# Factoring integers with elliptic curves

```@article{Lenstra1987FactoringIW,
title={Factoring integers with elliptic curves},
author={Hendrik W. Lenstra},
journal={Annals of Mathematics},
year={1987},
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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