I found the following algorithm to find the generator of an elliptic curve:
- Find the order of the curve - N.
- Choose any random point on the curve - P.
- Find the order of that point - n.
- Calculate co-factor - h=N/n.
- Find the generator - G=h x P.
Here, let us assume the order of the generator G is n_g. It accounts to say n_g x G=O. On replacing G from step 5, we can observe that n_g x (h x P)=O. From this we see that n_g x h >= n_g which makes P a stronger generator with an higher order.
How should I counter this argument?