Design of Nonlinear Filters with Guaranteed Lower Bounds on Sequence Complexity

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 239)

Abstract

Sequence generators based on LFSRs are currently used to produce pseudorandom sequences in cryptography. In this paper, binary sequences generated by nonlinearly filtering maximal length sequences are studied. Emphasis is on the parameter linear complexity of the filtered sequences. In fact, a method of computing all the nonlinear filters that generate sequences with a guaranteed linear complexity (\(LC\geq \binom{L}{k}\), where L is the LFSR length and k the filter’s degree) is introduced. The method provides one with a good structural vision on this type of generators as well as a practical criterium to design cryptographic sequence generators for stream ciphers.

Keywords

Nonlinear filter linear complexity cyclotomic coset Boolean function stream cipher cryptography 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    eSTREAM, the ECRYPT Stream Cipher Project, The eSTREAM Portfolio (2012), http://www.ecrypt.eu.org/documents/D.SYM.10-v1.pdf
  2. 2.
    Caballero-Gil, P., Fúster-Sabater, A.: A wide family of nonlinear filter functions with large linear span. Inform. Sci. 164, 197–207 (2004)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Golomb, S.: Shift-Register Sequences, revised edn. Aegean Park Press (1982)Google Scholar
  4. 4.
    Kolokotronis, N., Kalouptsidis, N.: On the linear complexity of nonlinearly filtered PN-sequences. IEEE Trans. Inform. Theory 49, 3047–3059 (2003)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Kolokotronis, N., Limniotis, K., Kalouptsidis, N.: Lower Bounds on Sequence Complexity Via Generalised Vandermonde Determinants. In: Gong, G., Helleseth, T., Song, H.-Y., Yang, K. (eds.) SETA 2006. LNCS, vol. 4086, pp. 271–284. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Limniotis, K., Kolokotronis, N., Kalouptsidis, N.: On the Linear Complexity of Sequences Obtained by State Space Generators. IEEE Trans. Inform. Theory 54, 1786–1793 (2008)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Lidl, R., Niederreiter, H.: Finite Fields. In: Enciclopedia of Mathematics and Its Applications 20, 2nd edn. Cambridge University Press, Cambridge (1997)Google Scholar
  8. 8.
    Peinado, A., Fúster-Sabater, A.: Generation of pseudorandom binary sequences by means of linear feedback shift registers (LFSRs) with dynamic feedback. Mathematical and Computer Modelling 57, 2596–2604 (2013)CrossRefGoogle Scholar
  9. 9.
    Robshaw, M., Billet, O. (eds.): New Stream Cipher Designs. LNCS, vol. 4986. Springer, Heidelberg (2008)MATHGoogle Scholar
  10. 10.
    Rueppel, R.A.: Analysis and Design of Stream Ciphers. Springer, New York (1986)MATHCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Information Security InstituteC.S.I.C.MadridSpain

Personalised recommendations