ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 12 Dec 2013 09:39:14 -0600Order of randomly generated elliptic curvehttps://ask.sagemath.org/question/9020/order-of-randomly-generated-elliptic-curve/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.
Thu, 31 May 2012 22:19:39 -0500https://ask.sagemath.org/question/9020/order-of-randomly-generated-elliptic-curve/Comment by twoforone for <p>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.</p>
<p>I could not understand the problem. Could you say something for me regarding this problem? Thank you in advance.</p>
https://ask.sagemath.org/question/9020/order-of-randomly-generated-elliptic-curve/?comment=19696#post-id-19696Example: b = 0x423d0900aeb5645491fee539c297946cbc6a4f1f5
Z.<x>=GF(2)[]
K.<a>=GF(2^163, 'a', modulus = x^163 + x^7 + x^6 + x^3 + 1)
bb = Z(b.digits(2))
E = EllipticCurve(K,[1, 1, 0, 0, bb])
print E.order() this is sample problem that I could not compute its order Volker BraunSun, 03 Jun 2012 20:30:39 -0500https://ask.sagemath.org/question/9020/order-of-randomly-generated-elliptic-curve/?comment=19696#post-id-19696Comment by Volker Braun for <p>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.</p>
<p>I could not understand the problem. Could you say something for me regarding this problem? Thank you in advance.</p>
https://ask.sagemath.org/question/9020/order-of-randomly-generated-elliptic-curve/?comment=19702#post-id-19702Can you post a sequence of commands that exhibits the problem?Sat, 02 Jun 2012 10:05:32 -0500https://ask.sagemath.org/question/9020/order-of-randomly-generated-elliptic-curve/?comment=19702#post-id-19702Answer by John Cremona for <p>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.</p>
<p>I could not understand the problem. Could you say something for me regarding this problem? Thank you in advance.</p>
https://ask.sagemath.org/question/9020/order-of-randomly-generated-elliptic-curve/?answer=15783#post-id-15783Sage 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!
Mon, 09 Dec 2013 22:48:54 -0600https://ask.sagemath.org/question/9020/order-of-randomly-generated-elliptic-curve/?answer=15783#post-id-15783Comment by nbruin for <p>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.</p>
<p>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.</p>
<p>Feel free to contribute something better!</p>
https://ask.sagemath.org/question/9020/order-of-randomly-generated-elliptic-curve/?comment=16541#post-id-16541In particular, trac tickets http://trac.sagemath.org/ticket/11448 http://trac.sagemath.org/ticket/11548 seem relevant.Thu, 12 Dec 2013 09:39:14 -0600https://ask.sagemath.org/question/9020/order-of-randomly-generated-elliptic-curve/?comment=16541#post-id-16541