I have a naive question, what is the nomenclature of exponentiation mean in ECC?
I was reading about exponential ElGamal, what does it mean if a generator point $G^x$ ? What does $G * \ldots * G$ actually mean?
I know what point double and point addition are, they are inline with scalar operations with the base point. How can two curve points be multiplied together?
In a group, where there is by definition only one operation, exponentiation means repeated application of the group operation, whatever that is. That is, if the group operation is noted $\circ$, $g$ is a group element, and $x$ is a positive integer, $g^x$ is short for $\underbrace{g\circ g\circ\dots\circ g}_\text{$x$ terms}$.
In elliptic curve groups, the operation is the point addition with which you are hopefully familiar.
