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Order of randomly generated elliptic curve

asked 2012-05-31 22:19:39 -0500

twoforone gravatar image

updated 2015-01-18 04:32:38 -0500

FrédéricC gravatar image

I was computing order of random elliptic curves over prime field with out any problem. But when it comes to computing order of elliptic curves over binary field(characteristic 2 field), it computes well for small values of a and b of the elliptic curve. The problem comes when a and b parameters are large, specifically for 163 bit elliptic curve parameters. I can generate random point of the elliptic curve of 163 bits. However, when I compute its order, it displays exhaust memory and then it exits and some times Jim dead message is displayed.

I could not understand the problem. Could you say something for me regarding this problem? Thank you in advance.

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Can you post a sequence of commands that exhibits the problem?

Volker Braun gravatar imageVolker Braun ( 2012-06-02 10:05:32 -0500 )edit

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answered 2013-12-09 22:48:54 -0500

John Cremona gravatar image

Sage is not magic. If no-one has implemented a procedure for computing orders of curves over such large binary fields, then it will revert to using a generaic procedure, and that will not work in reasonable time.

I think that the documentation does say something about this: apart from prime fields, where Sage uses a pretty good SEA implementation from PARI, the point-counting abilities are definitely not good enough for fields of cryptographic interest.

Feel free to contribute something better!

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nbruin gravatar imagenbruin ( 2013-12-12 09:39:14 -0500 )edit

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Asked: 2012-05-31 22:19:39 -0500

Seen: 278 times

Last updated: Dec 09 '13