Tags: elliptic curves
Rating:
Full walkthrough can be found here:
[https://youtu.be/TeadBmee8W8](https://youtu.be/TeadBmee8W8)
We can use Sage to do most of the heavy lifting:
```sage
E = EllipticCurve(GF(8011), [-43, 166])
sage: E.lift_x(59).order()
8043
sage: E.lift_x(752).order()
2681
sage: E.lift_x(318).order()
1149
G = E.lift_x(59)
Q = E.lift_x(273)
k = 3
y0 = k * G
c1 = (k*Q)[0]*19
c2 = (k*Q)[1]*87
print(y0, c1, c2)
```
jctf{(2029,3050),7836,3816}