Skip to main content

A Simple Linearisation of the Self-shrinking Generator

  • Conference paper
  • First Online:
Computer Aided Systems Theory – EUROCAST 2015 (EUROCAST 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9520))

Included in the following conference series:

  • 1539 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Paul, G., Maitra, S.: RC4 Stream Cipher and Its Variants. Discrete Mathematics and Its Applications. CRC Press, Taylor & Francis Group, Boca Raton (2012)

    MATH  Google Scholar 

  2. Bluetooth, Specifications of the Bluetooth system, Version 1.1. http://www.bluetooth.com/

  3. eSTREAM, the ECRYPT Stream Cipher Project, Call for Primitives. http://www.ecrypt.eu.org/stream/

  4. Yet Another SSL (YASSL). http://www.yassl.com

  5. Golomb, S.W.: Shift Register-Sequences. Aegean Park Press, Laguna Hill (1982)

    MATH  Google Scholar 

  6. Menezes, A.J., et al.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

  8. Fúster-Sabater, A.: Linear solutions for irregularly decimated generators of cryptographic sequences. Int. J. Nonlinear Sci. Numer. Simul. 15(6), 377–385 (2014)

    Article  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  10. Hu, Y., Xiao, G.: Generalized self-shrinking generator. IEEE Trans. Inf. Theory 50(4), 714–719 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  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. Fúster-Sabater, A., Caballero-Gil, P.: Linear solutions for cryptographic nonlinear sequence generators. Phys. Lett. A 369, 432–437 (2007)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  15. Wolfram, S.: Cellular automata as simple self-organizing system. Caltrech preprint CALT 68–938 (1982)

    Google Scholar 

  16. Blackburn, S.R.: The linear complexity of the self-shrinking generator. IEEE Trans. Inf. Theory 45(6), 2073–2077 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  17. Fúster-Sabater, A., Caballero-Gil, P.: Strategic attack on the shrinking generator. Theoret. Comput. Sci. 409(3), 530–536 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  19. Massey, J.L.: Shift-register synthesis and BCH decoding. IEEE Trans. Inf. Theory 15(1), 122–127 (1969)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sara D. Cardell .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Cardell, S.D., Fúster-Sabater, A. (2015). A Simple Linearisation of the Self-shrinking Generator. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2015. EUROCAST 2015. Lecture Notes in Computer Science(), vol 9520. Springer, Cham. https://doi.org/10.1007/978-3-319-27340-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-27340-2_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27339-6

  • Online ISBN: 978-3-319-27340-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics