I'm reading a bit about elliptical curve cryptography. The basic idea is to define a dot-operator on the points of an elliptic curve. Given a starting point $P$, and applying this dot-operation $n$ times, we get another point $Q = n. P$ on our curve.
- The public key: The used curve, the starting ($P$) and ending point ($Q$)
- The private key: The amount of dot-operations performed ($n$)
Suppose now Alice and Bob both have a public key and a private key in the same cryptosystem, and Alice wants to send Bob a secret message. How does this exactly happen?
Please keep things simple, cryptography is not my domain and I have zero experience with this. I'm aware that there may be duplicates, but all these answers are over my head. Thank you.