Algorithmic Number Theory

Volume 4076 of the series Lecture Notes in Computer Science pp 525-542

20 Years of ECM

  • Paul ZimmermannAffiliated withLORIA/INRIA Lorraine
  • , Bruce DodsonAffiliated withDept. of Math., Lehigh University

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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.