Diffie-Hellman Exchange

Public key security relies on the communicating parties sharing a secret key. A major
consideration is how both parties can come to share such a key. The obvious exchange
possibility is that of a face-to-face meeting, but this may be impractical for many reasons.
Therefore, a method of open exchange is required in which keys may be transferred
and yet remain secret.
The Diffie-Hellman Key Exchange is an exchange process that meets this requirement
of public exchange of private keys. The intention is that a third party should be
able to monitor this communication by the first two parties and yet not be able to
derive the key.
Parties Aand B communicate over a public insecure medium, for example, the Internet.
A and B agree on two large prime numbers, n and g, where (n-1)÷2 is also a prime
and certain conditions apply to g. As these numbers (n and g) are public, either A or B
may pick them.
 Now A picks a large (512 bit, etc.) number, x, and keeps it secret.
 Similarly, B picks a large secret number, y.
 A initiates key exchange by sending B a message containing n, g, gx mod n.
 B responds by sending A a message containing gy mod n.
 A takes B’s message and raises it to the xth power to get (gy mod n)x.
 B performs a similar operation to get (gx mod n)y.
 Both calculations yield gxy mod n.
 Both A and B now share a secret key gxy mod n