I need some help with the following statement from the book A Graduate Course in Applied Cryptography* - Dan Boneh and Victor Shoup, in 8.10.1 The key derivation problem, page 320 of v0.5:
Later, we will see examples of number-theoretic transformations that are widely used in public-key cryptography. Looking ahead a bit, we will see that for a large, composite modulus $N$, if $x$ is chosen at random modulo $N$, and an adversary is given $y := x^3 \bmod N$, it is hard to compute $x$.
To be specific, my doubt is related to how do we really prove that RSA problem can keep hard, despite small and known exponents $x^3 \bmod N$, for an adversary who doesn't know $x$. The authors said that "we will see examples" in the book. But I couldn't find them. Can you please give me some direction for such proof?