• The two prime numbers are p=23 and g=5 (in textbooks you might find q & a)
• The random secret keys of A and B are:
  • A chooses $x_A=6$
  • B chooses $x_B=15$ ….. given data

• Now compute the public key of each individual using the secret key

  • A’s public key using its secret key xA:

    $y_A = g^{xA} mod p$

    $y_A = 56 mod 23 =[(52 mod 23) * (52 mod 23) * (52 mod 23)]mod 23$

    $y_A = [2 * 2 * 2]mod 23= 8$

    $y_A = 8$

  • B’s public key using its secret key $x_B$:

    $y_B = g^{xB} mod p$

    $y_B = 515 mod 23= [ (56 mod 23)* (56 mod 23)*( 53 mod 23)]mod 23$

    $y_B =[8 * 8 *10]mod 23=640 mod 23= 19$

    $y_B =19$…. Here since we already had the powers of 5^6 from previous step, we used those…

• The above two public keys are now exchanged by both A and B. Now we shall compute the session keys as:

  • A will compute the session key using B’s public key:

    $K_{AB}= y_B^{xA}$ mod p

    $K_{AB}= 196 mod 23 = [(192 mod 23)*( 192 mod 23)*( 192 mod 23)]mod 23$

    $K_{AB}= 2$

  • B will compute session key using A’s public key:

    $K_{AB}= y_A^{xB}$ mod p = 815 mod 23 =2

  (Remember: both the session keys value will have to be the same …. )

  In this manner Diffie –Hellman KEY EXCHANGE protocol works. This protocol cannot be used for exchanging messages, only key are exchanged.

Diagramatic representation