A method for generating random data, the method comprising repeatedly performing a series of operations, and the series of operations comprising processing a seed value to generate a resulting value for use as the seed value in a subsequent performance of the series of operations and to generate output random data; wherein the series of operations also comprises: determining whether a predetermined amount of new truly random data is available; and if such data is available, modifying the generation of at least the resulting value in dependence on the new truly random data.