Karim BELABAS on Fri, 12 Oct 2001 11:27:37 +0200 (MEST) |
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Re: EC arithmetic |
On Tue, 9 Oct 2001, Erik Schlegel wrote: > Hello! > > I'm new in Pari. I need some instructions about EC arithmetic. > > 1) GP>E=ellinit(Mod([0,0,0,71,602],1009)) > Is this the only way to define any elliptic curve over finite field > F_p? What about over F_(p^n) or F_(2^n)? The elliptic curve module is rather primitive: over F_p^n, you won't be able to do much besides adding points [and it will be slow]. You can input such a curve more or less as above, but using POLMODs in INTMODs [ i.e working over F_p^n understood as Fp[X]/(T) ] E = ellinit([0,0,0,71,602] * Mod(Mod(1,1009), Mod(1,1009)*(x^2+1))) It is advised to write trivial scripts to facilitate such inputs, e.g global(ff1); INIT(p,T)= ff1 = Mod(1, Mod(1,p) * T); toff(x) = x * ff1 and results can be made more readable via repeated lifts, e.g Lift(x) = lift(lift(lift(x))) \\ one too many, but just in case... Hope this helps, Karim. -- Karim Belabas email: Karim.Belabas@math.u-psud.fr Dep. de Mathematiques, Bat. 425 Universite Paris-Sud Tel: (00 33) 1 69 15 57 48 F-91405 Orsay (France) Fax: (00 33) 1 69 15 60 19 -- PARI/GP Home Page: http://www.parigp-home.de/