Proving security of an encryption scheme
If you are working in an order $p$ prime order group which is generated by $g$, and $a$ as well as $r$ are drawn uniformly random from $\mathbb{Z}_p$, you can prove this secure under the decisional Diffie-Hellman (DDH) assumption (what you sketch here, is often referred to as modified ElGamal in the literature).

Informally speaking, under DDH you can show that $c_1$ looks like a random value. Now, once you have shown that $c_1$ looks random, you can view $g^r$ like a one-time pad on the message. 

See Section 3 of this paper for an excellent formal treatment.