Man-in-the-middle attack when Alice and Bob employ Diffie-Hellman key exchange. Here, Carol is the intruder. Compute and complete the unknown entries in the exchanges shown below.  Alice Carol (Intruder) Bob p=23 and α= 5 are known to all Choose kpri,A =a = 7   Choose kpri,B =b = 13 Alice’s public key: kpub,A = A= αa mod p = ??   Bob’s public key: kpub,B = B=αb mod p = ?? Alice sends A to Bob; intercepted by Carol     Bob sends B to Alice; intercepted by Carol   Carol chooses c=5; computes A’ = B’ =αc mod p = ??     Carol sends A’ to Bob as if it is A from Alice Carol sends B’ to Alice as if it is from Bob   Alice derives the shared secret key as K1= (B’)a mod p = ?? Carol derives K1= Ac mod p =  ??, and K2= Bc mod p = ?? Bob derives the shared secret key as K2= (A’)b mod p = ?? Session 1 established with key K1: verify that Alice and Carol have derived the same key K1     Session 2 established with key K2; verify that Carol and Bob have derived the same key K2

Alice

Carol (Intruder)

Bob

p=23 and α= 5 are known to all

Choose k_pri,A =a = 7

Choose k_pri,B =b = 13

Alice’s public key: k_pub,A = A= α^a mod p = ??

Bob’s public key: k_pub,B = B=α^b mod p = ??

Alice sends A to Bob; intercepted by Carol

Bob sends B to Alice; intercepted by Carol

Carol chooses c=5; computes A’ = B’ =α^c mod p = ??

Carol sends A’ to Bob as if it is A from Alice

Carol sends B’ to Alice as if it is from Bob

Alice derives the shared secret key as

K1= (B’)^a mod p = ??

Carol derives

K1= A^c mod p =  ??,

and K2= B^c mod p = ??

Bob derives the shared secret key as

K2= (A’)^b mod p = ??

Session 1 established with key K1: verify that Alice and Carol have derived the same key K1

Session 2 established with key K2; verify that Carol and Bob have derived the same key K2