Question

There are 2 parts with this question that utilize the Diffie-Hellman scheme with the following prime and root for both these parts of the question. Assistance is greatly appreciated.

Consider a Diffie-Hellman scheme with a common prime q = 11 and a primitive root a = 2.

a. If user A has public key YA= 4, what is A's private key XA?

b. If user B has public key YB=7, what is the shared secret key K?

Answer 1

In the Diffie-Hellman scheme, A's private key is 8 and the shared secret key between A and B is 9.

Step-by-step explanation:

In the Diffie-Hellman scheme, each user has a public key and a private key. The public key is calculated by raising the primitive root to the power of the private key modulo the prime. To calculate A's private key XA in this case, we need to find the value of XA that satisfies the equation 2^XA mod 11 = 4. In this case, XA = 8.

To calculate the shared secret key K between user A and user B, we raise the public key of the other user to our own private key modulo the prime. In this case, K = 7^8 mod 11 = 9.