Correlation Properties of Combiners with Memory in Stream Ciphers (Extended Abstract)

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 473)


In stream cipher design pseudo random generators have been proposed which combine the output of one or several LFSRs in order to produce the key stream. For memoryless combiners it is known that the produced sequence has correlation to sums of certain LFSR-sequences whose correlation coefficients c i satisfy the equation Σi c i 2 = 1. It is proved that a corresponding result also holds for combiners with memory.

If correlation probabilities are conditioned on side information, e.g. on known output digits, it is shown that new or stronger correlations may occur. This is exemplified for the summation cipher with two LFSRs where such correlations can be exploited in a known plaintext attack. A cryptanalytic algorithm is given which is shown to be successful for LFSRs of considerable length and with arbitrary feedback connection.


Boolean Function Correlation Property Side Information General Combiner Stream Cipher 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [1]
    W. Feller, An Introduction to Probability Theory and its Applications, Vol 1, John Wiley & Sons, Inc., 1968.Google Scholar
  2. [2]
    W. Meier, O. Staffelbach, Fast Correlation Attacks on Certain Stream Ciphers, Journal of Cryptology, Vol 1, No. 3, pp. 159–176, 1989.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    W. Meier, O. Staffelbach, Nonlinearity Criteria for Cryptographic Functions, Proceedings of Eurocrypt’89, Springer-Verlag, to appear.Google Scholar
  4. [4]
    W. Meier, O. Staffelbach, Correlation Properties of Combiners with Memory in Stream Ciphers, full paper to appear in the Journal of Cryptology.Google Scholar
  5. [5]
    R.A. Rueppel, Correlation Immunity and the Summation Generator, Advances in Cryptology—Crypto’85, Proceedings, pp. 260–272, Springer-Verlag, 1986.Google Scholar
  6. [6]
    R.A. Rueppel, Analysis and Design of Stream Ciphers, Springer-Verlag, 1986.Google Scholar
  7. [7]
    T. Siegenthaler, Correlation-Immunity of Nonlinear Combining Functions for Cryptographic Applications, IEEE Trans. Inform. Theory, Vol IT-30, pp. 776–780, 1984.MathSciNetCrossRefGoogle Scholar
  8. [8]
    O. Staffelbach, W. Meier, Cryptographic Significance of the Carry for Ciphers Based on Integer Addition, Proceedings of Crypto’90, Springer-Verlag, to appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  1. 1.HTL Brugg-WindischWindischSwitzerland
  2. 2.GRETAGRegensdorfSwitzerland

Personalised recommendations