Operation on elliptic curves Let $Y = xG$ be a point on an elliptic curve, $G$ the generator point and $x$ a scalar. Without knowing $x$, is it possible to calculate $x^nG$, being $n$ a natural number?
It is believed to be hard. In fact, even given $G, xG, x^2G,\dots,x^{n-1}G,x^{n+1}G,\dots,x^{2n}G$, you still can't compute $x^nG$; this is called the Generalized Diffie-Hellman Exponent assumption (see Fig. 1 here).