A. (Points 10) For the given scenario where Alice and Bob are trying to establish a shared secret key using Diffie-Hellman key exchange protocol, fill the values in the table. Show your work.

Parameter	Scenario
p, a large prime	23
, an integer in {2,3,, p-2}	3
P=23 and =3 are published
Alice chooses a in {2,3,, p-2}	5
Bob chooses b in {2,3,, p-2}	9
Alice computes A = a mod p, its public key
Bob computes B= b mod p, its public key
Alice and Bob exchange their public keys, A and B
Alice computes the shared key, KAB = Ba mod p
Bob computes the shared key, KAB = Ab mod p

(B) . (Points 11) For the given scenario where Alice is trying to send encrypted data to Bob, and Bob is trying to decrypt it, using Elgamal encryption scheme, fill the values in the table. Show your work.

Parameter	Scenario
Bob chooses p, a large prime	17
Bob chooses , primitive element in Z*p	3
Bob chooses Kpr = d {2,3, , p-2}	5
Bob computes Kpub = = d mod p
p, , and are sent to Alice
Alice chooses i in {2,3,, p-2}	7
Alice computes KE = i mod p
Alice computes KM = i mod p
Alices message to send is x Z*p	3
Alice encrypts message x, y=x*KM mod p
Alice sends KE and y to Bob
Bob computes KM = KEd mod p
Bob computes KM-1 mod p
Bob computes x = y* KM-1 mod p