Group of quadratic residue over Blum integer

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?

• Does it miss a $\mod$ ? Commented Jul 1, 2021 at 8:08
• That is right. I've made the corrections.
– Sean
Commented Jul 1, 2021 at 12:29
• How is $x \in QR_n$ is represented? E.g. If it is sampled uniformly from $[0; n\cdot ord(g))$, then these are indistinguishable since $x^2$ and $g^x$ are independent (because $x \mod n$ and $x \mod ord(g)$ are independent). Commented Jul 1, 2021 at 12:48
• Thanks very much for the insights? What about x^2 \mod \totient(n) is given. Then I guess the argument wouldn't apply?
– Sean
Commented Jul 1, 2021 at 19:55