Alice and Bob communicate over an insecure network and want to securely exchange

information. They decided to use a Caesar cipher for encryption and the Diffie$-$Hellman

key exchange for secure key generation. Alice and Bob decide to use the Diffie$-$Hellman

key exchange to generate a shared secret key for decrypting their messages. Figure $1$

shows the numerical representation of the alphabet.

a$)$If Alice chooses a private key $($a $=5)$ and Bob chooses a private key $($b $=7),$ and the agreed$-$upon base $($g $=3)$ with a prime modulus $($p $=17).$ Compute the shared secret key for Bob and Alice.

b$)$Decrypt the following encrypted terms.

i$.$DVC

ii$.$UOBLOBYC

iii.WPK

iv$.$FSBEC

v$.$SZ

c$)$Explain each of the decrypted terms in $($b$).$

$(4$ Marks$)$

$(5$ Marks$)$

$(5$ Marks$)$

d$)$Explain how the Diffie$-$Hellman key exchange is vulnerable to a man$-$in$-$the$-$middle attack.

$(4$ Marks$)$

e$)$Provide TWO $(2)$ possible solutions to overcome the vulnerability of the Diffie$-$ Hellman key exchange to man$-$in$-$the$-$middle attacks.