A method and deterministic random bit generator system operating in accordance with the method, for generating cryptographic keys and similar secret cryptographic inputs which are hard to guess. A entropy is input from an entropy source; and an initial seed is generated as a function of the entropy input. When a request to generate a cryptographic key is received a temporary seed is generated by applying the function to the seed. The requested cryptographic key is generated by applying a second function to the temporary seed; and output. A new seed is then generated by applying a third function to the temporary seed. In one embodiment of the subject invention all three functions are carried out by applying the same operator to appropriate inputs. In another embodiment of the subject invention new entropy is incorporated into the seed from time to time.