The Diffie-Hellman key exchange algorithm is named after its two inventors, Whitfield Diffie and Martin Hellman. The system, which can be used to establish a (symmetric) key, relies on the difficulty of the so-called discrete logarithm problem for its security.

There are two system-wide parameters, a prime number p and a value g, with g < p, such that for any number from n ∈ {1,2,...,p - 1}, there is some k for which n = g^k mod p. The number g is known as a "generator".

If our old friends Alice and Bob want to generate a shared secret key, they each generate a random secret value less than p - 1; call Alice's secret value a and Bob's secret value b. Then Alice computes a public value, g^a mod p, which she sends to Bob, and Bob create his public value g^b mod p, which he sends to Alice.

Alice then uses Bob's public value and her secret value to compute (g^b)^a mod p, while Bob computes (g^a)^b mod p. By elementary properties of exponents, these are equal, and this value is the shared secret.

Diffie-Hellman is subject to a man-in-the-middle (MiM) attack, as illustrated here.

To prevent the man-in-the-middle attack, your textbook suggests the following.

• Publish Diffie-Hellman numbers, g^a mod p, g^b mod p, etc. Note: With this scheme it is possible to establish a shared secret key without exchanging any messages.
• Authenticated Diffie-Hellman
  1. Encrypt DH exchange with a pre-shared secret (why bother with DH?)
  2. Encrypt DH value with other side's public key (???)
  3. Sign DH value with your private key
  4. Following DH exchange, send hash of DH value, your name and pre-shared secret
  5. Following DH exchange, send hash of pre-shared secret and DH value you transmitted