$[$Protocol$]$ Simulate the protocol in the file Driver.java. To help you with this problem, here is

a sample session:

$>$ java Driver

Usage: java Driver BBS$\_$p BBS$\_$q RSA$\_$Alice$\_$p RSA$\_$Alice$\_$q RSA$\_$Bob$\_$p RSA$\_$Bob$\_$q DH$\_$q

$>$

$>$ java Driver $7199127131137139149$

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

n $=1393$

s $=696$

Setting up DH with q $=149$

alpha $=147$

$*****$ Alice$$s side $*****$

p$=127$ q$=131$ n$=16637$ phi$($n$)=16380$ e$=181$ d$=181$

Ra $=591$

Xa $=49$

Ya $=83$

$******$ Bob$$s side $******$

p$=137$ q$=139$ n$=19043$ phi$($n$)=18768$ e$=137$ d$=137$

Rb $=84$

Xb $=74$

Yb $=148$

E$($PUa$,$Ra$)=8117$

E$($PRb$,$E$($PUa$,$Ra$))=5651$

E$($PUa$,$Yb$)=6137$

E$($PRb$,$E$($PUa$,$Yb$))=3945$

$*****$ Alice$$s side $*****$

Decrypted Ra $=591$

Decrypted Yb $=148$

K $=148$

E$($PUb$,$Rb$)=2550$

E$($PRa$,$E$($PUb$,$Rb$))=11851$

E$($PUb$,$Ya$)=1179$

E$($PRa$,$E$($PUb$,$Ya$))=2358$

$******$ Bob$$s side $******$

Decrypted Rb $=84$

Decrypted Ya $=83$

K $=148$

class Driver

$\{$

$/*$ complete the following method to simulate the protocol given in

$*$ the handout and match the output listed in the handout. You

$*$ must modify ALL and ONLY the lines marked with a "modify"

$*$ comment.

$*/$

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

$\{$

if $($args$.$length $!=7)$

$\{$

System.out.println$("$Usage: java Driver BBS$\_$p BBS$\_$q RSA$\_$Alice$\_$p $"+$

"RSA$\_$Alice$\_$q RSA$\_$Bob$\_$p RSA$\_$Bob$\_$q DH$\_$q$")$;

System.exit$(1)$;

$\}$

Primes.loadPrimes$()$;

$/*$ inputs for BBS computations $*/$

$/*($in this simulation, the BBS instance is shared by Alice and Bob$)*/$

int BBS$\_$p $=$ Integer.parseInt$($args$[0])$;

int BBS$\_$q $=$ Integer.parseInt$($args$[1])$;

BBS bbs $=$ new BBS$($BBS$\_$p$,$BBS$\_$q$)$;

$/*$ inputs for public$-$private key pair computations $*/$

int RSAa$\_$p $=$ Integer.parseInt$($args$[2])$;

int RSAa$\_$q $=$ Integer.parseInt$($args$[3])$;

int RSAb$\_$p $=$ Integer.parseInt$($args$[4])$;

int RSAb$\_$q $=$ Integer.parseInt$($args$[5])$;

$/*$ input for Diffie$-$Hellman computations $*/$

int DH$\_$q $=$ Integer.parseInt$($args$[6])$;

System.out.println$("$Setting up DH with q $="+$ DH$\_$q$)$;

int alpha $=$ Primes.pickAlpha$($DH$\_$q$)$;

System.out.println$("$alpha $="+$ alpha$)$;

System.out.println$("*****$ Alice's side $*****")$;

RSA RSAa $=$ new RSA$($RSAa$\_$p$,$ RSAa$\_$q$)$;

int Ra $=-1$; $/*$ modify: random integer $*/$

System.out.println$("$Ra $="+$ Ra$)$;

int Xa $=$ DH$\_$q $/3$;

System.out.println$("$Xa $="+$ Xa$)$;

int Ya $=-1$; $/*$ modify: first step in Diffie Hellman $*/$

System.out.println$("$Ya $="+$ Ya$)$;

System.out.println$("******$ Bob's side $******")$;

RSA RSAb $=$ new RSA$($RSAb$\_$p$,$ RSAb$\_$q$)$;

int Rb $=-1$; $/*$ modify: random integer $*/$

System.out.println$("$Rb $="+$ Rb$)$;

int Xb $=$ DH$\_$q $/2$;

System.out.println$("$Xb $="+$ Xb$)$;

int Yb $=-1$; $/*$ modify: second step in Diffie Hellman $*/$

System.out.println$("$Yb $="+$ Yb$)$;

$/*$ encrypt and sign Ra $*/$

int EPUa$\_$Ra $=-1$; $/*$ modify: encrypt step $*/$

int EPRb$\_$Ra $=-1$; $/*$ modify: sign step $*/$

System.out.println$("$E$($PUa$,$Ra$)="+$ EPUa$\_$Ra$)$;

System.out.println$("$E$($PRb$,$E$($PUa$,$Ra$))="+$ EPRb$\_$Ra$)$;

$/*$ encrypt and sign Yb $*/$

int EPUa$\_$Yb $=-1$; $/*$ modify: encrypt step $*/$

int EPRb$\_$Yb $=-1$; $/*$ modify: sign step $*/$

System.out.println$("$E$($PUa$,$Yb$)="+$ EPUa$\_$Yb$)$;

System.out.println$("$E$($PRb$,$E$($PUa$,$Yb$))="+$ EPRb$\_$Yb$)$;

System.out.println$("*****$ Alice's side $*****")$;

int RaDec $=-1$; $/*$ modify: value decrypted by Alice $*/$

System.out.println$("$Decrypted Ra $="+$ RaDec$)$;

int YbDec $=-1$; $/*$ modify: value decrypted by Alice $*/$

System.out.println$("$Decrypted Yb $="+$ YbDec$)$;

int K $=-1$; $/*$ modify: compute session key with Diffie Hellman $*/$

System.out.println$("$K $="+$ K$)$;

$/*$ encrypt and sign RB $*/$

int EPUb$\_$Rb $=-1$; $/*$ modify: encrypt step $*/$

int EPRa$\_$Rb $=-1$; $/*$ modify: sign step $*/$

System.out.println$("$E$($PUb$,$Rb$)="+$ EPUb$\_$Rb$)$;

System.out.println$("$E$($PRa$,$E$($PUb$,$Rb$))="+$ EPRa$\_$Rb$)$;

$/*$ encrypt and sign Yb $*/$

int EPUb$\_$Ya $=-1$; $/*$ modify: encrypt step $*/$

int EPRa$\_$Ya $=-1$; $/*$ modify: sign step $*/$

System.out.println$("$E$($PUb$,$Ya$)="+$ EPUb$\_$Ya$)$;

System.out.println$("$E$($PRa$,$E$($PUb$,$Ya$))="+$ EPRa$\_$Ya$)$;

System.out.println$("******$ Bob's side $******")$;

int RbDec $=-1$; $/*$ modify: value decrypted by Bob $*/$

System.out.println$("$Decrypted Rb $="+$ RbDec$)$;

int YaDec $=-1$; $/*$ modify: value decrypted by Bob $*/$

System.out.println$("$Decrypted Ya $="+$ YaDec$)$;

K $=-1$; $/*$ modify: compute session key with Diffie Hellman $*/$

System.out.println$("$K $="+$ K$)$;

$\}//$ main method

$\}//$ Driver class