ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 05 Dec 2016 13:23:14 -0600Random point on elliptic curve with specific orderhttp://ask.sagemath.org/question/35920/random-point-on-elliptic-curve-with-specific-order/ Hi!
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!
Mon, 05 Dec 2016 10:14:53 -0600http://ask.sagemath.org/question/35920/random-point-on-elliptic-curve-with-specific-order/Answer by Vova for <p>Hi!</p>
<p>I use the function <code>random_point()</code> 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).</p>
<p>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!</p>
<p>Thank you for your help!</p>
http://ask.sagemath.org/question/35920/random-point-on-elliptic-curve-with-specific-order/?answer=35922#post-id-35922Let 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.Mon, 05 Dec 2016 13:23:14 -0600http://ask.sagemath.org/question/35920/random-point-on-elliptic-curve-with-specific-order/?answer=35922#post-id-35922