There are public-key encryption schemes based on many different mathematical hardness assumptions, like the hardness of Decisional Diffie-Hellman problem, the hardness of the Factoring problem, the hardness of the RSA problem, etc.
But my question is, are there any public-key encryption schemes based on the hardness of the Discrete Log problem? Does the hardness of the Discrete Log problem even imply the existence of secure public-key encryption?