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Encyclopedia of Cryptography and Security pp 82–83Cite as

Combination generator

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A combination generator is a running-key generator for stream cipher applications. It is composed of several linear feedback shift registers (LFSRs) whose outputs are combined by a Boolean function to produce the keystream. Then, the output sequence \((s_t)_{t \geq 0}\) of a combination generator composed of n LFSRs is given by

$$ s_t = f(u_t^1, u_t^2,\ldots, u_t^n), \quad\qquad \forall t \geq 0, $$

where \((u_t^i)_{t \geq 0}\) denotes the sequence generated by the ith constituent LFSR and f is a function of n variables. In the case of a combination generator composed of n LFSRs over \({\bf F}_q\), the combining function is a function from \({\bf F}_q^n\) into \({\bf F}_q\).

figure 1_0-387-23483-7_70

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References

  1. Brynielsson, L. (1986). “On the linear complexity of combined shift register sequences.” Advances in Cryptology—EUROCRYPT'85, Lecture Notes in Computer Science, vol. 219, ed. F. Pichler. Springer-Verlag, Berlin, 156–160.

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  2. Canteaut, A. and E. Filiol (2001). “Ciphertext only reconstruction of stream ciphers based on combination generators.” Fast Software Encryption 2000, Lecture Notes in Computer Science, vol. 1978, ed. B. Schneier. Springer-Verlag, Berlin, 165–180.

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  3. Herlestam, T. (1986). “On functions of linear shift register sequences.” Advances in Cryptology—EUROCRYPT'85, Lecture Notes in Computer Science, vol. 219, ed. F. Pichler. Springer-Verlag, Berlin, 119–129.

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Authors
  1. Anne Canteaut
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Editors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

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© 2005 International Federation for Information Processing

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Canteaut, A. (2005). Combination generator. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_70

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