An apparatus for generating a random bit sequence has a ring oscillator which includes inverting digital devices and on which an oscillator signal can be tapped. An intermediate storage element monitors and stores fluctuating levels of the oscillator signal. At least two controllable switch devices for simultaneously exciting at least two harmonic wave edges of the ring oscillator are provided in a signal path of the ring oscillator. The phasing of the two harmonic wave edges and a potential convergence thereof are subject to statistical fluctuations, which are used as a basis for the random bit generation. A corresponding random number generator can be used in particular as an FPGA for security applications, such as cryptographic methods. The apparatus has substantially digital components, which are easy to produce in a standardized manner. A dedicated regulating circuit is not necessary. The apparatus is also robust toward exterior influences.