The elliptic curve factorization method (ECM) is considered one of the fastest ways to factor a large number into simpler parts. While it is theoretically possible to compute by hand, it is almost always done by computer due to the algorithms involved and the large amount of data that must be processed. Still, it is mainly used for factoring numbers with less than 25 digits. Other methods are better suited for larger numbers.
Instructions
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1
Choose an elliptic curve with the form y^2 = x^3 +ax + b, as well as a point, "P" on the curve.
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2
Determine a large number to factor based on the curve, e.g., (20!)P. This is the "characteristic" of the curve.
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3
Determine two points on the curve, e.g., "P" and "Q."
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4
Enter the data into an ECM calculator and compute the result.