RSA - Finding all possible encryption exponents
We know that $\varphi(x) \ge\sqrt{\frac{x}{2}}$. The size of $\varphi(n)$ is roughly the same of $n$, so $\varphi(\varphi(n))-1$ is still a intractably large number. This means finding all possible e's is infeasible because there are too many. No matter what algorithm you use, there is no way you can find all of them in polynomial time (in the security parameter).