Question

Consider the two parties ALICE and BOB uses the Diffie-Hellman key exchange technique. Assume that the modulus (p) is 5 and the primitive root (g) is 3. ALICE chooses 2 and BOB chooses 4 as their secrets respectively. What is the common secret key between the two parties?

(a) 1
(b) 5
(c) 3
(d) 2​

Answer 1

Answer:

c) 3

Step-by-step explanation:

Diffie-Hellman is the method to generate a shared secret between two people in such a way that the secret can not be seen by observing the communication. It is useful as one can use the technique to create an encryption key with someone, and then start encrypting their traffic with that key.

Primitive root = g = 3 (Given)

Modulus = p = 5 (Given)

Alice = Xa = 2  and  Bob = Xb = 4

Ya = 3² mod 5 = 2

Yb = 3~5 mod 5 = 3

We will assume the D-H key to be K.

K = YaXb mod 5

K = 2~5 mod 5 = 3

Or

K = YbXa mod 5

K = 4² mod 5 = 3

Thus, the common secret key between the two parties is 3.