ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 11 Dec 2017 00:11:35 +0100how to generate elliptic curve over Extension field GF(2^m) where m=113 using sagemathhttps://ask.sagemath.org/question/40051/how-to-generate-elliptic-curve-over-extension-field-gf2m-where-m113-using-sagemath/field is F(2^m) where m=113
E:y^2+xy=x^3+ax^2+b
a=003088250CA6E7C7FE649CE85820F7
b=00E8BEE4D3E2260744188BE0E9C723Sun, 10 Dec 2017 08:29:45 +0100https://ask.sagemath.org/question/40051/how-to-generate-elliptic-curve-over-extension-field-gf2m-where-m113-using-sagemath/Comment by vdelecroix for <p>field is F(2^m) where m=113
E:y^2+xy=x^3+ax^2+b
a=003088250CA6E7C7FE649CE85820F7
b=00E8BEE4D3E2260744188BE0E9C723</p>
https://ask.sagemath.org/question/40051/how-to-generate-elliptic-curve-over-extension-field-gf2m-where-m113-using-sagemath/?comment=40053#post-id-40053Is that your homework?Sun, 10 Dec 2017 09:53:39 +0100https://ask.sagemath.org/question/40051/how-to-generate-elliptic-curve-over-extension-field-gf2m-where-m113-using-sagemath/?comment=40053#post-id-40053Comment by slelievre for <p>field is F(2^m) where m=113
E:y^2+xy=x^3+ax^2+b
a=003088250CA6E7C7FE649CE85820F7
b=00E8BEE4D3E2260744188BE0E9C723</p>
https://ask.sagemath.org/question/40051/how-to-generate-elliptic-curve-over-extension-field-gf2m-where-m113-using-sagemath/?comment=40078#post-id-40078Tip: don't tick the "community wiki" checkbox when posting questions.
The "community wiki" tag is for questions that are not about Sage, but about Ask Sage itself.
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You need karma to be able to post links, to upvote questions and answers by others, etc.Sun, 10 Dec 2017 18:25:54 +0100https://ask.sagemath.org/question/40051/how-to-generate-elliptic-curve-over-extension-field-gf2m-where-m113-using-sagemath/?comment=40078#post-id-40078Comment by slelievre for <p>field is F(2^m) where m=113
E:y^2+xy=x^3+ax^2+b
a=003088250CA6E7C7FE649CE85820F7
b=00E8BEE4D3E2260744188BE0E9C723</p>
https://ask.sagemath.org/question/40051/how-to-generate-elliptic-curve-over-extension-field-gf2m-where-m113-using-sagemath/?comment=40079#post-id-40079To display inline code, use backticks. To display blocks of code
or error messages, separate them by a blank line from the rest
of the text, and indent them with 4 spaces, or select code lines
and click the "code" button (the icon with '101 010').
For instance, typing
If we define `f` by
def f(x, y):
return (x, y)
then `f(2, 3)` returns `(2, 3)` but `f(2)` gives:
TypeError: f() takes exactly 2 arguments (1 given)
will produce:
> If we define `f` by
>
> def f(x, y):
> return (x, y)
>
> then `f(2, 3)` returns `(2, 3)` but `f(2)` gives:
>
> TypeError: f() takes exactly 2 arguments (1 given)
Can you edit your question to do that?Sun, 10 Dec 2017 18:26:04 +0100https://ask.sagemath.org/question/40051/how-to-generate-elliptic-curve-over-extension-field-gf2m-where-m113-using-sagemath/?comment=40079#post-id-40079Answer by dan_fulea for <p>field is F(2^m) where m=113
E:y^2+xy=x^3+ax^2+b
a=003088250CA6E7C7FE649CE85820F7
b=00E8BEE4D3E2260744188BE0E9C723</p>
https://ask.sagemath.org/question/40051/how-to-generate-elliptic-curve-over-extension-field-gf2m-where-m113-using-sagemath/?answer=40095#post-id-40095As in [39628](https://ask.sagemath.org/question/39628/elliptic-curve-over-extension-field/)...
The **modulus** is also a big important part of the data, so i suppose the curve is the one displayed in:
[http://www.secg.org/SEC2-Ver-1.0.pdf](http://www.secg.org/SEC2-Ver-1.0.pdf), page 24, label `sect113r1` .
The answer is now
R.<T> = PolynomialRing( GF(2) )
F.<t> = GF( 2**113, modulus=X^113 + X^9 + 1 )
a = F.fetch_int( 0x003088250CA6E7C7FE649CE85820F7 )
b = F.fetch_int( 0x00E8BEE4D3E2260744188BE0E9C723 )
E = EllipticCurve( F, [ 1, a, 0, 0, b ] )
Comment:
We also have the order of the curve, from the reference, it is the value of the variable `n` below:
P = E.random_point()
n = 2*ZZ( 0x0100000000000000D9CCEC8A39E56F )
print n*P
print "Order: %s" % factor(n)
This gives (for "all random points"):
(0 : 1 : 0)
Order: 2 * 5192296858534827689835882578830703
sage: bool( (sqrt(q)-1)^2 < n )
True
sage: bool( n < (sqrt(q)+1)^2 )
True
Mon, 11 Dec 2017 00:11:35 +0100https://ask.sagemath.org/question/40051/how-to-generate-elliptic-curve-over-extension-field-gf2m-where-m113-using-sagemath/?answer=40095#post-id-40095