Proof of (in)distinguishability based on DDH/CDH/DL I am wondering whether or not it is known that the following problem is computationally infeasible while working in a group for which the DDH (or CDH or DL) assumption holds (as usual, g is a group generator):
Given the input tuple $(g, g^{\alpha_1}, g^{\alpha_2}, g^{y}, g^{z})$ where $z \in \{y \alpha_1, y \alpha_2\}$, the desired output is $g^{\alpha_i}$ (or simply $i$) such that $z = y\alpha_i$.
If it is not known, I would appreciate any suggestions for a reduction based proof.
The two given tuples are computationally indistinguishable. Here's a proof
Let tuples $T_1=(g, g^{\alpha_1}, g^{\alpha_2}, g^y, g^{\alpha_1y})$ and $T_2=(g,  g^{\alpha_1}, g^{\alpha_2}, g^y, g^{\alpha_2y})$
Lets take a tuple $T_3=(g, g^{\alpha_1}, g^{\alpha_2}, g^y, g^r)$ where $r \overset{$}\leftarrow  
 \mathcal{R}$. That is, for the purpose of the proof we generate a tuple with the last element being a random element of the group.
It's easy to see that $T_1 \approx T_3$ ($\approx$: notation for compuational indistinguishability) because of DDH assumption. Same way, $T_2 \approx T_3$ as well. Since we know that computational indistinguishability is transitive, that means $T_1 \approx T_2$.