20 Years of ECM

  • Paul Zimmermann
  • Bruce Dodson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4076)


The Elliptic Curve Method for integer factorization (ECM) was invented by H. W. Lenstra, Jr., in 1985 [14]. In the past 20 years, many improvements of ECM were proposed on the mathematical, algorithmic, and implementation sides. This paper summarizes the current state-of-the-art, as implemented in the GMP-ECM software.


Elliptic Curve Modular Multiplication Quadratic Domain Fermat Number Assembly Code 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Paul Zimmermann
    • 1
  • Bruce Dodson
    • 2
  1. 1.LORIA/INRIA LorraineVillers-lès-NancyFrance
  2. 2.Dept. of Math.Lehigh UniversityBethlehemUSA

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