Hashing based on the elliptic curve discrete logarithm problem

By | August 10, 2018

At a first look, one could use the elliptic curve discrete logarithm problem to grant for the onewayness of $H(x)=x*G$ (where $G$ is the generator point of the cyclic subgroup).

Additionally, $H(x)$ is homomorphic since $H(x+y)=H(x)+H(y)$, which could prove to be a useful property for a hash function in some applications.

What are some of the disadvantages or vulnerabilities that makes such a hashing scheme not popular in practice?