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:
- Alice and Bob agree on a prime number, p = 101, and a base number, g = 7.
- Alice chooses a secret number, a, which can be any positive integer less than p. Let's say Alice chooses a = 13.
- Bob also chooses a secret number, b, which can be any positive integer less than p. Let's say Bob chooses b = 19.
- 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.
- 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.
- Alice sends A to Bob, and Bob sends B to Alice.
- 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.
- 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.
- 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.