Skip to main content
SpringerLink
Log in

Multisequences with high joint nonlinear complexity

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

We introduce the new concept of joint nonlinear complexity for multisequences over finite fields and we analyze the joint nonlinear complexity of two families of explicit inversive multisequences. We also establish a probabilistic result on the behavior of the joint nonlinear complexity of random multisequences over a fixed finite field.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Breiman L.: Probability. SIAM, Philadelphia (1992).

  2. Dawson E., Simpson L.: Analysis and design issues for synchronous stream ciphers. In: Niederreiter H. (ed.) Coding Theory and Cryptology. Lecture Notes Series Institute of Mathematical Sciences at the National University of Singapore, vol. 1, pp. 49–90. World Scientific Publishing, River Edge (2002).

  3. Eichenauer-Herrmann J.: Statistical independence of a new class of inversive congruential pseudorandom numbers. Math. Comput. 60, 375–384 (1993).

  4. Erdmann D., Murphy S.: An approximate distribution for the maximum order complexity. Des. Codes Cryptogr. 10, 325–339 (1997).

  5. Gutierrez J., Shparlinski I.E., Winterhof A.: On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators. IEEE Trans. Inf. Theory 49, 60–64 (2003).

  6. Hawkes P., Rose G.G.: Exploiting multiples of the connection polynomial in word-oriented stream ciphers. In: Okamoto T. (ed.) Advances in Cryptology—ASIACRYPT 2000 (Kyoto). Lecture Notes in Computer Science, vol. 1976, pp. 303–316. Springer, Berlin (2000).

  7. Jansen C.J.A.: Investigations on nonlinear streamcipher systems: construction and evaluation methods. Ph.D. Thesis, TU Delft (1989).

  8. Jansen C.J.A.: The maximum order complexity of sequence ensembles. In: Davies D.W. (ed.) Advances in Cryptology—EUROCRYPT ’91. Lecture Notes in Computer Science, vol. 547, pp. 153–159. Springer, Berlin (1991).

  9. Jansen C.J.A., Boekee D.E.: The shortest feedback shift register that can generate a given sequence. In: Brassard G. (ed.) Advances in Cryptology—CRYPTO ’89. Lecture Notes in Computer Science, vol. 435, pp. 90–99. Springer, Berlin (1990).

  10. Lidl R., Niederreiter H.: Finite Fields. Cambridge University Press, Cambridge (1997).

  11. Limniotis K., Kolokotronis N., Kalouptsidis N.: Nonlinear complexity of binary sequences and connections with Lempel–Ziv compression. In: Gong G. et al. (eds.) Sequences and Their Applications—SETA 2006. Lecture Notes in Computer Science, vol. 4086, pp. 168–179. Springer, Berlin (2006).

  12. Limniotis K., Kolokotronis N., Kalouptsidis N.: On the nonlinear complexity and Lempel–Ziv complexity of finite length sequences. IEEE Trans. Inf. Theory 53, 4293–4302 (2007).

  13. Loève M.: Probability Theory, 3rd edn. Van Nostrand Reinhold, New York (1963).

  14. Meidl W., Winterhof A.: On the linear complexity profile of explicit nonlinear pseudorandom numbers. Inf. Process. Lett. 85, 13–18 (2003).

  15. Meidl W., Winterhof A.: On the linear complexity profile of some new explicit inversive pseudorandom numbers. J. Complex. 20, 350–355 (2004).

  16. Meidl W., Winterhof A.: On the joint linear complexity profile of explicit inversive multisequences. J. Complex. 21, 324–336 (2005).

  17. Meidl W., Winterhof A.: Linear complexity of sequences and multisequences. In: Mullen G.L., Panario D. (eds.) Handbook of Finite Fields, pp. 324–336. CRC Press, Boca Raton (2013).

  18. Niederreiter H., Winterhof A.: Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators. Acta Arith. 93, 387–399 (2000).

  19. Niederreiter H., Xing C.P.: Sequences with high nonlinear complexity. IEEE Trans. Inf. Theory 60, 6696–6701 (2014).

  20. Xing C.P.: Multi-sequences with almost perfect linear complexity profile and function fields over finite fields. J. Complex. 16, 661–675 (2000).

Download references

Acknowledgments

The first author is supported by the Austrian Science Fund (FWF) Project No. M 1767-N26.

Author information

Authors and Affiliations

  1. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstr. 69, 4040, Linz, Austria

    Wilfried Meidl & Harald Niederreiter

  2. Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34, 5020, Salzburg, Austria

    Harald Niederreiter

Authors
  1. Wilfried Meidl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Harald Niederreiter
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wilfried Meidl.

Additional information

Communicated by I. Shparlinski.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Meidl, W., Niederreiter, H. Multisequences with high joint nonlinear complexity. Des. Codes Cryptogr. 81, 337–346 (2016). https://doi.org/10.1007/s10623-015-0142-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-015-0142-y

Keywords

Mathematics Subject Classification

Search

Navigation