Problem $1.(100$ points$)$ In a public$-$key system using RSA, perform encryption and decryption for the following

$,$ and

:

$(1)$ Show encryption process. $(25$ points$)(2)$ Calculate private key

using three different methods learnt from class to be used for decryption. $(45$ points$)(2\mathrm{.}1)$ First Method. $(15$ points$)2$