I have an elliptic curve with the equation $ y^2 = x^3 + ax + b $ in modulo p, where p is prime.
I also have a point G on that curve.
How can I find another point that isn't a multiple of G?
I tried brute-forcing by trying all combinations of x and y, but since I'm working with 56+ digit primes this is not a very feasible way to find a point.
Is there a faster way?
Also, I'm looking for a point with y!=0 (to avoid the tangent being undefined).
I only need a single point, not all of them, but I can't find any.
The numbers are too large for me to find anything manually.
If someone is wondering, I'm using the P-192 curve as provided by the NIST:
- a = -3
- b = 2455155546008943817740293915197451784769108058161191238065
p = 6277101735386680763835789423207666416083908700390324961279
Gx = 602046282375688656758213480587526111916698976636884684818
- Gy = 174050332293622031404857552280219410364023488927386650641
NB: I'm still only in high school, so I might not understand some of the math you might find to be common knowledge, for which I'm sorry.