What is the Diffie-Hellman key exchange?

The Diffie-Hellman key exchange is a cryptographic protocol that allows two parties to establish a shared secret key over an insecure communication channel. It was developed by Whitfield Diffie and Martin Hellman in 1976 and is widely used in modern encryption systems.

In the Diffie-Hellman key exchange, both parties, let's call them Alice and Bob, agree on a large prime number, denoted as "p," and a primitive root modulo "p," denoted as "g." These values are publicly known.

The key exchange process begins with Alice and Bob independently selecting their secret values, denoted as "a" and "b" respectively. These secret values are kept private.

Alice then computes her public key by raising the primitive root "g" to the power of her secret value "a" modulo "p." This value, denoted as "A," is sent to Bob.

Similarly, Bob computes his public key by raising the primitive root "g" to the power of his secret value "b" modulo "p." This value, denoted as "B," is sent to Alice.

Upon receiving Bob's public key "B," Alice computes the shared secret key by raising it to the power of her secret value "a" modulo "p." Similarly, Bob computes the shared secret key by raising Alice's public key "A" to the power of his secret value "b" modulo "p."

Since both Alice and Bob used the same prime number "p" and primitive root "g," and performed the same modular exponentiation calculations, they will arrive at the same shared secret key. This shared secret key can then be used for symmetric encryption or other cryptographic purposes.

The beauty of the Diffie-Hellman key exchange lies in the fact that even if an eavesdropper intercepts the public keys "A" and "B," it is computationally infeasible for them to determine the secret values "a" and "b" or the shared secret key. This property is based on the difficulty of the discrete logarithm problem in modular arithmetic.

Overall, the Diffie-Hellman key exchange provides a secure method for two parties to establish a shared secret key without prior communication or the need for a trusted third party.