Eliptic curve over binary field

[mariusz...@gmail.com]

Hi,

I want to use eliptic curve y^2+xy=x^3+g^3x^2+g^3+1 over F(2^4) and add two points : (g^6,g^6)+(g,g^13). But I can find in sage tutorial how that in binary field.

[John Cremona]

I am assuming the g is the default generator for GF(16). In that case:

sage: F.<g> = GF(2^4)
sage: E = EllipticCurve(F,[1,g^3,0,0,g^3+1])
sage: E
Elliptic Curve defined by y^2 + x*y = x^3 + g^3*x^2 + (g^3+1) over
Finite Field in g of size 2^4
sage: P1 = E(g^6,g^6)
sage: P2 = E(g,g^13)
sage: P1+P2
(0 : g^3 + g + 1 : 1)


John Cremona

On 9 January 2014 05:47, <mariusz...@gmail.com> wrote:
> Hi,
>
> I want to use eliptic curve y^2+xy=x^3+g^3x^2+g^3+1 over F(2^4) and add two points : (g^6,g^6)+(g,g^13). But I can find in sage tutorial how that in binary field.
>

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