# Simplified ECC non-point public key example, how it works

I know that ECC public key is in fact point on curve calculated by $$(x,y) = k \times G$$ , while $$k$$ is random and $$G$$ is the base point, it performs "Point addition" which involves some math behind.

However, in many ECC examples, take this as example:

domain parameters $$(p, q, g)$$ and private/public key pair $$(b, g^b \bmod p)$$

The generation of the public key is simplified to power of base point $$g^b$$, yet it works perfectly well for the example. Im puzzled by how a $$(x,y)$$ 2-dimensional public key can be reduced to 1-dimensional and still work?

That reference doesn't talk about ECC as all; instead, it talks about traditional El Gamal in the group $$\mathbb{Z}_p^*$$.