Diffie Hellman

Question

 

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Is this in gaye portion 2022

Answer 1

Given that g is the primitive root and n is the modulus. Party A(sender) secret key be $K_{a}$ and let party B(receiver) secret key be $K_{b}$.

Party A is aware of g,n and $K_{a}$ whereas Party B is aware of g,n and $K_{b}$ . Message sent by A to B will be $M_{ab}$ = $g^{K_{a}}$modn and message sent by party B to A will be $g^{K_{b}}$modn

$M_{ab}$ = 11⁶ mod 23 = 9 

$M_{ba}$ = 11⁵ mod 23 = 5

The DH key for party A will be (Mba)⁶ mod 23 which is equal to DH key for party B which is, (Mab)⁵ mod 23.

(Mba)⁶ mod 23 = (Mab)⁵ mod 23 = (5)⁶ mod 23 = (9)⁵ mod 23 = 8