Implementing the Elliptic Curve Method of Factoring in Reconfigurable Hardware

  • Kris Gaj
  • Soonhak Kwon
  • Patrick Baier
  • Paul Kohlbrenner
  • Hoang Le
  • Mohammed Khaleeluddin
  • Ramakrishna Bachimanchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4249)


A novel portable hardware architecture for the Elliptic Curve Method of factoring, designed and optimized for application in the relation collection step of the Number Field Sieve, is described and analyzed. A comparison with an earlier proof-of-concept design by Pelzl, Šimka, et al. has been performed, and a substantial improvement has been demonstrated in terms of both the execution time and the area-time product. The ECM architecture has been ported across three different families of FPGA devices in order to select the family with the best performance to cost ratio. A timing comparison with a highly optimized software implementation, GMP-ECM, has been performed. Our results indicate that low-cost families of FPGAs, such as Xilinx Spartan 3, offer at least an order of magnitude improvement over the same generation of microprocessors in terms of the performance to cost ratio.


Cipher-breaking factoring ECM FPGA 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kris Gaj
    • 1
  • Soonhak Kwon
    • 2
  • Patrick Baier
    • 1
  • Paul Kohlbrenner
    • 1
  • Hoang Le
    • 1
  • Mohammed Khaleeluddin
    • 1
  • Ramakrishna Bachimanchi
    • 1
  1. 1.Dept. of Electrical and Computer EngineeringGeorge Mason UniversityFairfaxUSA
  2. 2.Inst. of Basic ScienceSungkyunkwan UniversitySuwonKorea

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