Why is the payload size is restricted when using RSA
When you're talking about RSA-1024, the "1024" refers to the bit length of n, so n is 128 bytes long. Now let's take a look at RSA decryption process :

In order to recover your plaintext, you will compute 
\begin{align*}
c^d \mod n &amp;= m^{e*d}\mod n\\
&amp; = m \mod n
\end{align*}
You can see that if $ m &gt; n$, i.e. if $m$ is more than 128 bytes (in case of RSA 1024), the result will not be $m$, hence the size limitation.