGoogle Scholar
  5. [Sieg 85]
    T. Siegenthaler: ‘Decrypting a Class of Stream Ciphers Using Ciphertext Only', IEEE Transactions on Computers, Vol. C-34, No.1, Jan. 1985, p. 81–85Google Scholar
  6. [YaGu 95]
    Y. Yang, B. Guo: ‘Further Enumerating Boolean Functions of Cryptographic Significance', Journal of Cryptology, 1995, 8: p. 115–122MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Markus Schneider
    • 1
  1. 1.Lehrgebiet KommunikationssystemeUniversity of HagenHagenGermany

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