Truly random number generation based on measurement of phase noise of a laser

We present a simple approach to realize truly random number generator based on measuring the phase noise of a single-mode vertical cavity surface emitting laser. The true randomness of the quantum phase noise originates from the spontaneous emission of photons and the random bit generation rate is ultimately limited only by the laser linewidth. With the final bit generation rate of 20 Mbit/s, the truly random bit sequence guaranteed by the uncertainty principle of quantum mechanics passes the three standard randomness tests (ENT, Diehard, and NIST Statistical Test Suites). Moreover, a continuously generated random bit sequence, with length up to 14 Gbit, is verified by two additional criteria for its true randomness.

Figure 1

(Color online) Schematic setup of TRNG based on the phase noise measurement using delayed self-homodyne method. BS, beam splitter; APD, avalanche photodetector with the low (high) cutoff frequency of 50 kHz (1 GHz). ADC, 8-bit binary analog-digital converter working at 40 MHz.

Figure 2

(Color online) (a) The quantum phase (classical amplitude) noise of the laser field is observed with (without) the beat signal. Inset is the power spectral density of the beat signal. (b) Autocorrelation function of the beat signal vs time interval. In our experiment, the sampling interval of 25 ns (40 MHz sampling rate) is chosen.

Figure 3

(Color online) A 200 ns trace of the APD-detected voltages of the beat signal (small black dots) is recorded at 10 GHz, while the random signal (big red dots) is sampled at 40 MHz rate (25 ns interval). The final random bit is obtained from the least significant bit (LSB, i.e., its parity) of a sequence of 8-bit binary derivatives obtained by performing subtraction between two consecutive sampled voltages (shown in the bottom strip).

Figure 4

(Color online) (a) The statistical bias $\left(B\right)$ of the final random bit sequence. It can be seen that $B<1.5/\sqrt{N}$ always holds and converges to zero for large bit sequence, where $p\left(1\right)$ is the probability of ones in sequence. (b) The absolute value of the first-order correlation coefficient $\left|a_1\right|$ of the final random bit sequence. It can be seen that $\left|a_1\right|<3/\sqrt{N}$ always holds and $\left|a_1\right|$ converges to zero for large bit sequence.