"Lenstra's elliptic curve factorization method," given by Leo Lai on 27th January 2016 as a guest speaker in the Churchill Computer Science Talks Series ( ). Leo's talk addresses something incredibly important to computer science: computational number theory. Computational number theory has deep links to cryptography and security, and one of the most fundamental problems is the factorization of huge numbers, the subject of this talk. Abstract: Integer factorization is an important problem in computational number theory with many applications in cryptography. Elliptic curves, on the other hands, are mathematical objects whose study predates the notion of computation by more than a century. In 1987, Lenstra described a new factoring algorithm using elliptic curves, which is still one of the fastest special purpose factorization algorithms invented so far. Conversely, the desire to rigorously analyze this algorithm has produced new results in number theory. This talk will describe his algorithm. No knowledge beyond basic number theory is required.