Given $N$, $m$ and $Q$, find an elliptic curve $E$ and a point $P$ such that $Q=[m]P$ over $E(\mathbb{Z}/N\mathbb{Z})$.

Question

Here $[m]$ is the scalar multiplication. $N$ is NOT a prime number.

When $m=2$ and $E$ is given, this becomes the square root problem.

I'd like to know whether this problem is solvable for big $m$ (and if yes, how to solve it).

Any hint will be appreciated.