Extracting Private Keys in Diffie Hellman
This is as hard as computing the discrete logarithm: Assume you have an algorithm $\mathcal{A}$ that given $g^a$, $g^b$ and $g^{ab}$ efficiently computes $a$ and $b$ for uniform $a$ and $b$. You can use this algorithm to compute discrete logarithms as follows: Given $h = g^a$, choose a uniform $b$, compute $g^b$ and $h^b = g^{ab}$. Now give $g^a$, $g^b$ and $g^{ab}$ to $\mathcal{A}$ to obtain $a$, the discrete logarithm of $h$.