The above is an app for communications between Alice and Bob using the UDP protocol. You should be family

with this app and its function before doing this assignment.

This app, however, it is not secure$.$ What you are going to do is to secure it$.$ For simplicity, there is no GUI

required in this assignment. That is$,$ messages are simply typed on the sender$$s window and printed on the

receiver$$s window. The looping should continue until the connection is terminated.

Idea:

When Alice$($Bob$)$ wants to communicate with Bob$($Alice$),$ she$($he$)$ needs to input:

$$ Remote IP$,$ Remote Port, Remote PK $($receiver$)$

$$ Local IP$,$ Local Port, Local PK $($sender$)$

The above info can be stored in a file and read it when using it$.$ please use the local IP: $127\mathrm{.}0\mathrm{.}0\mathrm{.}1$ inside the file

for simplifying the marking process.

Here, pk refers to the user$$s public key. That is$,$ the secure communication requires that Alice and Bob know

the other$$s public key first. Suppose that

$$ pk$\_$R is the receiver$$s public key, and sk$\_$R is the receiver$$s secret key.

$$ pk$\_$S is the sender$$s public key and sk$\_$S is the sender$$s secret key.

Adopted Cryptography includes:

$$ H$,$ which is a cryptography hash function $($the SHA$-1$ hash function$).$

$$ E and D$,$ which are encryption algorithm and decryption algorithm of symmetric$-$key encryption $($AES for

example$)$

$$ About the key pair, sk$=$x and pk$=$g$^$x$.($based on cyclic groups$)$

You can use an open$-$source crypto library or some open$-$source code to implement the above cryptography.

What you need to code is the following algorithms.

When the sender inputs a message M and clicks $$Send$,$ the app will do as follows before sending it to the

receiver.

$$ Choose a random number r $($nonce$)$ from Z$\_$p and compute g$^$r and TK$=($pk$\_$R$)^$r$.$

$$ Use TK to encrypt M denoted by C$=$E$($TK$,$ M$)$

$$ Compute LK$=($pk$\_$R$)^\{$sk$\_$s$\}.$

$$ Compute MAC$=$H$($LK $||$ g$^$r $||$ C $||$ LK$).$ Here, $||$ denotes the string concatenation.

$$ Send $($g$^$r$,$ C$,$ MAC$)$ to the receiver.

$$ The sender part should display M and $($g$^$r$,$ C$,$ MAC$)$

That is$,$ for security purpose, M is replaced with $($g$^$r$,$ C$,$ MAC$)$

Note: TK can be seen as a shared secret key that can be computed by both two parties.

When the receiver receives $($g$^$r$,$ C$,$ MAC$)$ from the sender$,$ the app will do as follows.

$$ Compute TK$=($g$^$r$)^\{$sk$\_$R$\}.$

$$ Compute LK$=($pk$\_$S$)^\{$sk$\_$R$\}$

$$ Compute MAC$=$H$($LK $||$ g$^$r $||$ C $||$ LK$).$ Here, $||$ denotes the string concatenation.

$$ If MAC$=$MAC$,$ go to next step. Otherwise, output $$ERROR$$

$$ Compute M$=$D$($TK$,$ C$).$

The receiver part should display

$**$The decryption on$**$

$($g$^$r$,$ C$,$ MAC$)$

$**$is$**$

M$($or ERROR$)$

Note: the receiver can reply the message. The receiver becomes the sender$,$ and the seconder becomes receiver.

Coding requirement:

You can use any open$-$source code as you like. You can use a crypto library or some open$-$source code to

implement the encryption and hashing functions and the related group generation and key pair generation. You

should cite the source if you use a downloaded code.