I've been reading about The discrete logarithm problem as of recent and i decided to try it out on a small portion of numbers myself and i actually came to a mental gridlock after watching this Video.
In the video, he uses the mod p which is prime to find a specific generator point (which is also prime) that could iterate all possible points(which i know that
G is constant throughout the curve. but why use the order of the curve to find a suitable generator point.). And he also mentions that some numbers can't provide all possible digits that can iterate through all possible values.
But what baffles me the most is that the real values like the generator point and the order of the curves for example
secp192ri is/are not prime. And did i mention that all the answers on the discrete logarithm problem online ALL had prime generator points and the order of the curve were also prime. Can i get a breakdown as of what is going on?
Any opinions would be appreciated.