A computer-implemented method generates a random number in a cloud-based random number server. The cloud-based random number server identifies multiple entropy sources. The cloud-based random number server identifies multiple disjointed entropy sources from the multiple entropy sources, which are logically and functionally independent of one another. The cloud-based random number server randomly selects multiple disparate entropy sources from the multiple disjointed entropy sources, and then receives multiple entropic values from the multiple disparate entropy sources, where each of the multiple disparate entropy sources supplies an entropic value that describes a type of entropic event not found in other entropy sources from the multiple disparate entropy sources. The cloud-based random number server mixes the multiple entropic values to create a combined entropic value, which is input into a random number generator to generate a random number for use by a client computer.