A hardware random number generator (RNG) has a source of entropy for providing a bit stream (DIS) comprising successive bits of a first state and a second state. The RNG includes a first digital corrector circuit configured to provide from two successive bits in the bit stream an output bit of an output bit stream according to a first scheme to ensure that bits in the output bit stream are independent from one another. A serially connected second digital corrector circuit ensures that the bits in the output bit stream are also unbiased, so that the output bit stream is truly random. A Gaussian generator connected to an output of either the first corrector or the second corrector generates from the output bit stream words having standard Gaussian deviates.