|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). Cheers, Bill.