Why $e>n^{3/2}$ prevents Wiener's attack
In Wiener's attack $k$ is a small number ($k&lt;d$). If we set $e^{'}=e+t\phi(n)$ for some large $t$ then $e^{'}$ can be used in place of $e$ for message encryption.Also the k became a big number and we can't using of Wiener's attack.For more detail you can see "Twenty Years of Attacks on the RSA Cryptosystem".