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Random point on elliptic curve with specific order [closed]

asked 2016-12-05 10:14:53 -0500

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I use the function random_point() to pick a point at random on an elliptic curve, but I was wondering if there is a way to pick a point at random that has a specific order (or some useful geometric property that allows me to do that).

So far, brute forcing seems the only way to me (pick a point at random, check its order and iterate until it has the wanted order) but it's obviously very naive!

Thank you for your help!

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Closed for the following reason duplicate question by tmonteil
close date 2016-12-05 14:51:04.608241

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answered 2016-12-05 13:23:14 -0500

Vova gravatar image

Let n be the order of your curve. Let k be desired order of the point. Let P be the random point that you obtained. Compute Q = (n/k)*P With high probability, Q will have order k. Check that. If Q is not of order k, pick a new random point P and repeat the process.

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Asked: 2016-12-05 10:14:53 -0500

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Last updated: Dec 05 '16