
And the correct answer is the second and third options.

The first one is not true. Alice can determine the key using

the typical DiffieHellman protocol as discussed in the Unit 3

by taking the value G to the power Y and raising

it to the power X. The fourth option is not true; adding the

hash to the message actually increases the size of it.

To see whether second and third options are true, let’s take

a look at what could happen without including the hash.

So Alice picks the value X, calculates G of X and

encrypts G of X with Bob’s public key. She then tries to send

this to Bob. Now, you could intercept the message, then

send a different value to Bob, Bob recalculate the key,

G of X prime Y. Bob would then send G of Y which Mallory

could intercept and send a new value to Alice.

Alice would then calculate a nonsense key and have no

idea that the key she has calculated is worthless. Adding the

hash value of the key to this protocol allows Alice to verify

that she has a valid key that came from Bob and not

from some attacker in the middle.