Random numbers play an indispensable role for a wide range of applications in many modern commercial and scientific fields, such as stochastic simulations, statistical sampling, lotteries, and even cryptography protocols [1,2]. It is an essential step to distinguish the generation process of random numbers. In computer software, the system of generating random numbers directly from computational algorithms is called pseudorandom number generation (PRNG), which normally starts from a small string of bits called seeds. Although the output random numbers generated by PRNG may be a perfectly uniform distribution in statistics, the properties of a strong period and predictability exist. They are not suitable for areas with high security requirements, which may result in unexpected errors or open loopholes such as in cryptography. On the contrary, true random number generations (TRNGs) are based on measuring some unpredictable physical processes to generate random numbers. The final bit sequences have high security and true randomness. Quantum random number generations (QRNGs) are an essential case of physical TRNGs where the inherent randomness based on the quantum physical phenomenon is extracted. Quantum random bits are the best guarantee to provide high-quality random numbers under the condition of ensuring security. Over the past few decades, various practical QRNG schemes have been proposed and demonstrated, for instance, single photon splitting by a beam splitter [3,4], homodyne detection of the vacuum field noise [5–8], phase diffusion in lasers [9–11], amplified spontaneous emission (ASE) noise [12–15], and the intensity fluctuation of spontaneous emission from light emitting diodes (LEDs) or atoms [16–18]. Other kinds of QRNGs based on untrusted devices have been developed that can resist stronger attacks in theory. For example, device-independent (DI) schemes require the violation of a Bell inequality [19–21], and semi-DI (or self-testing) approaches need only a partial characterization of the whole device [22–25].

Despite much progress, most QRNG schemes have the same features: expensive optical or electrical setups, complex system structure, huge size, and so on. These disadvantages have prevented them from becoming widespread for practical and commercial applications on-shelf. For instance, for a single photon beam splitting scheme, the final generation rate of random bits is limited mainly by the dead time of a single photon detector (SPD) [4]. For the detection of vacuum field noise, the influence of classical noise and a complex post-processing procedure are key challenges for practical applications of this scheme [5–7]. For the phase noise scheme of lasers, a fiber Mach–Zehnder interferometer (MZI) with a length imbalance makes it difficult for the system to remain stable for a long time. Moreover, the use of complex and bulky light sources and detector devices also brings great challenges to the integration of the whole system [2]. From a practical point of view, many experimental approaches aim to reduce the size and price and improve the generation rate of QRNGs. Thus, a large number of high-speed, real-time, compact, and integrated QRNG schemes have been demonstrated [26–31].

 

Fig. 1. (a) Structure of linear optocoupler. LED, light emitting diode; PD, photodetector; 1, anode; 2, cathode; 3, emitter; 4, collector. When the ports of 1, 2 and 3, 4 of the linear optocoupler are respectively applied with appropriate voltages, the photodetector will receive light radiation from the LED and generate the corresponding output signal, which is linear with the light intensity. (b) Process of light emitting from the LED. When the LED is applied with an appropriate voltage, holes in the p region and electrons in the n region will recombine randomly in the active area to emit photons. This process is similar to the spontaneous emission of atoms and belongs to the quantum random process guaranteed by quantum mechanics.

Download Full Size | PDF

In this work, we present a compact, simple, and low-cost experimental scheme of QRNG based on a linear optocoupler. A linear optocoupler is a semiconductor device that features low cost and compactness or integration. In general, its structure consists mainly of a semiconductor light emitting element at the input and a photoresponse element at the output, which are arranged on an insulating substrate in such a manner that they oppose each other. As shown in Fig. 1(a), the light source and receiver are usually a LED and photodetector (PD), respectively. They are integrated or packaged together in which the p-n junction of the former is perpendicular to a light receiving face of the latter [32]. When an appropriate voltage is applied to the LED, it will emit photons. Then, the PD will output electrical signals that are linear to the received light emission intensity from the LED. Therefore, the linear optocoupler completes the whole conversion process of electricity–light–electricity.

Before showing the experimental setup and scheme of QRNG based on a linear optocoupler, here we recall the light emission theory and process of LEDs. It is composed mainly of a p-n junction, as shown in Fig. 1(b). When an appropriate voltage is applied to the LED, holes in the p region and electrons in the n region recombine randomly in the active region, during which photons are emitted. This process is similar to the spontaneous emission of atoms, where the particles of the excited state spontaneously transition to the ground state, and then photons are emitted. Therefore, the light emission process of LEDs also belongs to the quantum random process guaranteed by quantum mechanics. The inherent randomness of LEDs is reflected in the fluctuation of light intensity. The values of light intensity of two consecutive measurements are considered to be mutually independent when the time interval of two measurements exceeds the coherence time ${\tau _c}$ of the light source, which depends on the spectral width $\Delta \nu$ of the LED by ${\tau _c} \simeq \frac{1}{{\pi \Delta \nu}}$ [9]. The probability density distribution of light intensity with the number of emitted photons $n$ is given by [16]

According to the above analysis, the light emission process of the LED integrated into the linear optocoupler belongs to an inherent quantum phenomenon guaranteed by quantum mechanics [16]. When the light intensity from the LED is detected by the PD, the output electrical signal is linear to the emission intensity due to the linearity of the optocoupler. Thus, quantum random numbers can be generated by the measurement of intensity fluctuations from the LED in a linear optocoupler. In this Letter, we propose and realize a simple, compact, and low-cost scheme of QRNG based on a linear optocoupler where the processes of light radiation and detection have been completed. The unique setup and advantages play an important role in promoting the practical, commercial, and compact development of QRNG technology.

 

Fig. 2. Design block diagram of the experimental model and its actual picture integrated on the printed circuit board. ADC, an 8-bit analog-to-digital converter. The process of light emission from the LED and detection of the PD is completed in the linear optocoupler. Then, the output signals are finally amplified and digitized by the amplifier and the ADC, respectively. The final random bits are generated after post-processing from raw sequences.

Download Full Size | PDF

Figure 2 is the experimental setup including the design block diagram and the actual image integrated on the printed circuit board (PCB), which shows the simple and compact design. The detailed design block diagram of the QRNG module consists mainly of three parts. The first includes the quantum source and detector, where the light intensity of the LED is detected by the PD integrated in the linear optocoupler. Then, the output detection signal from the PD is amplified by an external electrical amplifier for a higher signal-to-noise ratio (SNR). Finally, the signal is sampled, digitized, and stored by an analog-to-digital converter (ADC) with 8-bit vertical resolution, and the post-processing procedure is applied by the computer. The sampling rate is 9.77 MSa/s, and the amplitude of the temporal waveform is adjusted so that most of the signal voltages are included with 8-bit vertical resolution. Furthermore, the noise from the PD and amplifier circuit is considered when the LED is not working. As shown in Fig. 3(a), the temporal waveforms of signal and noise are measured, which shows that the quantum signal noise is dominant. The output signal oscillates irregularly, which shows good randomness of the intensity fluctuation. The blue histogram in Fig. 3(b) shows the distribution of the signal where the symmetry is shown by comparing it with the red fitting curve.

 

Fig. 3. (a) Temporal waveforms measurement of the optical signal and noise from the PD and the amplifier circuit, where the quantum noise is dominant. (b) The blue histogram distribution of the signal voltage shows good symmetry compared with the red fitting curve. (c) Influence of power input voltage on min-entropy, where min-entropy remains almost stable as the input voltage of the power changes. (d) Influence of operating environment temperature on min-entropy. When the temperature changes, min-entropy basically stays stable in our design.

Download Full Size | PDF

In addition, to evaluate the randomness quality precisely contained in the measured raw data, an essential parameter of min-entropy is introduced. Min-entropy of the raw bits related to the probability of the distribution is defined as ${H_\infty} = - \mathop {\log}\nolimits_2 \max P(i)$, where $\max P(i)$ is the probability of the most likely event in the distribution. According to the distribution of the output detection signal by our measurement, raw data of each detection comprise min-entropy of 4.49 bits. To evaluate the robustness of the setup, the influence of the operating environment including the power supply voltage and operating temperature is considered. Due to the special design of the regulator circuit in our setup, the output signal is not noticeably affected by the input voltage of the power. As shown in Fig. 3(c), the corresponding min-entropy remains almost stable with the change in power supply voltage. Moreover, min-entropy basically stays stable with the change in environment temperature, as shown in Fig. 3(d). Therefore, our setup is robust against fluctuation of the operating environment.

Finally, we employ a random number extraction procedure based on the SHA-256 algorithm by the computer to remove the bias of raw bits and improve the quality of the out random sequences, which extracts 4.41 bits per eight raw bits. The final generation speed of the obtained random bits is determined by the sampling rate and min-entropy. The NIST-Statistical Test Suite (STS) is used to test the quality of the final random bits. The results show that all of the random bit streams pass the test with a significance level of 0.01, as shown in Table 1. Furthermore, to quantify the independence of the two adjacent or delayed bits in the final random sequences, we statistically calculate autocorrelation coefficient ${\rho _k}$ at lag $k$ bit with 10 Mbits, where the formula is expressed as [12]

Table 1. Result of NIST Statistical Randomness Test Suite, Using 1000 Samples of 1 Mb and Significance Level $\alpha = 0.01$^a,^b

View Table

 

Fig. 4. Autocorrelation coefficients of ${10^7}$ bits extracted random numbers after SHA-256 procedure with 200-bit delay, which has a standard deviation of $3.16 \times {10^{- 4}}$.

Download Full Size | PDF

In summary, we propose and implement a compact, simple, and low-cost QRNG scheme based on a linear optocoupler. The intensity fluctuation of the LED is measured directly by a PD where the output amplitude is linear to the emission intensity of the light source. The quantum randomness originates from a random recombination between holes of the p region and electrons of the n region of the LED, which is similar to the spontaneous emission of atoms. There is no need for an additional optical coupling system for detection, a bulky detector, or integration technology. In addition, the system is robust against fluctuation of the operating environment by our measurement. This scheme has the potential to be extended to a parallel and real-time design by a field programmable gate array (FPGA) for a higher generation rate, which still maintains the characteristics of low cost and compact structure. This will be of great significance to promote the practical and commercial development of QRNG.