Suppose Alice and Bob use Diffie$-$Hellman Key Exchange to create a

symmetric key. Assume also that Alice and Bob selected the values a and

b$,$ respectively, as shown in the figure below. Accordingly, Alice computes

$g^a$ mod $p$ and sends it to Bob, while Bob computes $g^b$ mod $p$ and sends it

to Alice. Trudy wants to perform a man$-$in$-$the$-$middle attack to establish a

single symmetric key with both Alice and Bob. Is this possible? if yes, what

value will Trudy calculate and send to Alice, given that Trudy chose the

value $t?$

Alice, a

Trudy, $t$

Bob, b

Yes, this is possible. Trudy will send mod $\{$:$p)$ to Alice

No$,$ Trudy cannot establish a single symmetric key with both Alice and

Bob

Yes, this is possible. Trudy will send $(g^{at}$ mod p$)$ to Alice

Yes, this is possible. Trudy will send mod p$)$ to Alice

Yes, this is possible. Trudy will send mod p$)$ to Alice