python. code

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$)-$ Findad in $[1,$m$)$suchthatedmodm$=1($youwillneedaloopforthis$)$

$-$ 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$)=$ yd 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

Part II $($RSA Cryptosystem$)$ Problem $6($RSA Library$)$

$\_$primes$($lo$,$ hi$)$

$-$ Create an empty list

$-$ Foreachp in $[$lo$,$hi$),$ifpisaprime,addptothelist $-$ Return the list

$\_$sample$($a$,$ k$)$

$-$ Create a list b that is a copy $($not an alias$)$ of a $-$ Shuffle the first k elements of b

$-$ Return a list containing the first k elements of b

$\_$choice$($a$)$

$-$ Get a random number r in $[0,$ l$),$ where l is the number of elements in a $-$ Return the element in a at the index r