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Get a half point of a point on elliptic curve.

asked 2024-02-02 23:02:25 +0200

Yos gravatar image

updated 2024-02-03 10:28:12 +0200

FrédéricC gravatar image

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

What shoud I do?

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Find the order $N$ of $E$ and compute $\frac{N+1}2P$ ?

Max Alekseyev gravatar imageMax Alekseyev ( 2024-02-03 05:38:47 +0200 )edit

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answered 2024-02-04 20:26:50 +0200

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: 2024-02-02 23:02:25 +0200

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Last updated: Feb 04