$[$BBS algorithm$]$ Implement the methods in BBS$.$java.

class BBS

$\{$

$/*$ the numerical components of the BBS algorithm $*/$

int p$,$ q$,$ n$,$ s$,$ X;

$/*$ Check that the p and q values are appropriate for the BBS algorithm.

$*$ If either one is not appropriate, throw an exception with a meaningful

$*$ message. Otherwise, compute and assign the values of n$,$ s$,$ and X$\_0($the

$*$ latter is stored in X$).$

$*$ Must produce the EXACT output shown in the handout, such as:

$*$ Setting up BBS with p $=7$ and q $=199$

$*$ n $=1393$

$*$ s $=696$

$*/$

BBS$($int p$,$ int q$)$ throws Exception

$\{$

System.out.println$("$Setting up BBS with p $="+$ p $+"$ and q $="+$ q$)$;

$/*$ To be completed $($you MUST keep the line above$)*/$

$\}//$ constructor

$/*$ return the largest integer less than or equal to n$/2$ that is

$*$ relatively prime to n$.$

$*/$

private int chooseS$()$

$\{$

$/*$ To be completed $*/$

return $-1$; $/*$ Delete this line in your submission $*/$

$\}//$ chooseS method

$/*$ use the BBS algorithm to update X and return the next random

$*$ bit $($with true representing a $1$ bit and false representing a $0$

$*$ bit.

$*/$

boolean getNextRandomBit$()$

$\{$

$/*$ To be completed $*/$

return false; $/*$ Delete this line in your submission $*/$

$\}//$ getNextRandomBit method

$/*$ use the BBS algorithm to return the next random integer value;

$*$ to keep values small, the $20$ most significant bits must be equal

$*$ to $0$; the remaining bits are produced by BBS from most to least

$*$ significant $($i$.$e$.,$ from left to right$)$

$*/$

int getRandomInt$()$

$\{$

$/*$ To be completed $*/$

return $-1$; $/*$ Delete this line in your submission $*/$

$\}//$ getRandomInt method

$/*$ This method is used for testing.

$*$ Do NOT modify it$.$

$*/$

public static void main$($String$[]$ args$)$ throws Exception

$\{$

if $($args$.$length $!=2)$

$\{$

System.out.println$("$Usage: java BBS