Bill Allombert on Sat, 02 Apr 2011 19:27:30 +0200

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Re: ECC modelling

On Sat, Apr 02, 2011 at 06:33:27PM +0300, Eugene N wrote:
> Thank you very much, Bill
> I will try to understand the scripts you provided (especially one with
> vectors, for i am new to gp syntax). This is very kind of you!
> Unfortunately i installed the older version of pari and am now reinstalling
> the latest one (in mine ffgen was missing).

Ah yes, you need PARI 2.4.3.

> One more question: if i were to generate EC(GF(2^m)) random points, i would
> have to choose random x, solve an equation and obtain corresponding y.

you can use random(E) to get random points on the curve. There is also a function
ellordinate(E,x) which return the possible values for y.

> Does pari provides something for square roots in GF(2^m)?

Yes, you can use sqrt(). However for mathematical reason, you cannot use squareroots to
find ordinate of points on curves in characteristic 2, instead you have to
solve Artin-Shreier equations (see polrootsff).