$1.$ Stream Ciphers $[2$ marks$]$

Alice has designed a mobile app for one$-$on$-$one chat among her friends in the class.

However, the messages are transmitted over a channel that broadcasts to all devices

in the class. Since Alice$$s friends like to gossip, it is important that only the intended

recipient is able to read the messages. Alice has devised the following method to deal

with the problem.

Each user is assigned a $10-$character long ID$.$ Each message is at most $256-$character

long. The structure of messages is provided below:

$1$

Structure of the message: $[10-$character long sender name$][$a character separator $$:$]$

$[10-$character long receiver name$][$a character separator $$:$][235$ characters for the

gossip$]$

Example message: alicexoxxo:bobko$0$oo$0$l: eve likes to snoop

Each message is XORed with a $256-$byte long shared key between Alice and Bob. The

output ciphertext is the same size as the message $($i$.$e$.,42-$bytes for the above message

from Alice to Bob$).$ The key is changed every day. The app is updated each month

over a secure communication channel $($not the broadcast medium mentioned above$)$

and it receives the keys for the relevant pair of users $($i$.$e$.,$ Alice receives the shared key

between Alice$-$Bob and Alice$-$Eve$).$

$1.$a Use openssl CLI to generate $256-$random bytes $($the key$).$ Please provide the

command that you used and the generated key in hexadecimal. $[0\mathrm{.}25$ mark$]$

$1.$b Create a message with your name in gossip text from Alice to Bob $($e$.$g$.,$ for

the course instructor it will be: $$alicexoxox:bobko$0$oo$0$l:hassan$).$ Provide the

ciphertext using the key constructed in $1.$a and the stream cipher construction

discussed above $[0\mathrm{.}25$ mark$]$

$1.$c Assume you are Eve and you want to obtain the shared key between Alice and

Bob. You only have one encrypted message between Alice and Bob, and no

information about the gossip in the message. Would you be able to recover the

complete or partial key. Also provide the rationale for your answer $[0\mathrm{.}5$ marks$]$

$1.$d Assume you are Eve and you want to obtain the shared key between Alice and

Bob. You only have two $256-$byte encrypted messages between Alice and Bob,

and no further information about the gossip in the messages. Would you be able

to recover the complete or partial key. Also provide the rationale for your answer

$[0\mathrm{.}5$ marks$]$

$1.$e Assume you are Mallory and you know the plaintext and ciphertext pairs corresponding to the message $$alicexoxox:bobko$0$oo$0$l: eve likes to snoop$.$ You want

to modify the message such that it reads $$alicexoxox:bobko$0$oo$0$l: eve likes the

calm$.$ Is it possible? If yes, how and if no$,$ why not? $[0\mathrm{.}5$ marks