Method and apparatus for generating large numbers of encryption keys

Entropy obtained from a series of key generation exchanges may be combined with entropy from a strong entropy source to allow the strong entropy to be stretched to generate a larger number of keys for use on a communication network, without requiring additional information from the group members and without requiring the entropy source to be increased in size or in number. In one embodiment, nonces exchanged during an initial key exchange are used to generate additional key material that is then fed, together with a fresh random secret, to another pseudo-random function to generate an additional key stream. The fresh ransom secret may be generated at the GCKS from a physical entropy source or other entropy source, and may be changed at will by the GCKS to further increase the strength of the keys. The methods are particularly useful for group key management where a large number of keys are required to be generated in a short time frame.