Customising Hardware Designs for Elliptic Curve Cryptography

  • Nicolas Telle
  • Wayne Luk
  • Ray C. C. Cheung
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3133)


This paper presents a method for producing hardware designs for Elliptic Curve Cryptography (ECC) systems over the finite field GF(2 m ), using the optimal normal basis for the representation of numbers. A design generator has been developed which can automatically produce a customised ECC hardware design that meets user-defined requirements. This method enables designers to rapidly explore and implement a design with the best trade-offs in speed, size and level of security. To facilitate performance characterisation, we have developed formulæfor estimating the number of cycles for our generic ECC architecture. The resulting hardware implementations are among the fastest reported, and can often run several orders of magnitude faster than software implementations.


Elliptic Curve Smart Card Hardware Design Elliptic Curve Cryptography Cryptographic Hardware 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bednara, M., Daldrup, M., Gathen, J., Shokrollahi, J., Teich, J.: Reconfigurable Implementation of Elliptic Curve Crypto Algorithms.In: Reconfigurable Architectures Workshop (2002)Google Scholar
  2. 2.
    Bednara, M., et al.: Tradeoff Analysis of FPGA Based Elliptic Curve Cryptography. In: Proc. IEEE International Symposium on Circuits and Systems, vol.  V, pp. 797–800 (2002)Google Scholar
  3. 3.
    Celoxica : Handel-C Language Reference Manual for DK2.0, Document RM-1003-4.0 (2003)Google Scholar
  4. 4.
    Ernst, M., et al.: Rapid Prototyping for Hardware Accelerated Elliptic Curve Public-Key Cryptosystems. In:Proc. Workshop on Rapid System Prototyping, pp. 24-29 (2001)Google Scholar
  5. 5.
    Gura, N., et al.: An end-to-end systems approach to elliptic curve cryptography. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 349–365. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Jung, M., Madlener, F., Ernst, E., Huss, S.A.: A Reconfigurable Coprocessor for Finite Field Multiplication in G(2 m) .In: IEEE Workshop on Heterogeneous reconfigurable SoC (2002)Google Scholar
  7. 7.
    Kerins, T., et al.: Fully Parameterizable Elliptic Curve Cryptography Processor over GF(2m). In: Glesner, M., Zipf, P., Renovell, M. (eds.) FPL 2002. LNCS, vol. 2438, pp. 750–759. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Leong, P.H.W., Leung, K.H.: A Microcoded Elliptic Curve Processor using FPGA Technology. IEEE Transactions on VLSI Systems 10(5), 550–559 (2002)CrossRefGoogle Scholar
  9. 9.
    López, J., Dahab, R.: Fast Multiplication on Elliptic Curves over GF(2m) without precomputation. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 316–327. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  10. 10.
    Mastrovito, E.D.: VLSI Architectures for Computation in Galois Fields, PhD Thesis, Linköping University (1991)Google Scholar
  11. 11.
    Nguyen, N., Gaj, K., Caliga, D., El-Ghazawi, T.: Implementation of Elliptic Curve Cryptosystems on a Reconfigurable Computer. In: Int. Conf. on Field Prog. Tech., pp. 60–67 (2003)Google Scholar
  12. 12.
    Orlando, G., Paar, C.: A High Performance Reconfigurable Elliptic Curve for GF(2m). In: Paar, C., Koç, Ç.K. (eds.) CHES 2000. LNCS, vol. 1965, pp. 41–56. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  13. 13.
    Pietiläinen, H.: Elliptic Curve Cryptography on Smart Cards, MSc Thesis, Helsinki University of technology (2000)Google Scholar
  14. 14.
    Rosing, M.: Implementing Elliptic Curve Cryptography. Manning Ed (1999)Google Scholar
  15. 15.
    Rosner, M.: Elliptic Curve Cryptosystems on Reconfigurable hardware, MSc Thesis,Worcester Polytechnic Institute (1998)Google Scholar
  16. 16.
    Woodbury, A.: Efficient Algorithms for Elliptic Curve Cryptosystems on Embedded Systems, MSc Thesis, Worcester Polytechnic Institute (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Nicolas Telle
    • 1
  • Wayne Luk
    • 1
  • Ray C. C. Cheung
    • 1
  1. 1.Department of ComputingImperial CollegeLondonEngland

Personalised recommendations