Factoring integers with elliptic curves

@article{Lenstra1986FactoringIW,
  title={Factoring integers with elliptic curves},
  author={Hendrik W. Lenstra},
  journal={Annals of Mathematics},
  year={1986},
  volume={126},
  pages={649-673}
}
  • H. Lenstra
  • Published 1 November 1987
  • Mathematics
  • Annals of Mathematics
This paper is devoted to the description and analysis of a new algorithm to factor positive integers. It depends on the use of elliptic curves. The new method is obtained from Pollard's (p - 1)-method (Proc. Cambridge Philos. Soc. 76 (1974), 521-528) by replacing the multiplicative group by the group of points on a random elliptic curve. It is conjectured that the algorithm determines a non-trivial divisor of a composite number n in expected time at most K( p)(log n)2, where p is the least… 
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