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Combination Generator

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Encyclopedia of Cryptography and Security

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Related Concepts

Boolean Functions; Linear Feedback Shift Register; Stream Cipher

Definition

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 as depicted on Fig. 1. Then, the output sequence \({({s}_{t})}_{t\geq 0}\) of a combination generator composed of \(n\) LFSRs is given by

$$ {s}_{t} = f\left ({u}_{t}^{1},{u}_{ t}^{2},\ldots,{u}_{ t}^{n}\right )\!,\qquad \forall t \geq 0, $$

where \({\left ({u}_{t}^{i}\right )}_{t\geq 0}\) denotes the sequence generated by the \(i\)-th constituent LFSR and \(f\) is a function of \(n\) variables. In the case of a combination generator composed of \(n\) LFSR over F q, the combining function is a function from F q n into F q.

Combination Generator. Fig. 1
figure 1_338

Combination generator

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Recommended Reading

  1. Brynielsson L (1986) On the linear complexity of combined shift register sequences. In: Advances in cryptology - EUROCRYPT ’85. Lecture notes in computer science, vol 219. Springer, Heidelberg, pp 156–160

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  2. Canteaut A, Filiol E (2001) Ciphertext only reconstruction of stream ciphers based on combination generators. In: Fast software encryption – FSE 2000. Lecture notes in computer science, vol 1978. Springer, Heidelberg, pp 165–180

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  3. Herlestam T (1986) On functions of linear shift register sequences. In: Advances in cryptology – EUROCRYPT ’85. Lecture notes in computer science, vol 219. Springer, Heidelberg, pp 119–129

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  4. Göttfert R, Niederreiter H (1995) On the minimal polynomial of the product of linear recurring sequences. Finite Fields Appl 1(2):204–218

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  5. Hell M, Johansson T, Brynielsson L (2009) An overview of distinguishing attacks on stream ciphers. Cryptogr Commun 1(1):71–94

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  6. Johansson T, Meier W, Muller F (2006) Cryptanalysis of Achterbahn. In: Fast software encryption – FSE 2006. Lecture notes in computer science, vol 4047. Springer, Heidelberg, pp 1–14

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  7. Naya-Plasencia M (2007) Cryptanalysis of Achterbahn-128/80. In: Fast software encryption – FSE 2007. Lecture notes in computer science, vol 4593. Springer, Heidelberg, pp 73–86

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  8. Rueppel RA, Staffelbach OJ (1987) Products of linear recurring sequences with maximum complexity. IEEE Trans Inform Theory 33(1):124–131

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Author information

Authors and Affiliations

  1. Project-Team SECRET, INRIA Paris-Rocquencourt, B.P. 105, 78153, Le Chesnay, France

    Anne Canteaut (Dr.)

Authors
  1. Anne Canteaut
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Editors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

  2. Center for Secure Information Systems, George Mason University, Fairfax, VA, 22030-4422, USA

    Sushil Jajodia

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Canteaut, A. (2011). Combination Generator. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_338

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