discuss how diffie-hellman key exchange works

Answer 1

The Diffie-Hellman key exchange is a cryptographic protocol that allows two parties to establish a shared secret key over an insecure channel. This shared key can then be used for secure communication using symmetric encryption.

The process of Diffie-Hellman key exchange is as follows:

1. Both parties, let's call them Alice and Bob, agree on a prime number, p, and a base, g. These values are public and can be known by anyone. The security of the Diffie-Hellman protocol relies on the difficulty of solving the discrete logarithm problem.

2. Alice and Bob each choose a secret number, a and b respectively, which are randomly generated and kept private.

3. Using the formula A = g^a mod p, Alice calculates her public value A, and using the formula B = g^b mod p, Bob calculates his public value B.

4. Alice and Bob exchange their public values A and B.

5. Alice computes the shared secret key K using Bob's public value B and her secret value a using the formula K = B^a mod p.

6. Similarly, Bob computes the shared secret key K using Alice's public value A and his secret value b using the formula K = A^b mod p.

7. At this point, both Alice and Bob have independently computed the same value for the shared secret key K. This key can now be used for symmetric encryption to secure their communication.

It is important to note that even though an eavesdropper can observe the public values A and B, and even intercept the entire communication, they cannot compute the original secret values a and b or the shared secret key K, assuming the prime number p and base g are sufficiently large. This is because solving the discrete logarithm problem is computationally infeasible for large prime numbers and bases.

Diffie-Hellman key exchange provides a secure method for establishing a shared secret key between two parties without the need for any prior communication or shared secret. It is widely used in various protocols, such as Transport Layer Security (TLS), Secure Shell (SSH), and Virtual Private Networks (VPNs).