Skip to main content
SpringerLink
Log in

Applications of linearised and sub-linearised polynomials to information security

  • Conference paper
  • First Online:
Book cover Information Security and Privacy (ACISP 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1438))

Included in the following conference series:

Abstract

Polynomials have been used in various security systems. We direct our attention to the polynomials that can be used in a Massey-Omura type cryptosystem. For the benefit of the reader we introduce the original Massey-Omura cryptosystem. We then introduce other classes of polynomials which satisfy the conditions required for this system to function. In particular, we focus on the classes of linearised and sub-linearised polynomials. These polynomials exhibit special compositional behaviour under certain conditions, allowing us to construct Massey-Omura type cryptosystems.

This work was partially supported by an Australian Research Council grant

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S.D. Cohen, Exceptional polynomials and the reducibility of substitution polynomials, L'Enseignement Math. 36 (1990), 53–65.

    MATH  Google Scholar 

  2. M. Giesbrecht, Factoring in skew-polynomial rings over finite fields, J. Symbolic Computation (to appear).

    Google Scholar 

  3. M. Henderson and R. Matthews, Composition behaviour of linearised and sub-linearised polynomials over a finite field, preprint.

    Google Scholar 

  4. N. Koblitz, A Course in Number Theory and Cryptography, Springer-Verlag, New York, Berlin, 1987.

    Google Scholar 

  5. R. Lidl, G.L. Mullen, and G. Turnwald, Dickson Polynomials, Pitman Monographs and Surveys in Pure and Appl. Math., vol. 65, Longman Scientific and Technical, Essex, England, 1993.

    Google Scholar 

  6. R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia Math. Appl., vol. 20, Addison-Wesley, Reading, 1983, (now distributed by Cambridge University Press).

    Google Scholar 

  7. G.L. Mullen and T.P. Vaughan, Cycles of linear permutation over a finite field, Linear Algebra Appl. 108 (1988), 63–82.

    Article  MATH  MathSciNet  Google Scholar 

  8. W.B. Müller and R. Nöbauer, Some remarks on public-key cryptosystems, Studia Sci. Math. Hungar. 16 (1981), 71–76.

    MATH  MathSciNet  Google Scholar 

  9. H. Niederreiter, Some new cryptosystems based on feedback shift register sequences, Math. J. Okayama Univ. 30 (1988), 121–149.

    MATH  MathSciNet  Google Scholar 

  10. O. Ore, On a special class of polynomials, Trans. Amer. Math. Soc. 35 (1933), 559–584, Errata, ibid. 36, 275 (1934).

    Article  MATH  MathSciNet  Google Scholar 

  11. P.K.S. Wah and M.Z. Wang, Realization and Application of the Massey-Omura Lock, Proc. Internat. Zurich Seminar, March 6–8 1984, pp. 175–182.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Discrete Mathematics and Computing, Department of Computer Science and Electrical Engineering, University of Queensland, 4072, Queensland, Australia

    Marie Henderson

Authors
  1. Marie Henderson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Colin Boyd Ed Dawson

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Henderson, M. (1998). Applications of linearised and sub-linearised polynomials to information security. In: Boyd, C., Dawson, E. (eds) Information Security and Privacy. ACISP 1998. Lecture Notes in Computer Science, vol 1438. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0053736

Download citation

  • DOI: https://doi.org/10.1007/BFb0053736

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64732-4

  • Online ISBN: 978-3-540-69101-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation