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Ephemeral Diffie-Hellman

In Ephemeral Diffie-Hellman key exchange, two parties called Alice and Bob agree on a prime p, and a generator g of the field Z^* p. This field consists of the set of integers that have no non-trivial factors in common with p. The parties follow this protocol:

Alice selects random number a from the field. This number remains secret for the duration of the key exchange. Alice calculates g^a mod p and sends it to Bob (see the Diffie-Hellman Key Exchange diagram below).
Bob selects random number b from the field, calculates g^b mod p and sends it to Alice (see the Diffie-Hellman Key Exchange diagram below).
Alice, knowing g, a and g^b mod p, calculates the shared secret (g^b)^a = g^ab mod p.
Bob, knowing g, b and g^a mod p, calculates the shared secret (g^a)^b = g^ab mod p.

Both Alice and Bob now have the same shared secret as the key with which to perform symmetric encryption. Eve, the eavesdropper, knows g, g^a and g^b, however being unaware of either a or b, is unable to calculate g^ab from g^a and g^b.
This difficulty arises from the Diffie-Hellman problem which is based upon the discrete logarithm problem in which x cannot be easily calculated from g^x mod p. Ephemeral Diffie-Hellman does not provide authentication, since neither party has guarantees about the entity with which it is communicating.