How to Generate a Diffie-Hellman Key for Secure Communication

What is the process to generate a Diffie-Hellman key for secure communication?

How can Alice and Bob use the Diffie-Hellman key to securely communicate?

Answer:

To generate a Diffie-Hellman key for secure communication, Alice and Bob can follow the steps outlined below:

The Diffie-Hellman key allows Alice and Bob to securely communicate by sharing a secret that cannot easily be determined by an eavesdropper. To generate a Diffie-Hellman key for Alice and Bob with given prime number p = 101 and base number g = 7, they can follow these steps:

1. Alice and Bob agree on a prime number, p = 101, and a base number, g = 7.
2. Alice chooses a secret number, a, which can be any positive integer less than p. Let's say Alice chooses a = 13.
3. Bob also chooses a secret number, b, which can be any positive integer less than p. Let's say Bob chooses b = 19.
4. Alice computes A, which is equal to g raised to the power of a, modulo p. In this case, A = (7^(13)) % 101, which equals 58.
5. Bob computes B, which is equal to g raised to the power of b, modulo p. In this case, B = (7^(19)) % 101, which equals 1.
6. Alice sends A to Bob, and Bob sends B to Alice.
7. Alice computes the shared secret key, K, using Bob's value of B and her own secret value, a. The formula is K = B raised to the power of a, modulo p. In this case, K = (1^(13)) % 101, which equals 1.
8. Bob computes the shared secret key, K, using Alice's value of A and his own secret value, b. The formula is K = A raised to the power of b, modulo p. In this case, K = (58^(19)) % 101, which equals 1.
9. Both Alice and Bob now have the same shared secret key, which is 1 in this example.

By following these steps, Alice and Bob can generate a Diffie-Hellman key for secure communication.