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I have an elliptic curve defined by y^2 = x^3 + 1062282974404935987005872930817*x + 1204388198013706813607478558721 over Finite Field of size 2017313518945563799802055961909.

And I want to get a point on this curve of order 3569809307570934983774171.

How can I get it?

Nat Mordvaniuk
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1 Answers1

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Easily you can see that the order of E, is 2017313518945565643070719128784. The main stage is that you find the generator(s) of E, and with SageMath they are:

H_1 = (651721743085147348480059087840, 277924022187240437411690075386)

and

H_2 = (364767631279436218861124076682, 0)

But you can see that the order of H_1 is 1008656759472782821535359564392, so

G = 565104 * H_1

G = (1144674520220442511918931779419, 850803345221750997044804585048)

is the desired point on E.

Lisbeth
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