MaplePrimes - answers and comments on Question, Maple examples about Elliptic curve on Galois field GF(p^m)

The ?GF package will allow you to compute over GF(p^k

John May — Fri, 20 Aug 2010 04:11:32 Z

The ?GF package will allow you to compute over GF(p^k):

(**)G16 := GF(2,4);
                                            4
                        G16 := Z[2] [T] / <T  + T + 1>

(**)a := G16:-PrimitiveElement();
                                              3
                                a := 1 + T + T

(**)b := G16:-random();
                                            2
                                  b := T + T

(**)G16:-`+`(a,b);
                                       2    3
                                  1 + T  + T

(**)G16:-`*`(a,b);
                                         2    3
                                1 + T + T  + T

google?

Axel Vogt — Fri, 20 Aug 2010 22:42:49 Z

Using Google shows a lot, and especially points to Rusin's pages for an overview.

Re: The GF package will allow you to compute over GF(p^k):

nhau — Sat, 21 Aug 2010 09:37:36 Z

Thanks a lot, John!

By the way, do you happen to know how to map a number to a point on elliptic on GF(p^m)? With the package GF you guided, I think I can use GF:-input to map a number to an element in GF(p^m). But I don't know how to map this element to a point on elliptic curve.

If you know any procedure to do this, please help me.

Thanks very much in advance,

re: google?

nhau — Tue, 24 Aug 2010 20:52:11 Z

Thanks Axel!

I have tried google but most of links I see are related to elliptic on Fp. I haven't seen a link that shows example of using maple to implement elliptic on GF(p^m). Maybe I'm not lucky.

The scalar multiplication algorithm I'm learning is at

http://reference.kfupm.edu.sa/content/f/a/fast_elliptic_curve_algorithm_combining__1179570.pdf

I'm just new with Maple, if you see any link that may help me in this case, please share with me.

Thank you very much,

hmm ...

Axel Vogt — Tue, 24 Aug 2010 23:00:25 Z

that sounds a bit lame to me: already the first reply by John May has it and Google's 6 entry shows "Maple Code"

You have to look into the links and 'study' it a bit.

At a second thought: what do you really want and know? Scalar multiplication (this is just multiple addition here, no?) or a fast coding?

PS: this is another example for "no updates shown for 'recent contributions', so the thread will die"
I certainly do not want to subscribe to my answers and stumbled over it again just by accident

Maple code for elliptic curve calculations over GF(2,m)

DuncanA — Wed, 25 Aug 2010 00:04:30 Z

@nhau

http://maths.dur.ac.uk/Ug/projects/library/PR4/000419461r.pdf

This pdf file contains maple code for elliptic curve calculations over GF(2,m). They don't use the GF package, but use modp1 polynomial representation.

Duncan