8. (15 points) Alice and Bob wish to create a secure connection, so they use the

Question

8. (15 points) Alice and Bob wish to create a secure connection, so they use the Diffie-Hellman key ex change. They select the public values of p 43 and g9 (a) Alice chooses a secret value of a 3. Calculate her initial message to Bob (b) Bob responds with 10. Calculate the shared secret value (c) The Diffie-Hellman key exchange has an important vulnerability. Describe how Trudy might inter- cept communication between Alice and Bob if they are not careful. What measures can they take to defend against this attack?

Explanation / Answer

a)

Given,

In Diffie Helman keychange p = 43, g = 9

Secret key of Alice, a = 3

Alice sends the value of ga (mod p) to Bob.

Message = ga (mod p)

= 93 (mod 43)

= 41

b) Given Bob sends a value of 10 to Alice. Let B = 10

Shared secret key , K = Ba (mod p)

= 103 (mod 43)

= 11

c)

Trudy can come in the middle and create one key between Alice and herself and the other key between bob and
herself and pretending as Alice to Bob and as Bob to Alice, he can decrypt/encrypt the messages. This is known as Man in the middle attack. To prevent this attack , both parties need to authenticate themselves to the other using some preshared key mechanism , digital signature mechanism etc.

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