An identity provider discovery service operative at a service provider is described. The system comprises an interface for receiving data elements which are assigned to individual transactions and require processing before delivery into the data warehouse. The set of changes is analyzed and it is determined that the set of changes includes two or more of: a subset of row-level changes, a subset of statement-level changes, and a subset of procedure-level changes. The verifier does not need to obtain a different public key for each signer, since the signature scheme is \u201cidentity-based\u201d; the number of PKGs may be fewer than the number of signers. The immiscibility of the polar impurities in the gas-expanded solvent enables separation of the polar impurities from the gas-expanded solvent. In a further embodiment the crystal surfaces are cylindrically curved.