A method and arrangement for generating binary sequences of random numbers uses the principle of random selection of the path of photons on a beam splitter and generating a random number by using two detectors (D1₀, D2₁) downstream from a beam splitter (ST2). To generate photons, a light source (L) of a low power is used, and an additional beam splitter (ST1) is connected upstream from the beam splitter (ST2). The photons emitted by the light source (L) during a predefined measurement time are split by the beam splitters (ST1, ST2) arranged one after the other in the beam path of the light source (L). The random sequence is generated when the splitting of the photons matches a predefined photon scheme.