GATE | Gate IT 2005 | Question 79

Suppose that two parties A and B wish to setup a common secret key (D-H key) between themselves using the Diffie-Hellman key exchange technique. They agree on 7 as the modulus and 3 as the primitive root. Party A chooses 2 and party B chooses 5 as their respective secrets. Their D-H key is
(A) 3
(B) 4
(C) 5
(D) 6


Answer: (B)

Explanation:
Primitive root = g = 3
Modulus = p = 7
Xa = 2   and   Xb = 5

Ya = 3² mod 7 = 2
Yb = 3⁵ mod 7 = 5

We assume D-H key to be K.

K = Ya^Xb mod 7
K = 2⁵mod 7 = 4
Or
K = Yb^Xa mod 7
K = 5² mod 7 = 4


Thus, option (B) is correct.


Please comment below if you find anything wrong in the above post.


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