Skip to main content
SpringerLink
Log in

Efficient FPGA Implementation of a Programmable Architecture for GF(p) Elliptic Curve Crypto Computations

  • Published:
Journal of Signal Processing Systems Aims and scope Submit manuscript

Abstract

This paper presents a processor architecture for elliptic curve cryptography computations over GF(p). The speed to compute the Elliptic-curve point multiplication over the prime fields GF(p) is increased by using the maximum degree of parallelism, and by carefully selecting the most appropriate coordinates system. The proposed Elliptic Curve processor is implemented using FPGAs. The time, area and throughput results are obtained, analyzed, and compared with previously proposed designs showing interesting performance and features.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Miller, V. (1986). Elliptic curves in cryptography. Lecture Notes in Computer Science No. 218 on Advances in Cryptology Crypto’85 (pp. 417–246). Germany: Springer-Verlag Berlin.

  2. Koblitz, N. (1987). Elliptic curve cryptosystems. Mathematics on Computation, 48(177), 203–209. doi:10.2307/2007884.

    Article  MATH  MathSciNet  Google Scholar 

  3. Cohen, H., Miyaji, A., & Ono T. (1998) Efficient elliptic curve exponentiation using mixed coordinates. Lecture Notes in Computer Science on Advances in Cryptology—ASIACRYPT 98 (vol. 1514, pp. 51–65).

  4. Certicom, http://www.secg.org/collateral/proposal-for-sec1v2.pdf, Certicom Proposal to Revise SEC 1: Elliptic Curve Cryptography, Version 1.0, Prepared by Daniel R. L. Brown, January 14, 2005, accessed 29 April 2008.

  5. Certicom, http://www.certicom.com/index.php?action=ecc_tutorial,home, Online elliptic curve cryptography tutorial, accessed 29 April 2008.

  6. Gutub, A. (2006). Merging GF(p) elliptic curve point adding and doubling on pipelined VLSI cryptographic ASIC architecture. International Journal of Computer Science and Network Security—IJCSNS, 3A(6), 44–52.

    Google Scholar 

  7. Gutub, A. (2003). VLSI core architecture for GF(p) elliptic curve crypto processor. IEEE 10 th International Conference on Electronics, Circuits and Systems—ICECS (pp. 84–87). United Arab Emirates: University of Sharjah.

  8. Miyaji, A. (1992). Elliptic curves over Fp suitable for cryptosystems. Lecture Notes In Computer Science; Vol. 718 on Advances in cryptology—AUSCRUPT 92 (pp. 479–491). Australia.

  9. Gutub, A., & Ibrahim, M. (2003). High radix parallel architecture for GF(p) elliptic curve processor. IEEE Conference on Acoustics, Speech, and Signal Processing, ICASSP 2003 (pp. 625–628). Hong Kong.

  10. Montgomery, P. (1985). Modular multiplication without trial division. Mathematics on Computation, 44(170), 519–521. doi:10.2307/2007970.

    Article  MATH  Google Scholar 

  11. Blum, T., & Paar, C. (1999). Montgomery modular exponentiation on reconfigurable hardware. 14 th IEEE Symposium on Computer Arithmetic—ARITH-14 (pp. 70–77).

  12. Brickell, E. (1983). A fast modular multiplication algorithm with application to two key cryptography. In D. Chaum, R. Rivest & A. Sherman (Eds.), Advances in Cryptology—CRYPTO 82 (pp. 51–60). Ney York: Plenum. Santa Barbara, California, USA.

    Google Scholar 

  13. http://www.nsa.gov last acceded in 29 April 2008.

  14. Bernal, A., & Guyot, A. (1998). Design of a modular multiplier based on Montgomery’s algorithm. 13 th Conference on Design of Circuits and Integrated Systems—DCIS’98 (pp. 680–685).

  15. Wu, C., & Chou, Y. (1994). General modular multiplication by block multiplication and table lookup. IEEE International Symposium on Circuits and Systems—ISCAS’94 (vol. 4, pp. 295–298). London, UK.

  16. Eldridge, S., & Walter, C. (1993). Hardware implementation of Montgomery’s modular multiplication algorithm. IEEE Transactions on Computers, 42(6), 693–699. doi:10.1109/12.277287.

    Article  Google Scholar 

  17. Eberle, H., Gura, N., Shantz, S., Gupta, V., Rarick, L., & Sundaram, S. (2004). A public-key cryptographic processor for RSA and ECC. Proceedings of the 15 th IEEE International Conference on Application-Specific Systems, Architectures and Processors (pp. 98–110).

  18. Satoh, A., & Takano, K. (2003). A scalable dual-field elliptic curve cryptographic processor. IEEE Transactions on Computers, 52(4), 449–460. doi:10.1109/TC.2003.1190586.

    Article  Google Scholar 

  19. Orlando, G., & Paar, C. (2001). A scalable GF(p) elliptic curve processor architecture for programmable hardware. Lecture Notes in Computer Science on Cryptographic Hardware and Embedded Systems—CHES, 2001, 348–363.

    MathSciNet  Google Scholar 

  20. Ors, S., Batina, L., Preneel, B., & Vandewalle, J. (2003). Hardware implementation of an elliptic curve processor over GF(p). Proceedings of IEEE International Conference on Application-Specific Systems, Architectures, and Processors—ASAP’03 (pp. 433–443).

  21. Gutub, A. (2007). Efficient utilization of scalable multipliers in parallel to compute GF(p) elliptic curve cryptographic operations. Kuwait Journal of Science & Engineering (KJSE) (vol. 34, no. 2, pp. 165–182).

  22. Francis, C., Daly, A., & Marnane, W. (2005). A scalable dual mode arithmetic unit for public key cryptosystems. International Conference on Information Technology: Coding and Computing—ITCC’05 (vol. I, pp. 568–573).

Download references

Acknowledgments

Authors would like to thank both Computer Engineering Departments in Jordan University of Science and Technology, Irbid, Jordan, and King Fahd University of Petroleum & Minerals (KFUPM), Dhahran, Saudi Arabia, for supporting this research and the fruitful cooperation and collaboration between the universities in the region.

Author information

Authors and Affiliations

  1. Computer Engineering Department, Jordan University of Science and Technology, Irbid, Jordan

    Lo’ai Ali Tawalbeh & Abidalrahman Mohammad

  2. Computer Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia

    Adnan Abdul-Aziz Gutub

Authors
  1. Lo’ai Ali Tawalbeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abidalrahman Mohammad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Adnan Abdul-Aziz Gutub
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adnan Abdul-Aziz Gutub.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tawalbeh, L.A., Mohammad, A. & Gutub, A.AA. Efficient FPGA Implementation of a Programmable Architecture for GF(p) Elliptic Curve Crypto Computations. J Sign Process Syst Sign Image Video Technol 59, 233–244 (2010). https://doi.org/10.1007/s11265-009-0376-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11265-009-0376-x

Keywords

Search

Navigation