Skip to main content
SpringerLink
Log in

On Elements of High Order in Finite Fields

  • Conference paper
Cryptography and Computational Number Theory

Part of the book series: Progress in Computer Science and Applied Logic ((PCS,volume 20))

Abstract

We provide a more careful analysis of a construction of elements high order in finite fields which has recently been proposed by S. Gao. In particular, we improve and generalize one of his results.

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. I. F. Blake, S. Gao and R. Mullin, Normal and self-dual normal bases from factor ization of cx q+1 + dx q - ax - b, SIAM J. Discr. Math. 7 (1994), 499–512.

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Gao, Elements of provable high orders in finite fields, Proc. Amer. Math. Soc., 127 (1999), 1615–1623.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. von zur Gathen and I. Shparlinski, Orders of Gauss periods in finite fields, Appl. Algebra in Engin., Commun. and Computing, 9 (1998), 15–24.

    Article  MATH  Google Scholar 

  4. J. von zur Gathen and I. Shparlinski, Constructing elements of large order in finite fields and Gauss periods, Proc. the 13th Symp. on Appl. Algebra, Algebraic Algorithms, and Error-Correcting Codes, Hawaii, 1999, Lect. Notes in Comp. Sci., 1719 (1999), Springer-Verlag, Berlin, 404–409.

    Google Scholar 

  5. J. von zur Gathen and I. Shparlinski, Gauss periods in finite fields, Proc. 5th Conference of Finite Fields and their Applications, Augsburg, 1999, (to appear).

    Google Scholar 

  6. V. M. Sidel’nikov, On the normal bases of a finite field, Matem. Sbornik, 133 (1987), 497–507 (in Russian), translation in Math. USSR Sbornik, 61 (1988), 485–494.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi “Roma Tre”, Largo San Leonardo Murialdo 1, I-00146, Roma, Italy

    Alessandro Conflitti

Authors
  1. Alessandro Conflitti
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, National University of Singapore, 2 Science Drive 2, 117543, Singapore

    Kwok-Yan Lam

  2. Department of Computing, Macquarie University, NSW, 2109, Australia

    Igor Shparlinski

  3. Department of Computer Science, University of Wollongong, NSW, 2522, Australia

    Huaxiong Wang

  4. Department of Mathematics, National University of Singapore, 2 Science Drive 2, 117543, Singapore

    Chaoping Xing

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Basel AG

About this paper

Cite this paper

Conflitti, A. (2001). On Elements of High Order in Finite Fields. In: Lam, KY., Shparlinski, I., Wang, H., Xing, C. (eds) Cryptography and Computational Number Theory. Progress in Computer Science and Applied Logic, vol 20. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8295-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8295-8_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9507-1

  • Online ISBN: 978-3-0348-8295-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation