ECC on Your Fingertips: A Single Instruction Approach for Lightweight ECC Design in GF(p)

  • Debapriya Basu RoyEmail author
  • Poulami Das
  • Debdeep Mukhopadhyay
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9566)


Lightweight implementation of Elliptic Curve Cryptography on FPGA has been a popular research topic due to the boom of ubiquitous computing. In this paper we propose a novel single instruction based ultra-light ECC crypto-processor coupled with dedicated hard-IPs of the FPGAs. We show that by using the proposed single instruction framework and using the available block RAMs and DSPs of FPGAs, we can design an ECC crypto-processor for NIST curve P-256, requiring only 81 and 72 logic slices on Virtes-5 and Spartan-6 devices respectively. To the best of our knowledge, this is the first implementation of ECC which requires less than 100 slices on any FPGA device family.


Elliptic curve Single instruction URISC SBN FPGA Hard-IPs 


  1. 1.
    Daly, A., Marnane, W., Kerins, T., Popovici, E.: An FPGA implementation of a GF(p) ALU for encryption processors. Microprocess. Microsyst. 28(56), 253–260 (2004). Special Issue on FPGAs: Applications and DesignsCrossRefGoogle Scholar
  2. 2.
    Batina, L., Mentens, N., Sakiyama, K., Preneel, B., Verbauwhede, I.: Low-cost elliptic curve cryptography for wireless sensor networks. In: Buttyán, L., Gligor, V.D., Westhoff, D. (eds.) ESAS 2006. LNCS, vol. 4357, pp. 6–17. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Güneysu, T., Paar, C.: Ultra high performance ECC over NIST primes on commercial FPGAs. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 62–78. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Satoh, A., Takano, K.: A scalable dual-field elliptic curve cryptographic processor. IEEE Trans. Comput. 52, 449–460 (2003)CrossRefGoogle Scholar
  5. 5.
    Orlando, G., Paar, C.: A scalable \(GF\)(\(p\)) elliptic curve processor architecture for programmable hardware. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 356–371. Springer, Heidelberg (2001)Google Scholar
  6. 6.
    Alrimeih, H., Rakhmatov, D.: Pipelined modular multiplier supporting multiple standard prime fields. In: 2014 IEEE 25th International Conference on Application-Specific Systems, Architectures and Processors (ASAP), pp. 48–56, June 2014Google Scholar
  7. 7.
    Roy, D.B., Mukhopadhyay, D., Izumi, M., Takahashi, J., Multiplication, T.B.: An efficient strategy to optimize DSP multiplier for accelerating prime field ECC for NIST curves. In: The 51st Annual Design Automation Conference, DAC 2014, San Francisco, CA, USA, 1–5 June 2014, pp. 177:1–177:6 (2014)Google Scholar
  8. 8.
    Kim, C.-J., Yun, S.-Y., Park, S.-C.: A lightweight ECC algorithm for mobile RFID service. In: Proceedings of the 5th International Conference on Ubiquitous Information Technologies and Applications (CUTE 2010), pp. 1–6, December 2010Google Scholar
  9. 9.
    He, D., Kumar, N., Chilamkurti, N., Lee, J.-H.: Lightweight ECC based RFID authentication integrated with an ID verifier transfer protocol. J. Med. Syst. 38(10), 116 (2014)CrossRefGoogle Scholar
  10. 10.
    Varchola, M., Güneysu, T., Mischke, O.: MicroECC: a lightweight reconfigurable elliptic curve crypto-processor. In: International Conference on Reconfigurable Computing and FPGAs, ReConFig 2011, Cancun, Mexico, November 30–December 2, 2011, pp. 204–210 (2011)Google Scholar
  11. 11.
    Vliegen, J., Mentens, N,. Genoe, J., Braeken, A., Kubera, S., Touhafi, A., Verbauwhede, I:. A compact FPGA-based architecture for elliptic curve cryptography over prime fields. In: 21st IEEE International Conference on Application-Specific Systems Architectures and Processors, ASAP 2010, Rennes, France, 7–9 July 2010, pp. 313–316 (2010)Google Scholar
  12. 12.
    Tawalbeh, L.A., Mohammad, A., Gutub, A.A.-A.: Efficient FPGA implementation of a programmable architecture for GF(p) elliptic curve crypto computations. Signal Process. Syst. 59(3), 233–244 (2010)CrossRefGoogle Scholar
  13. 13.
    Ghosh, S., Alam, M., Chowdhury, D.R., Gupta, I.S.: Parallel crypto-devices for GF(P) elliptic curve multiplication resistant against side channel attacks. Comput. Electr. Eng. 35(2), 329–338 (2009)CrossRefzbMATHGoogle Scholar
  14. 14.
    Xilinx Inc.: Virtex-II and Virtex-II Pro X FPGA User Guide, 14 February 2011Google Scholar
  15. 15.
    Driessen, B., Güneysu, T., Kavun, E.B., Mischke, O., Paar, C., Pöppelmann, T.: IPSecco: a lightweight and reconfigurable IPSec core. In: International Conference on Reconfigurable Computing and FPGAs, ReConFig 2012, Cancun, Mexico, 5–7 December 2012, pp. 1–7 (2012)Google Scholar
  16. 16.
    Pöpper, C., Mischke, O., Güneysu, T.: MicroACP - a fast and secure reconfigurable asymmetric crypto-processor. In: Goehringer, D., Santambrogio, M.D., Cardoso, J.M.P., Bertels, K. (eds.) ARC 2014. LNCS, vol. 8405, pp. 240–247. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  17. 17.
    Himmighofen, A., Jungk, B., Reith, S.: On a FPGA-based method for authentication using edwards curves. In: 8th International Workshop on Reconfigurable and Communication-Centric Systems-on-Chip (ReCoSoC), Darmstadt, Germany, 10–12 July 2013, pp. 1–7 (2013)Google Scholar
  18. 18.
    Fan, J., Batina, L., Verbauwhede, I.: Light-weight Implementation options for curve-based cryptography: HECC is also ready for RFID. In: ICITST, pp. 1–6. IEEE (2009)Google Scholar
  19. 19.
    Kavun, E.B., Yalcin, T.: RAM-based ultra-lightweight FPGA implementation of PRESENT. In: International Conference on Reconfigurable Computing and FPGAs (ReConFig 2011), pp. 280–285, November 2011Google Scholar
  20. 20.
    Hankerson, D., Menezes, A.J., Vanstone, S.: Guide to Elliptic Curve Cryptography. Springer, New York (2003)zbMATHGoogle Scholar
  21. 21.
    Mavaddat, F., Parhamt, B.: URISC: the ultimate reduced instruction set computer. Int. J. Electr. Eng. Educ. 25, 327–334 (1988)CrossRefGoogle Scholar
  22. 22.
    Gilreath, W.F., Laplante, P.A.: Computer Architecture : A Minimalist Perspective. The Springer International Series in Engineering and Computer Science. Springer, New York (2003)CrossRefzbMATHGoogle Scholar
  23. 23.
    Naccache, D.: Is theoretical cryptography any good in practice? In: CHES (2010)Google Scholar
  24. 24.
    Tsoutsos, N.G., Maniatakos, M.: Investigating the application of one instruction set computing for encrypted data computation. In: Gierlichs, B., Guilley, S., Mukhopadhyay, D. (eds.) SPACE 2013. LNCS, vol. 8204, pp. 21–37. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  25. 25.
    Liu, A., Ning, P., Tinyecc,: A configurable library for elliptic curve cryptography in wireless sensor networks. In: IPSN, pp. 245–256. IEEE Computer Society (2008)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Debapriya Basu Roy
    • 1
    Email author
  • Poulami Das
    • 1
  • Debdeep Mukhopadhyay
    • 1
  1. 1.Secured Embedded Architecture Laboratory (SEAL), Department of Computer Science and EngineeringIndian Institute of Technology KharagpurKharagpurIndia

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