Factorization Method of the Elliptic Curve
نویسندگان
چکیده
Abstract The elliptic curve is an important topic in number theory. In 1987, Lenstra discovered the elliptic-curve factorization method (ECM). [4] Nevertheless, until now, no research can have complete detailed codes Wolfram Mathematica. This article will state definition of curve, analyze this ECM algorithm, and build a code s Finally, completed for 1820099 by experiment, which prove that ECM, but it may take much time to calculate.
منابع مشابه
Finding Suitable Curves for the Elliptic Curve Method of Factorization
Using the parametrizations of Kubert, we show how to produce in nite families of elliptic curves which have prescribed nontrivial torsion over Q and rank at least one. These curves can be used to speed up the ECM factorization algorithm of Lenstra. We also brie y discuss curves with complex multiplication in this context.
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ژورنال
عنوان ژورنال: Journal of physics
سال: 2022
ISSN: ['0022-3700', '1747-3721', '0368-3508', '1747-3713']
DOI: https://doi.org/10.1088/1742-6596/2371/1/012005