An integer factoring algorithm based on elliptic divisibility sequences
Naotoshi Sakurada, Junichi Yarimizu, Naoki Ogura, Shigenori Uchiyama · JSIAM Letters · 2012
In 1948, Ward defined elliptic divisibility sequences satisfying a certain recurrence relation. An elliptic divisibility sequence arises from any choice of elliptic curve and initial point on that curve. In this paper, we propose a factorization algorithm based on elliptic divisibility sequences. We then discuss our implementations of the algorithm and its optimization, and estimate the computational complexity.