Imagine that you are given a point $P$ so that $P=a\times G$. If you have no knowledge of $a$ is that possible to calculate point $I$ so that $I$ is the modular inverse of $P$?
We know that over prime fields each member has a modular inverse, which means for $a\in \Bbb F_n$ there exists $x$ so that $ax\equiv 1\pmod n$. Now, My question is, is that possible to calculate point $I$ on the same curve as $P$ for which the equation $I=x\times G$ holds. This is to happen with no knowledge of either $a$ or $x$.
If such algorithm exists or become discovered in future will that be considered a weakness to the security of elliptic curves?