Re: Elliptic Curve Creation and Scalar Multiplication

[Richard Heylen <richardheylen@gmail.com>]

The help for the elliptic curve functions can be obtained in gp by typing ?5

? E=ellinit(Mod([0,0,0,1,1],11));

This sets up an elliptic curve y^2=x^3+x+1 over F_14

? ellgroup(E)

%2 = [14]

? ellordinate(E,1)

This finds y coordinates (if any) of points on the curve for a particular x coordinate.

%3 = [Mod(6, 11), Mod(5, 11)]

We therefore know [1,5] is on the curve

? ellorder(E,[1,5]) 

%4 = 14

? ellpow(E,[1,5],2)

%5 = [Mod(3, 11), Mod(3, 11)]

? ellorder(E,[3,3])

%6 = 7

On Sun, 3 Nov 2019 at 15:36, Tiago Mendes <tiagovazmendes7@gmail.com> wrote:

Good afternoon,

I am using the PARI C Library and need some help. This is what i want to do:

- Create an Elliptic Curve over a Finite Field  F_q

- Make scalar multiplication  over this Elliptic Curve  ( the one above ) , this is,

 

 i need to calculate something like k*P where k is a scalar    

Obrigado,

os meus cumprimentos

Tiago Mendes

tiagovazmendes7@gmail.com