The algorithm is completely analogous to Diffie-Hellman key exchange in that you efficiently raise a number to a power $n$ times and send the result over while keeping $n$ as private key.

The only difference is that a different group is used: instead of using the cyclic group, we use the elliptic curve group of an elliptic curve over a finite field.

Variant of Diffie-Hellman key exchange based on elliptic curve cryptography.