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Diffie–Hellman key exchange is a method of securely exchanging cryptographic keys over a public communication channel and was one of the first public-key protocols as conceived by Ralph Merkle and named after Whitfield Diffie and Martin Hellman.
It allows two parties to establish a shared secret key that can be used for secure communication, without the need for the two parties to share any secret information beforehand.
The Diffie–Hellman key exchange is based on the idea of using public-key cryptography, in which each party has a public key and a private key. The public key can be shared with anyone, while the private key must be kept secret.
The Diffie–Hellman key exchange works as follows:
- Both parties agree on a large prime number and a generator.
- Each party generates a secret number (the private key) and computes a public key using the agreed-upon prime number and generator.
- Both parties exchange their public keys.
- Each party uses the other party's public key and their own private key to compute the shared secret key.
The shared secret key can then be used to encrypt and decrypt messages between the two parties. Because the shared secret key is derived from both parties' private keys, it is secure as long as both private keys remain secret.
Diffie–Hellman key exchange is widely used in a variety of cryptographic protocols and is an important part of many secure communication systems.
Here's how it works:
- Alice and Bob agree on a prime number (p) and a base number (g). These values are publicly known.
- Alice chooses a secret number (a) and computes A = g^a mod p. Alice sends A to Bob.
- Bob chooses a secret number (b) and computes B = g^b mod p. Bob sends B to Alice.
- Alice computes the shared secret key K = B^a mod p.
- Bob computes the shared secret key K = A^b mod p.
Since both Alice and Bob have computed the same value for K, they now have a shared secret key that can be used to encrypt and decrypt messages. The key exchange is secure because it is computationally infeasible for an eavesdropper to determine the secret numbers a and b from the publicly known values of A, B, p, and g.
Diffie–Hellman key exchange is widely used in secure communication protocols such as HTTPS and SSH.
