Let $x$ be a random element from $QR_n$, the quadratic residue group over Blum integer n (where $n=p*q$ and $p$ and $q$ are safe primes), and $g$ a generator of $QR_n$. Are the following computationally indistinguishable?
$$(x^2 \mod n, g^x) (r^2 \mod n, g^x)$$
The intuition is that it's hard to compute $x$ from $x^2$ and $g^x$. Could this be reduced to some standard assumptions?