Subject of study. This study models the generation process of random bit sequences using an array of coupled lasers. It is based on quantum dot (QD) micropillars with optical feedback that is realized via a mirror positioned at some distance from the array. A model of the array of coupled micropillar lasers consists of QD laser rate equations accounting for the global optical feedback. Aim of study. This study aimed to numerically model and analyze a random number generator using an array of coupled lasers based on QD micropillars. Method. The dynamic behavior was modeled through numerical integration of the delayed differential equation system using a semi-implicit Euler method implemented using the Julia programming language. To generate sequences of random bits, an algorithm was used that involved the sampling of the total field intensity of the array, normalization and discretization with 12 bit resolution, conversion of discretized values to bit representation, selection of four less significant bits, and concatenation of the bit values into the final sequence. Main results. The process of generating a sequence of random bits at the rate of 400 Gb/s, which met the criteria of NIST 800-22 statistical tests for the p-value of 0.01 at the sampling rate of total field intensity of the array equal to 100 Gsamples/s and a sequence length of 11,142,860 bits, was modeled. The model of an array of coupled lasers based on QD micropillars with optical feedback was analyzed using bifurcation analysis. The feedback time delay signature was traced in the chaotic signal of the emission intensity. However, it did not affect the quality of the random number generation. Practical significance. The optical feedback resulted in the chaotic generation of an array of lasers based on the QD micropillars, which can be used to generate random numbers.
Subject of study. This study models the generation process of random bit sequences using an array of coupled lasers. It is based on quantum dot (QD) micropillars with optical feedback that is realized via a mirror positioned at some distance from the array. A model of the array of coupled micropillar lasers consists of QD laser rate equations accounting for the global optical feedback. Aim of study. This study aimed to numerically model and analyze a random number generator using an array of coupled lasers based on QD micropillars. Method. The dynamic behavior was modeled through numerical integration of the delayed differential equation system using a semi-implicit Euler method implemented using the Julia programming language. To generate sequences of random bits, an algorithm was used that involved the sampling of the total field intensity of the array, normalization and discretization with 12 bit resolution, conversion of discretized values to bit representation, selection of four less significant bits, and concatenation of the bit values into the final sequence. Main results. The process of generating a sequence of random bits at the rate of 400 Gb/s, which met the criteria of NIST 800-22 statistical tests for the p-value of 0.01 at the sampling rate of total field intensity of the array equal to 100 Gsamples/s and a sequence length of 11,142,860 bits, was modeled. The model of an array of coupled lasers based on QD micropillars with optical feedback was analyzed using bifurcation analysis. The feedback time delay signature was traced in the chaotic signal of the emission intensity. However, it did not affect the quality of the random number generation. Practical significance. The optical feedback resulted in the chaotic generation of an array of lasers based on the QD micropillars, which can be used to generate random numbers.
The paper investigates the results of random number generation with arrays of coupled quantum-dot micropillar lasers. The micropillars array laser generation is modeled based on the rate equations for quantum dot lasers. The numerical simulation of the dynamics for the arrays of coupled quantum-dot micropillar lasers is carried out utilizing the semi-implicit Euler method, implemented in Julia programming language. The algorithm of random bit sequence generation consists of the following steps: sampling the values of the total field intensity for coupled micropillar lasers; normalizing and discretizing the obtained values per resolution of the 8-bit analog-to-digital converter; extracting the four least significant bits from the bit representation of the sampled values; concatenating the bit values in a single sequence. The possibility of the bit sequences generation having an equiprobable distribution of zeros and ones with a performance of up to 400 Gbit/s was shown utilizing a random number generator based on an array of coupled quantum-dot micropillar lasers for sequences with a length of 14285716 bits at a sampling rate of 100 gigasamples per second and four least significant bits extraction. The resulting bit sequences successfully passed 14 NIST 800-22 statistical tests for the p-value equal to 0.01. The proposed method can be applied to develop random number generators based on larger arrays of coupled quantum-dot micropillar lasers. The results can be utilized in the experimental implementation of random number generators based on arrays of coupled quantum-dot micropillar lasers.
Semiconductor laser diodes subjected to recurrent optical feedback are of interest in many high-speed applications. Here we exploit the chaotic terminal voltage dynamics in order to generate random bit streams. Further, a comparison of the voltage dynamics to the commonly utilized optical intensity is performed, and it is found that the voltage is a superior source for generating random numbers because the dynamics suppress the delay-signature and its distribution is more symmetric. Importantly, the system demonstrated here is significantly simpler to implement by eliminating the need for optical to electrical conversion and can be connected directly into electronic applications where GS/s random bit streams are desired
Absolutely secure communication should be implemented only through the ‘one-time pad' proposed by Shannon, requires that physical random numbers with rates matched with the associated communication systems be used as secret keys. With the wide application of the WDM technology in optical communication, the single channel rate of the current digital communication system has exceeded 10 Gb/s and developed towards 100 Gb/s. To ensure the absolute security of such a large capacity communication, a large number of real-time, and secure random numbers are needed.#br#Secure random numbers are commonly produced through utilizing physical random phenomena, called physical random number generators. However, conventional physical random number generators are limited by the low bandwidth of the applied entropy sources such as thermal noise, photon-counting and chaotic electrical circuits, and thus have typical low bit rates of the order of Mb/s.#br#In recent years, chaotic lasers attracted wide attention due to their generation of secure, reliable and high-speed random number sequences, and so due to their coherent merits such as high bandwidth, large amplitude fluctuation and ease of integration. There have been lots of schemes based on laser chaos for high-speed random number generation, but most of them execute the random number extractions from the associated laser chaos in the electrical domain and thus their generation rates are faced with the well-known ‘electrical bottleneck'. On the other hand, all-optical random number generation (AO-RNG) methods are all signal processes in the optical domain, so they can efficiently overcome this rate limitation and have a great potential in generating ultrafast random numbers of several dozens or hundreds of Gb/s. However, there is no experimental report on its realization of AO-RNG. One of the obstacles in the way for the AO-RNG achievement is to implement the fast and real-time all-optical sampling of the entropy signals (i.e., laser chaos).#br#In this paper, we present a principal experimental demonstration of the feasibility in the all-optical sampling of the chaotic light signal through constructing a TOAD-based all-optical sampler with a polarization-independent semiconductor optical amplifier (SOA). Specifically, we experimentally generate chaotic laser signals using an optical feedback semiconductor laser and finally complete a 5 GSa/s real-time and high-fidelity all-optical sampling of the chaotic laser with a bandwidth of 6.4 GHz. Further experimental results show that whether the optical sampling period is proportional to the external cavity feedback time or not has a great effect on the weak periodic suppression of the chaotic signal: only when both of them are out of proportion, can the weak periodicity of the original chaotic signal be effectively eliminated; and this is favorable for the generation of high-quality physical random numbers. To the best of our knowledge, it is the first time to realize all-optical sampling of chaotic signal in experiments.
Random numbers have great application value in the fields of secure communications, which are commonly used as secret keys to encrypt the information. To guarantee that the information is absolutely secure in the current high-speed communication, the applied random keys should possess a generation speed not less than the encrypted data rate, according to one-time pad theory found by Shannon (Shannon C E 1949 Bell.Syst.Tech.J. 28 656) Pseudo-random numbers generated by algorithm may easily reach a fast speed, but a certain periodicity makes them difficult to meet the aforementioned demand of information security. Utilizing physical stochastic phenomena can provide reliable random numbers, called physical random number generators (RNGs). However, limited by the bandwidth of the conventional physical sources such as electronic noise, frequency jitter of oscillator and quantum randomness, the traditional physical RNG has a generation speed at a level of Mb/s typically. Therefore, real-time and ultrafast physical random number generation is urgently required from the view of absolute security for high-speed communication today. With the advent of wideband photonic entropy sources, in recent years lots of schemes for high-speed random number generation are proposed. Among them, chaotic laser has received great attention due to its ultra-wide bandwidth and large random fluctuation of intensity. The real-time speed of physical RNG based on chaotic laser is now limited under 5 Gb/s, although the reported RNG claims that an ultrafast speed of Tb/s is possible in theory. The main issues that restrict the real-time speed of RNG based on chaotic laser are from two aspects. The first aspect is electrical jitter bottleneck confronted by the electrical analog-to-digital converter (ADC). Specifically, most of the methods of extracting random numbers are first to convert the chaotic laser into an electrical signal by a photo-detector, then use an electrical ADC driven by radio frequency (RF) clock to sample and quantify the chaotic signal in electronic domain. Unfortunately, the response rate of ADC is below Gb/s restricted by the aperture jitter (several picoseconds) of RF clock in the sample and hold circuit. The second aspect comes from the complex post-processes, which are fundamental in current RNG techniques to realize a good randomness. The strict synchronization among post-processing components (e.g., XOR gates, memory buffers, high-order difference) is controlled by an RF clock. Similarly, it is also an insurmountable obstacle to achieve an accurate synchronization due to the electronic jitter of the RF clock. In this paper, we propose a method of ultrafast multi-bit physical RNG based on chaotic laser without any post-process. In this method, a train of optical pulses generated by a GHz mode-locked laser with low temporal jitter at a level of fs is used as an optical sampling clock. The chaotic laser is sampled in the optical domain through a low switching energy and high-linearity terahertz optical asymmetric demultiplexer (TOAD) sampler, which is a fiber loop with an asymmetrical nonlinear semiconductor optical amplifier. Then, the peak amplitude of each sampled chaotic pulse is digitized by a multi-bit comparator (i.e., a multi-bit ADC without sample and hold circuit) and converted into random numbers directly. Specifically, a proof-of-principle experiment is executed to demonstrate the aforementioned proposed method. In this experiment, an optical feedback chaotic laser is used, which has a bandwidth of 6 GHz. Through setting a sampling rate to be 5 GSa/s and selecting 4 LSBs outputs of the 8-bit comparator, 20 Gb/s (=5 GSa/s4 LSBs) physical random number sequences are obtained. Considering the ultrafast response rate of TOAD sampler, the speed of random numbers generated by this method has the potential to reach several hundreds of Gb/s as long as the used chaotic laser has a sufficient bandwidth.
We investigate two optical sources used for random number generation: superluminescent diode (SLD) and semiconductor lasers. Amplified spontaneous emission noise is generated in the SLD and chaotic intensity fluctuation is generated in a semiconductor laser. We investigate the performance of random number generation for both optical sources. For single-bit generation of random numbers, the maximum generation rate is 8.33 Gb/s for both the SLD and the laser with a similar bandwidth of ~15 GHz. For multibit generation schemes, we obtain the generation rate up to 400 Gb/s for both the SLD and the laser. The overall characteristics are similar between the SLD and the laser, since similar bandwidths of the RF spectra are used. The probability density function of the SLD is more symmetric than that of the chaotic laser. This fact results in slightly good performance of random number generation using the SLD for multibit generation.