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2016-12-14 07:52:30 -0500 answered a question sage code for Elliptic curve scalar multiplication

Yes, if the values P (point) and scalar k are already defined, just do k*P Note: k can be either predefined, or just be any integer that you type in.

2016-12-06 08:17:39 -0500 commented answer Pick a point at random on an elliptic curve with specific order

It should have the same randomness, but at the level of points of order k. The informal 'proof': if you have a set of random points, which you multiply all by the same scalar (n/k), then you will get a 'compressed with respect to order k', set, which will carry through the randomness to that level.

2016-12-05 13:23:53 -0500 answered a question Pick a point at random on an elliptic curve with specific order

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.

2016-12-05 13:23:14 -0500 answered a question Random point on elliptic curve with specific order

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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2016-10-19 13:56:35 -0500 asked a question How to define Sage function with Optional arguments?

I need to define a Sage function with optional arguments. The number of mandatory arguments is 2 and there are up to 3 optional arguments. How do I do this is Sage?

2016-08-26 12:33:56 -0500 commented answer Unable to start pari

try installing gmp, then gp2c

2016-08-25 15:01:01 -0500 answered a question Unable to start pari

Try installing the optional package: gp2c

2016-07-18 07:47:59 -0500 asked a question Large Integer Factorization

I am trying to factor a 520-bit integer in Sage. At some point, I get:

Warning: MPQS: number too big to be factored with MPQS, giving up.

But it seems to still be running. Is it continuing the factorization?

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2016-06-30 08:45:01 -0500 commented answer Why was sea.py removed?

Thanks. Yes, I understand that it is no longer used. My major concern is that in the original sea.py, we had an option of early abort (if we are searching only for prime order elliptic curves). The current cardinality functions do not offer that. Any suggestions how this can be done?

2016-06-29 13:10:45 -0500 asked a question Why was sea.py removed?

I noticed that sea.py link text has been removed. I need the cardinality function for elliptic curves with early abort option, however, it does not seem to be available. Any suggestions what could be done here?

2016-06-29 07:55:29 -0500 commented answer Early abort for E.cardinality()

It seems that earlier version of sage had an option of passing to cardinality function an early abort command. For example, something like this: https://www.ma.utexas.edu/users/torna...

However, there is no more sea.py file. Do you have any ideas how to do something similar for the most current version of sage (7.2)?

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2016-06-28 11:13:55 -0500 answered a question Error with .cardinality(algorithm='sae') for elliptic curve

It should be 'sea' instead of 'sae'. Also, you would get the same result if you replace the line by return E.cardinality_pari()

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2016-06-27 15:03:02 -0500 asked a question Early abort for E.cardinality()

I loop through curves to find one with prime cardinality. In order to speed up the process, it would be convenient to have early abort option, so that whenever some prime factor of cardinality is found, the algorithm skips that curve and goes to the next one. Any suggestions how this can be done?