Skip to main content
SpringerLink
Log in

Analysis of the Linear Complexity in Pseudorandom Sequence Generators

  • Conference paper
Book cover Computational Science and Its Applications – ICCSA 2013 (ICCSA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7975))

Included in the following conference series:

  • 1727 Accesses

Abstract

In this paper, binary sequences generated by nonlinearly filtering maximal length sequences are studied. Specifically, the parameter linear complexity of the filtered sequences has been considered and analyzed. In fact, a method of computing all the nonlinear filters that generate sequences with a cryptographically large linear complexity has been developed. The procedure is based on the concept of equivalence classes of nonlinear filters and on the addition of filters from different classes. Three distinct representations of nonlinear filters have been systematically addressed. The method completes the class of nonlinear filters with guaranteed linear complexity found in the cryptographic literature.

Research partially supported by CDTI (Spain) under Project Cenit- HESPERIA as well as by Ministry of Science and Innovation and European FEDER Fund under Project TIN2011-25452/TSI.

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

Access this chapter

Log in via an institution
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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Nagaraj, N.: One-Time Pad as a nonlinear dynamical system. Commun Nonlinear Sci. Numer Simulat. 17, 4029–4036 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. eSTREAM, the ECRYPT Stream Cipher Project,The eSTREAM Portfolio (2012), http://www.ecrypt.eu.org/documents/D.SYM.10-v1.pdf

  3. Robshaw, M., Billet, O. (eds.): New Stream Cipher Designs. LNCS, vol. 4986. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  4. Menezes, A.J., et al.: Handbook of Applied Cryptography. CRC Press, New York (1997)

    MATH  Google Scholar 

  5. Paar, C., Pelzl, J.: Understanding Cryptography. Springer, Heidelberg (2010)

    Book  MATH  Google Scholar 

  6. Rueppel, R.A.: Analysis and Design of Stream Ciphers. Springer, New York (1986)

    Book  MATH  Google Scholar 

  7. Tan, S.K., Guan, S.U.: Evolving cellular automata to generate nonlinear sequences with desirable properties. Applied Soft Computing 7, 1131–1134 (2007)

    Article  Google Scholar 

  8. Golomb, S.: Shift-Register Sequences, revised edn. Aegean Park Press, Laguna Hills (1982)

    Google Scholar 

  9. Fúster-Sabater, A., Caballero-Gil, P., Delgado-Mohatar, O.: Deterministic Computation of Pseudorandomness in Sequences of Cryptographic Application. In: Allen, G., Nabrzyski, J., Seidel, E., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2009, Part I. LNCS, vol. 5544, pp. 621–630. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Fúster-Sabater, A., Caballero-Gil, P.: Chaotic modelling of the generalized self-shrinking generator. Appl. Soft Comput. 11, 1876–1880 (2011)

    Article  Google Scholar 

  11. A. Marsaglia, Test of DIEHARD (1998), http://stat.fsu.edu/pub/diehard/

  12. Massey, J.L.: Shift-Register Synthesis and BCH Decoding. IEEE Trans. Information Theory 15(1), 122–127 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  13. Caballero-Gil, P., Fúster-Sabater, A.: A wide family of nonlinear filter functions with large linear span. Inform. Sci. 164, 197–207 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. 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)

    Article  MathSciNet  Google Scholar 

  15. 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)

    Chapter  Google Scholar 

  16. Lee, K., O’Sullivan, M.E.: List decoding of Hermitian codes using Gröbner bases. Journal of Symbolic Computation 44(12), 1662–1675 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Respondek, J.S.: On the confluent Vandermonde matrix calculation algorithm. Applied Mathematics Letters 24(2), 103–106 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Respondek, J.S.: Numerical recipes for the high efficient inverse of the confluent Vandermonde matrices. Applied Mathematics and Computation 218(5), 2044–2054 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Lidl, R., Niederreiter, H.: Finite Fields. In: Enciclopedia of Mathematics and Its Applications, 2nd edn., vol. 20. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  20. Ronjom, S., Helleseth, T.: A New Attack on the Filter Generator. IEEE Trans. Information Theory 53(5), 1752–1758 (2007)

    Article  MathSciNet  Google Scholar 

  21. Rønjom, S., Cid, C.: Nonlinear Equivalence of Stream Ciphers. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 40–54. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Information Security Institute, C.S.I.C., Serrano 144, 28006, Madrid, Spain

    Amparo Fúster-Sabater

Authors
  1. Amparo Fúster-Sabater
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. L-I.S.U.T. - D.A.P.I.t. Facoltà Ingegneria, Università degli Studi della Basilicata, Viale dell’Ateneo Lucano, 10, 85100, Potenza, Italy

    Beniamino Murgante

  2. Covenant University, Canaanland OTA, Nigeria

    Sanjay Misra

  3. Partimento di Scienze e Tecnologie per LAgricoltura, le Foreste, la Natura e lEnergia, Università degli Studi della Tuscia, Via S. Camillo de Lellis, snc, 01100, Viterbo, Italy

    Maurizio Carlini

  4. Dipartimento di Scienze dell’Ingegneria Civile e dell’Architecttura, Politecnico di Bari, Via Orabona, 4, 70125, Bari, Italy

    Carmelo M. Torre

  5. International University VNU-HCM, Quarter 6, Linh Trung, Thu Duc, Ho Chi Minh City, Vietnam

    Hong-Quang Nguyen

  6. School of Business Systems, Monash University, 3800, Clayton, VIC, Australia

    David Taniar

  7. Department of Intelligent Informatics, Kyushu Sangyo University, 2-3-1 Matsukadai, 813-8503, Higashi-ku, Fukuoka, Japan

    Bernady O. Apduhan

  8. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fúster-Sabater, A. (2013). Analysis of the Linear Complexity in Pseudorandom Sequence Generators. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2013. ICCSA 2013. Lecture Notes in Computer Science, vol 7975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39640-3_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39640-3_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39639-7

  • Online ISBN: 978-3-642-39640-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation