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Get a half point of a point on elliptic curve.

asked 1 year ago

Yos gravatar image

updated 1 year ago

FrédéricC gravatar image

Let E be an elliptic cuve on finite field, PE be a rational point. Then, I want to get one of point QE such that 2Q=P.

What shoud I do?

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Find the order N of E and compute N+12P ?

Max Alekseyev gravatar imageMax Alekseyev ( 1 year ago )

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answered 1 year ago

Luca gravatar image

The method P.division_points(n) gives the list of all rational points Q such that nQ = P. It works for any base field.

sage: E = EllipticCurve([1,0])
sage: P = E(0)
sage: P.division_points(2)
[(0 : 0 : 1), (0 : 1 : 0)]
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Asked: 1 year ago

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Last updated: Feb 04 '24