$3.$Hybrid Cryptosystems Alice and Bob, who wish to exchange confidential messages. They use

an insecure communication channel where an attacker, Eve, is capable of eavesdropping on

messages but cannot modify them.

Alice and Bob have agreed on using a public$-$key cryptosystem and a symmetric

cryptosystem with specific parameters $($e$.$g$.,$ RSA $2048$ and AES$256).$ Also, assuming they

also agree a hash function with specific parameters $($SHA$-256).$ Alice has a public

key$/$private key pair, $(P{K}_A$;$S{K}_A).$ Bob has a public key$/$private key pair, $(P{K}_B$;$S{K}_B).$ Alice

and Bob each know one another's public keys. To protect the confidentiality of their

communication and being computationally efficient, Alice and Bob use a protocol that

consists of a setup phase and a chat phase. During setup phase, Alice and Bob will exchanged

a symmetric key $K_{A-B}$ securely$,$ which will be used for chat phase.

Note: Your solution should only use as few a number of symmetric and$/$or public keys as

necessary. Be specific in describing the algorithms$/$approaches and steps that Alice takes.

$($e$.$g$.,$ don't just say "Alice encrypts something". If she encrypts it$,$ state the algorithm and

specific key she uses.

Question a$)$ During the setup phase, describe the basic steps how Alice and Bob will

establish and exchange a symmetric key $K_{A-B}$ securely$.$

Question b$)$ During the chat phase, describe how Alice and Bob communicate securely using

the generated key $K_{A-B}.$

Question c$)$ During the chat phase, how do Alice can authenticate herself and Bob can verify

the message does come from Alice.

Question d$)$ During the chat phase, how Alice and Bob can verify the message has not been

corrupted or altered in transit.

$4.$Digital Signature Steps using Public key Crypto and Hash. Suppose Sender Alice send a

plaintext $P$ to a Receiver Bob and help Bob to verify Alice is the sender and message $P$ has not

been changed. Filling the blank with keywords so that Bob can verify Alice is the sender and

message $P$ has not been changed.

Alice needs to send a plaintext document $P$ with a digital signature to Bob.

Alice generates a small digest $d$ from $P$ using $.$

Alice encrypts $d$ with key and sends the resulting digital signature to Bob.

Bob decrypts the signature using key to obtain the original digest $d.$

Bob also applie: $,$ o the received $P$ to produce a digest $d^{\text{'}}$ and compares $d^{\text{'}}$ to $d.$

Since d$\text{'}$ was produced from $P$ and d could only have been produced by Alice, the

equality

proves that Alice is the producer of $P$ and $P$ has not been altered in transit