Give a CPA-attack on Elgamal when used with $\mathbb{Z}_p^*$ We know that if the decisional Diffie-Hellmann problem is hard then the Elgamal encryption is CPA-secure. One show that if the chosen group is $\mathbb{Z}_p^*$ then the decisional Diffie-Hellman problem is not hard. For instance, one realizes that $g^{ab}$ is a square with probability $3/4$ with an argument based on the parity of $a,b$. Therefore, it makes self to ask the following question:


  Is there a CPA-attack on Elgamal when used with $\mathbb{Z}_p^*$?


I need some help on the way to go here. Should I try to build a distinguisher using the above fact about the Diffie-Hellman problem? Or does is just come from the algebraic structure of the group?
HINT

You already have a hint given in the problem statement: 


  $g^{ab}$ is a square with probability $3/4$ with an argument based on the parity of $a,b$.


You should start by making sure you understand why is this the case. Then, once you do that, think about what it means to break DDH: it means distinguishing things that look like $g^c$ for a random $c$ from things of the form $g^{ab}$ for random $a,b$. Given the hint above, can you find a feature that differs between these two?