DiffieHellman

Diffie-Hellman key exchange is a method for two parties to establish a shared secret over an insecure channel without prior arrangements. It relies on public parameters and the difficulty of the discrete logarithm problem to allow both sides to derive the same value independently.

In the classic finite-field version, the participants agree on a large prime p and a generator g of the multiplicative group modulo p. Each party selects a private exponent a or b and computes A = g^a mod p and B = g^b mod p, respectively. The values A and B are exchanged. Each party then computes the shared secret as s = B^a mod p = A^b mod p = g^{ab} mod p. The shared secret is typically processed with a key-derivation function to produce symmetric encryption and integrity keys.

History and usage. Diffie and Hellman introduced the protocol in 1976, presenting a method for secure key exchange over open networks. It is widely used in secure communication protocols, including TLS, SSH, and IPsec. Variants include finite-field Diffie-Hellman and Elliptic Curve Diffie-Hellman (ECDH), the latter offering comparable security with smaller key sizes. Ephemeral variants, such as DHE or ECDHE, provide forward secrecy by generating fresh private keys for each session.

Security considerations. Diffie-Hellman assumes authenticated endpoints; without authentication, it is vulnerable to man-in-the-middle attacks. Proper parameter generation and validation, secure random number generation, and timing-attack protections are important. Elliptic-curve variants are common today due to efficiency, while standard DH remains in use in many systems.