An integer factoring algorithm based on elliptic divisibility sequences

Naotoshi Sakurada; Junichi Yarimizu; Naoki Ogura; Shigenori Uchiyama

doi:10.14495/jsiaml.4.21

JSIAM Letters

Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617

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An integer factoring algorithm based on elliptic divisibility sequences

Naotoshi Sakurada, Junichi Yarimizu, Naoki Ogura, Shigenori Uchiyama

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Keywords: elliptic divisibility sequence, elliptic curve, elliptic curve method

JOURNAL FREE ACCESS

2012 Volume 4 Pages 21-23

DOI https://doi.org/10.14495/jsiaml.4.21

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Abstract

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.

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