c$)$ Gr$$ainne wants to communicate confidentially with Diarmuid. She generates an RSA

public key, which is denoted KG $=($e$,$ n$),$ and its corresponding private key, which is

denoted K$1$

G $=($d$,$ n$).$

Which of the following pairs of RSA keys are valid RSA keys? Demonstrate why the

public and private key pairs do$,$ or do not meet the RSA conditions as part of your

answer.

$($i$)$ First key pair $($e$,$ n$)=(5,37)$ and $($d$,$ n$)=(11,37).$

$($ii$)$ Second key pair $($e$,$ n$)=(5,91)$ and $($d$,$ n$)=(41,91).$