So, addition under a particular elliptic curve is isomorphic to multiplication under integer modulo groups... But for some reason the author keeps referring to

So, addition under a particular elliptic curve is isomorphic to multiplication under integer modulo groups... But for some reason the author keeps referring to the underlying group as "Diffie-Hellman" instead of the process operating on some group. The result is interesting, the journey to get there was very confusing.