A Simple Linearisation of the Self-shrinking Generator

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9520)


Nowadays stream ciphers are the fastest among the encryption procedures, thus they are performed in many practical applications. Irregularly decimated generators are very simple sequence generators to be used as keystream generators in stream ciphers. In this paper, a linearisation method for the self-shrinking generator has been developed. The proposal defines linear structures based on cellular automata (rules 102 or 60) able to generate the self-shrunken sequence. The obtained cellular automata are simple, easy to be implemented and can be extended to other sequence generators in a range of cryptographic interest.


Self-shrinking generator Self-shrunken sequence Cellular automata Rule 102 Rule 60 Stream cipher Cryptography 



The work of the first author was partially supported by Generalitat Valenciana (Spain) with reference APOSTD/2013/081 and by FAPESP with number of process 2015/07246-0. The work of the second author was supported by Ministerio de Ciencia e Innovación (Spain) under Project TIN2014-55325C2-1-R and by Comunidad de Madrid (Spain) under Project CIBERDINE, S2013/ICE3095-CM.


  1. 1.
    Paul, G., Maitra, S.: RC4 Stream Cipher and Its Variants. Discrete Mathematics and Its Applications. CRC Press, Taylor & Francis Group, Boca Raton (2012)MATHGoogle Scholar
  2. 2.
    Bluetooth, Specifications of the Bluetooth system, Version 1.1.
  3. 3.
    eSTREAM, the ECRYPT Stream Cipher Project, Call for Primitives.
  4. 4.
    Yet Another SSL (YASSL).
  5. 5.
    Golomb, S.W.: Shift Register-Sequences. Aegean Park Press, Laguna Hill (1982)MATHGoogle Scholar
  6. 6.
    Menezes, A.J., et al.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)MATHGoogle Scholar
  7. 7.
    Peinado, A., Fúster-Sabater, A.: Generation of pseudorandom binary sequences by means of LFSRs with dynamic feedback. Math. Comput. Model. 57(11–12), 2596–2604 (2013)CrossRefGoogle Scholar
  8. 8.
    Fúster-Sabater, A.: Linear solutions for irregularly decimated generators of cryptographic sequences. Int. J. Nonlinear Sci. Numer. Simul. 15(6), 377–385 (2014)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Meier, W., Staffelbach, O.: The self-shrinking generator. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 205–214. Springer, Heidelberg (1995) CrossRefGoogle Scholar
  10. 10.
    Hu, Y., Xiao, G.: Generalized self-shrinking generator. IEEE Trans. Inf. Theory 50(4), 714–719 (2004)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Das, A.K., Ganguly, A., Dasgupta, A., Bhawmik, S., Chaudhuri, P.P.: Efficient characterisation of cellular automata. IEE Proc. E: Comput. Digit. Tech. 137(1), 81–87 (1990)Google Scholar
  12. 12.
    Fúster-Sabater, A., Caballero-Gil, P.: Linear solutions for cryptographic nonlinear sequence generators. Phys. Lett. A 369, 432–437 (2007)CrossRefMATHGoogle Scholar
  13. 13.
    Fúster-Sabater, A., Pazo-Robles, M.E., Caballero-Gil, P.: A simple linearization of the self-shrinking generator by means of cellular automata. Neural Netw. 23(3), 461–464 (2010)CrossRefGoogle Scholar
  14. 14.
    Coppersmith, D., Krawczyk, H., Mansour, Y.: The shrinking generator. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 22–39. Springer, Heidelberg (1994) CrossRefGoogle Scholar
  15. 15.
    Wolfram, S.: Cellular automata as simple self-organizing system. Caltrech preprint CALT 68–938 (1982)Google Scholar
  16. 16.
    Blackburn, S.R.: The linear complexity of the self-shrinking generator. IEEE Trans. Inf. Theory 45(6), 2073–2077 (1999)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Fúster-Sabater, A., Caballero-Gil, P.: Strategic attack on the shrinking generator. Theoret. Comput. Sci. 409(3), 530–536 (2008)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Caballero-Gil, P., Fúster-Sabater, A., Pazo-Robles, M.E.: Using linear equations to model nonlinear cryptographic sequences. Int. J. nonlinear Sci. Numer. Simul. 11(3), 165–172 (2010)CrossRefGoogle Scholar
  19. 19.
    Massey, J.L.: Shift-register synthesis and BCH decoding. IEEE Trans. Inf. Theory 15(1), 122–127 (1969)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Departamento de Estadística e Investigación OperativaUniversidad de AlicanteAlicanteSpain
  2. 2.Instituto de Tecnologías Físicas y de la Información (CSIC)MadridSpain

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