Skip to main content
SpringerLink
Log in

An algorithm for DLP on anomalous elliptic curves over Fp

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

This paper improves the method of discrete logarithm on anomalous elliptic curves, and establishes an isomorphism from E(Fp) to Fp which can be more easily implemented. Fruthermore, we give an optimized algorithm for discrete logarithm on anomalous elliptic curves E(Fp).

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. Menezes, A., Okamoto, T. S. A., Vanstone, S. A., Reducing elliptic curve logarithm in a finite field, IEEE Transactions on Information Theory, 1993, 39(5): 1639–1646.

    Article  MATH  MathSciNet  Google Scholar 

  2. Semaev, I., Evalution of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p, Math. of Computation, 1998, 67(221): 353–358.

    Article  MATH  MathSciNet  Google Scholar 

  3. Smart, N., The discrete logarithm problem on elliptic curves of trace one, Journal of Cryptology, 1999, 12(3): 193–196.

    Article  MATH  MathSciNet  Google Scholar 

  4. Satoh, T., Araki, K., Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves, Comm. Math. Univ., 1998, 47: 81–92.

    MATH  MathSciNet  Google Scholar 

  5. Frey, G., Ruck, H., A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves, Math. Comp., 1994, 62(206): 855–874.

    Article  MathSciNet  Google Scholar 

  6. Shikata, J., Zheng, Y., Suzuki, J., Realizing, H. I., The Menezes-Okamoto-Vanstone(MOV) reduction efficiently for ordinary elliptic curves, IEICE Transactions on Fundamentals, E, 2000, 83(4): 756–763.

    Google Scholar 

  7. Silverman, J., The Arithmetic of Elliptic Curves, New York: Springer-Verlag, 1986.

    MATH  Google Scholar 

  8. Ruck, H. -G., On the discrete logarithm in the divisor class group of curves, Math. of Computation, 1999, 68: 805–806.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Information Security, Graduate School, Chinese Academy of Sciences, 100039, Beijing, China

    Yuefei Zhu & Dingyi Pei

Authors
  1. Yuefei Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dingyi Pei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dingyi Pei.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhu, Y., Pei, D. An algorithm for DLP on anomalous elliptic curves over Fp . Sci. China Ser. A-Math. 45, 773–777 (2002). https://doi.org/10.1360/02ys9084

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1360/02ys9084

Keywords

Search

Navigation