$.$ Suppose Alice wants her friends to encrypt email messages before sending them to her. Computers represent text as long numbers $(01$ for$$A$,02$ for$$B$,...26$ for $$Z$),$ so an email message is just a very big number. The RSA Encryption Scheme is often used to encrypt and then decrypt electronic communications

Alice$$s Setup: Alice$$s Setup:

Chooses two prime numbers.

Calculates the product n $=$ pq$.$

Calculates m $=($p $1)($q $1).$

Chooses numbers e and d so that ed has a remainder of $1$ when divided by m$.$

Publishes her public key $($n$,$e$).$

p $=11$ and q $=3.$

n $=$ pq $=11\backslash$times $3=33.$

m $=($p $1)($q $1)=10\backslash$times $2=20.$

If e $=3$ and d $=7,$ then ed $=21$ has a remainder of $1$ when divided by m $=20.$

Publish $($n$,$e$)=(33,3).$

Bob encrypts a message M for Alice:

Finds Alice$$s public key $($n$,$e$).$

Finds the remainder C when Me is divided by n$.$

Sends ciphertext C to Alice.

Bob encrypts message M $=14$ :

$($n$,$e$)=(33,3).$

When $143=2744$ is divided by $33,$ the remainder is C $=5.$

Sends ciphertext C $=5$ to Alice.

Alice receives and decrypts ciphertext C:

Uses her private key $($n$,$d$).$

Finds remainder R when Cd is divided by n$.$

R matches the message M that Bob wanted to send to Alice!

Alice decrypts ciphertext C $=5$:

$($n$,$d$)=(33,7).$

When $57=78125$ is divided by $33,$ the remainder is R $=14.$

R $=14=$ M$,$ the original message from Bob!

Cat wants to send the message M $=12$ to Alice. Using Alice$$s public and private keys, calculate the ciphertext C$,$ and the value for R when Alice recovers the message.

$2.$ Using the RSA$\_$lib.py and AES library, please design the hybrid encryption following the protocol:

s$1.$ Bob generates the public key$/$secret key using RSA.

s$2.$ a$.$Alice generates the session key and uses Bob's public key to encrypt the session key, then she sends the ciphertext to Bob.

b$.$ Alice also uses the session key to encrypt the first message: "Hello, Bob" using the AES mechanism.

s$3.$ a$.$ Bob uses the secret key to decrypt the ciphertext and obtain the session key.

b$.$ Bob uses the decrypted session key to decrypt the first message and receives "Hello, Bob".

s$4.$ Bob and Alice will communicate together using the session key.

s$5.$ After five rounds, Alice will generate the new session key and uses the same protocol to send Bob the new session key.

Please also print on the screen all the steps that are required in the above protocol.

$3.$ Please write the scenario$/$protocol using the hybrid encryption schemes $($public key$/$secret key encryption$)$ that you know$/$learn in reality.

Topic$3\_$Message Encryption.py

RSA$\_$lib.py