RSA algorithm$]$ Implement the methods in RSA.java.

class RSA

$\{$

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

int p$,$ q$,$ n$,$ phiOfN, e$,$ d;

$/*$ this constructor takes the value of p and q and initializes all of the

$*$ instance variables of the RSA object with the following constraints on

$*$ e and d:

$*1.$ e and d are both prime numbers and relatively prime to phi$($n$),$

$*2.1<$ e $<$ phi$($n$)$ AND e $<=$ d AND $0<$ e $*$ d $<=$ Primes.SKY$,$

$*3.$ e $*$ d $=1+$ k $*$ phi$($n$),$ for some positive integer k$,$ and

$*4.$ the values of e and d are such that k is the smallest value that

$*$ satisfies the previous condition.

$*$ This constructor must print the instance variables with the

$*$ following format $($only one line of output allowed$)$:

$*$

$*$ p$=3$ q$=5$ n$=15$ phi$($n$)=8$ e$=3$ d$=3$

$*$

$*$ If it is not possible to satisfy all of the conditions above, then this

$*$ constructor must throw an exception with the following message:

$*$ "Cannot handle this case."

$*/$

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

$\{$

$/*$ To be completed $*/$

$\}//$ constructor

$/*$ compute and return: a$^$e mod m

$*$ The implementation of this method MUST follow the pseudocode on

$*$ Slide $9-10$ as closely as possible with the addition of "modulo

$*$ operations" wherever needed.

$*$ Hint: Watch out for integer overflow situations. You must handle those

$*$ without any try$/$catch blocks and without any additional tests.

$*$ This method may not send anything to standard output.

$*/$

public static int modularExponent$($int a$,$ int e$,$ int m$)$

$\{$

$/*$ To be completed $*/$

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

$\}//$ modularExponent method

$/*$ return the ciphertext produced by this RSA instance for the input

$*$ plaintext m

$*$ This method may not send anything to standard output.

$*/$

public int encrypt$($int m$)$

$\{$

$/*$ To be completed $*/$

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

$\}//$ encrypt method

$/*$ return the plaintext produced by this RSA instance for the input

$*$ ciphertext c

$*$ This method may not send anything to standard output.

$*/$

public int decrypt$($int c$)$

$\{$

$/*$ To be completed $*/$

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

$\}//$ decrypt method

$/*$ This method is used for testing.

$*$ Do NOT modify it$.$

$*/$

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

$\{$

Primes.loadPrimes$()$;

if $($args$.$length $==1)$

$\{$

Primes.loadPrimes$()$;

if $($args$[0].$equals$("$constructor$"))$

$\{$

new RSA$(5,7)$;

new RSA$(17,11)$;

new RSA$(11,3)$;

new RSA$(7,13)$;

$\}$ else if $($args$[0].$equals$("$modExp$"))$

$\{$

System.out.format$("\%$d$^\%$d mod $\%$d $=\%$d

$",$

$23,20,29,$modularExponent$(23,20,29))$;

System.out.format$("\%$d$^\%$d mod $\%$d $=\%$d

$",$

$23,391,55,$modularExponent$(23,291,55))$;

System.out.format$("\%$d$^\%$d mod $\%$d $=\%$d

$",$

$31,397,55,$modularExponent$(31,397,55))$;

$\}$ else if $($args$[0].$equals$("$encrypt$"))$

$\{$

System.out.format$("$RSA$(\%$d$,\%$d$)$: encrypt$(\%$d$)=\%$d

$",$

$5,7,3,($new RSA$(5,7)).$encrypt$(3))$;

System.out.format$("$RSA$(\%$d$,\%$d$)$: encrypt$(\%$d$)=\%$d

$",$

$7,13,10,($new RSA$(7,13)).$encrypt$(10))$;

System.out.format$("$RSA$(\%$d$,\%$d$)$: encrypt$(\%$d$)=\%$d

$",$

$11,17,88,($new RSA$(11,17)).$encrypt$(88))$;

$\}$ else if $($args$[0].$equals$("$decrypt$"))$

$\{$

System.out.format$("$RSA$(\%$d$,\%$d$)$: decrypt$(\%$d$)=\%$d

$",$

$5,7,33,($new RSA$(5,7)).$decrypt$(33))$;

System.out.format$("$RSA$(\%$d$,\%$d$)$: decrypt$(\%$d$)=\%$d

$",$

$7,13,82,($new RSA$(7,13)).$decrypt$(82))$;

System.out.format$("$RSA$(\%$d$,\%$d$)$: decrypt$(\%$d$)=\%$d

$",$

$11,17,11,($new RSA$(11,17)).$decrypt$(11))$;

$\}$

$\}$

$\}//$ main method

$\}//$ RSA class