The functionality of the system rests on the fact that if C $$ M e $($mod n$),$ then M $$ Cd $($mod n$).$ The security

of the system rests on the fact that if all an attacker knows is e$,$ n$,$ and the encrypted message C$,$ is is very hard

computationally to work backwards and determine M $.$

$1)$ Your published encryption keys are n $=3127,$ and e $=2121.$ Note, this corresponds to p $=53,$ q $=59.$

Show that GCD$($e$,($p $1)($q $1))=1,$ and show your steps.

$2)$ Determine a decryption key d for this system. Show your steps.