Skip to main content
SpringerLink
Log in

Hyperelliptic Curves with Compact Parameters

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

Abstract

We present a family of hyperelliptic curves whose Jacobians are suitable for cryptographic use, and whose parameters can be specified in a highly efficient way. This is done via complex multiplication and identity-based parameters. We also present some novel computational shortcuts for these families.

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. Brown E., Myers B.T., Solinas J.A. (2000). Elliptic curves with compact parameters, Tech. Report, Centre for Applied Cryptographic Research. ttp://www.cacr.math.uwaterloo.ca/techreports/2001/corr2001-68.ps

  2. J. Buhler N. Koblitz (1998) ArticleTitleAn application of lattice basis reduction to Jacobi sums and hyperelliptic cryptosystems Bulletin of the Australian Mathematical Society. 58 147–154

    Google Scholar 

  3. Gallant R., Lambert R., Vanstone S. (2001). Faster point multiplication on curves with efficient complex multiplication. Advances in Cryptology—CRYPTO 2001. Springer-Verlag pp. 190–200

  4. Hasse H. (1979). Number Theory. Akademie-Verlag

  5. Ireland K., Rosen M. (1982). A Classical Introduction to Modern Number Theory. Springer-Verlag

  6. Iwasawa K. (1975). A note on Jacobi sums, Istituto Nazionale di Alta Matematica, Symposia Mathematica, Vol. 15. Academic Press

  7. Lange T. Formulae for arithmetic on genus 2 hyperelliptic curves, 2003, http://www.ruhr-uni-bochum.de/itsc/tanja/preprints.html

  8. F. Lemmermeyer (1995) ArticleTitleThe Euclidean algorithm in algebraic number fields Exposition in Mathematics. 13 IssueID5 385–416

    Google Scholar 

  9. Lidl R., Niederreiter H. (1983). Finite Fields, Encyclopedia of Mathematics and its Applications. 20: Addison-Wesley

  10. Marcus D. (1977). Number Fields. Springer-Verlag

  11. Stichtenoth H. (1993). Algebraic Function Fields and Codes. Springer-Verlag

  12. Washington L.C. (1982). Introduction to Cyclotomic Fields. Springer-Verlag

  13. Waterhouse W.C. (1969). Abelian Varieties over Finite Fields, Ann. scient. Éc. Norm. Sup., 4e série, t.2 (1969)

Download references

Author information

Authors and Affiliations

  1. Virginia Tech, Blacksburg, VA, 24061-0123, USA

    Ezra Brown

  2. Wheaton College, Wheaton, IL, 60187, USA

    Bruce T. Myers

  3. National Security Agency, Ft. Meade, MD, 20755-6511, USA

    Jerome A. Solinas

Authors
  1. Ezra Brown
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bruce T. Myers
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jerome A. Solinas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ezra Brown.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brown, E., Myers, B.T. & Solinas, J.A. Hyperelliptic Curves with Compact Parameters. Des Codes Crypt 36, 245–261 (2005). https://doi.org/10.1007/s10623-004-1718-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-004-1718-0

Keywords

Search

Navigation