First, we need to understand the difference between Ed25519 and X25519. For that I recommend Montgomery curves and their arithmetic by Craig Costello and Benjamin Smith, which is where I learned most of the underlying mechanics of Montgomery curves. The high level summary is that the twisted Edwards curve used by Ed25519 and the Montgomery curve used by X25519 are birationally equivalent: you can convert points from one to the other, and they behave the same way.

source: HN