Question

The Diffie-Hellman equations are Y(A)=. α ^X(A) mod q and K=Y(B) ^X(A) mod q.  Y(A) and  Y(B)  are the public keys of A and B; X(A) is the private key of A; K is the shared key, α is a primitive root of q. Suppose that q=13,  α=2, X(A)=2 and Y(B)=4. Find the followings: (Showing your work)

• A’s public key
• The shared key

Answer 1

Solution:

Given,

=>Diffie-Hellman algorithm is used.

=>Private key of A (X(A)) = 2

=>Private key of B (X(B)) = 4

=>q = 13 and = 2

Explanation:

Finding public key of A's:

=>Public key of A (Y(A)) = ^X(A) mod q

=>Public key of A (Y(A)) = 2^2 mod 13

=>Public key of A (Y(A)) = 4 mod 13

=>Public key of A (Y(A)) = 4

Finding value of Y(B):

=>Public key of B (Y(B)) = ^X(B) mod q

=>Public key of B (Y(B)) = 2^4 mod 13

=>Public key of B (Y(B)) = 16 mod 13

=>Public key of B (Y(B)) = 3

Finding shared key:

=>Shared key(K) = Y(B)^X(A) mod q

=>Shared key(K) = 3^2 mod 13

=>Shared key(K) = 9 mod 13

=>Shared key(K) = 9

I have explained each and every part with the help of statements attached to it.