Re: Elliptic Curve Creation and Scalar Multiplication

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Sun, Nov 03, 2019 at 06:04:36PM +0000, Richard Heylen wrote:
> 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

If you want to do it in C with libpari
you should look at the functions FpE_mul, FpXQE_mul and FlxqE_mul.

Cheers,
Bill.