keygen$($lo$,$ hi$)$

$-$ Get a list of primes from the interval $[$lo$,$ hi$)$

$-$ Sample two distinct random primes p and q from that list

$-$ Set n and m to pq and $($p $1)($q $1),$ respectively

$-$ Get a list primes from the interval $[2,$ m$)$

$-$ Choose a random prime e from the list such that e does not divide m $($you will need a loop for this$)$

$-$ Find a d in $[1,$ m$)$ such that ed mod m $=1($you will need a loop for this$)$

$-$ Return the tuple$1($n$,$ e$,$ d$)$

encrypt$($x$,$ n$,$ e$)$

$-$ Implement the function E $($x$)=$ xe mod n

decrypt$($y$,$ n$,$ d$)$

$-$ Implement the function D$($y $)=$ y d mod n

$1$ A tuple is like a list, but is immutable. You create a tuple by enclosing comma$-$separated values within matched parentheses, eg$,$ a $=(1,2,3).$ If a is a

tuple, a$[$i$]$ is the ith element in it