MadeEasy Test Series: Computer Networks - Network Security

Question

DH key exchange algorithm is used to establish a session between sender and receiver with n=23 and g=5. The sender's secret key is 6 and the receiver's secret key is 15. What is the secret key between the receiver and sender?

 

 

Please explain with solution

 

P.S: Answer is given as 2

Answer 1

yes ans 2.

Answer 2

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

$M_{ab}$ = 5⁶ mod 23 = 8 

$M_{ba}$ = 5¹⁵ mod 23 = 19

The DH key for party A will be (Mba)⁶ mod 23 which is equal to DH key for party B which is, (Mab)¹⁵ mod 23.

(Mba)⁶ mod 23 = (Mab)¹⁵ mod 23 = (19)⁶ mod 23 = (8)¹⁵ mod 23 = 2

Answer 3

Generator = 5
Prime Modulos = 23
Now the secret key of sender(A) : 6
A will send [(5^6 mod 23) = 8] to Receiver

Secret Key of Receiver(B) : 15
B will send [(5^15 mod 23) = 19] to sender

After exchanging keys, A and B will generate a common secret key, which they will use for encryption.
Common secret key generated by A : 19^6 mod 23 (= 2)
Common secret key generated by B : 8^15 mod 23 (= 2)

Comments

How did you find (5^15 mod 23) = 19 ?

Answer 4

Both sender and receiver knows the base 'g' and 'n'. Now they both calculate A and B and send to each other. Using A and B both can calculate their keys.