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Lenstra’s Factorisation Method Based on Elliptic Curves

  • N. M. Stephens
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 218)

Abstract

The purpose of this exposition is to explain the method due to H.W. Lenstra, Jr. [1] of determining a non-trivial factor, p, of a composite number, n. The method uses the theory of elliptic curves and has a n expected running time of L (p)√2 where L(p)=exp (√log p log log p). The aim of the exposition is to be completely elementary. with an introduction to the arithmetic of elliptic curves sufficient to enable the reader to follow the later section explaining the method. The paper ends with a few remarks on techniques for the practical implementation of the algorithm.

6. References

  1. 1.
    H.W. Lenstra Jr. Elliptic Curve Factorisation and Primality Testing. Paper to Computational Number Theory Conference at Arcata, California. August 1985.Google Scholar
  2. 2.
    R. Silverman, Paper to Computational Number Theory Conference at Arcata, California. August 1985.Google Scholar
  3. 3.
    N. Koblitz. Introduction to Elliptic Curves and Modular Forms. Springer-Verlag 1984.Google Scholar
  4. 4.
    P.L. Montgomery. Experiences using Elliptic Curve Method of Factorisation. Paper to Computational Number Theory Conference at Arcata, California. August 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • N. M. Stephens
    • 1
  1. 1.University CollegeCardiffGreat Britain

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