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We present numerically an all-optical approach to generate fast physical random numbers. This approach is based on chaotic self-pulsations, a kind of chaos superimposed on periodic pulse trains. Two-section semiconductor lasers (TSSLs) can exhibit this phenomenon of chaos, under an appropriate external optical injection. Simulations demonstrate that, without sampling and postprocessing procedures, this technique can produce random numbers at gigabit per second rates through directly quantizing the chaotic self-pulsations via an all-optical flip-flop. Further simulation results show that the random number generation rate can be continuously and easily tuned in a large range from 5 to 10 Gb/s by adjusting some control parameters of the TSSL subject to continuous-wave optical injection, such as injection strength, frequency detuning, gain current, and absorber bias. Moreover, our numerical studies show that these generated random numbers sequences above with the proposed method can pass successfully standard benchmark tests for randomness. [ABSTRACT FROM PUBLISHER]