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Random Number Generation using the Terminal Voltage of an External-Cavity Semiconductor Laser

Michael J. Wishon, Nianqiang Li, C. Y. Chang, Daeyoung Choi, David S. Citrin, Alexandre Locquet

Published Nov 15, 2017• 0 citations
OpenAlex

Abstract

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

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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.

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Laser-based generation of random numbers

Ian S. Osborne

Optoelectronics The security of our digital networks is underpinned by the ability to generate streams of random numbers or bits. As networks expand in an ever-connected way, the challenge is to increase the generation rate of the random numbers to keep pace with demand. Kim et al. designed a chip-scale laser diode that generates random bits at an ultrahigh rate (see the Perspective by Fischer and Gauthier). By tailoring the geometry of the cavity, they were able to exploit the spatiotemporal interference of many lasing modes to generate picosecond-scale emission intensity fluctuations in space and time, producing ultrafast random bit streams in parallel. Such a device will find a wide range of applications requiring an ultrafast, compact, robust, and energy-efficient random bit generator. Science , this issue p. [948][1]; see also p. [889][2] [1]: /lookup/doi/10.1126/science.abc2666 [2]: /lookup/doi/10.1126/science.abg5445

Science•Feb 25, 2021•0 citations
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
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.
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.
We describe a method of generating physical random numbers by means of a diode laser that has an extremely wide-band frequency-noise profile. Fluctuations in the laser frequency affect the intensity of the light transmitted through the optical frequency discriminator, detected thereafter as random fluctuations. This allows us to simultaneously generate 8 random bit streams, due to the parallel processing of 8-digit binary numbers sampled by an 8-bit analog-to-digital converter. Finally, we generated physical random numbers at a rate of 3 Gbit/s, by combining one data stream with another stream that is delayed by 2 ms, by exclusive-OR.
Fast and reliable random number generation (RNG) is a key requirement for, e.g., secure telecommunication or quantum simulations. This has driven the development of physical random number generators to replace deterministic, pseudo-random number generators. Semiconductor lasers exhibiting chaotic dynamics induced for example by optical feedback [1] can provide up to 1 Tbit/s, but their speed is ultimately limited by the time scales of the laser dynamics. Parallel RNG via spatial or spectral multiplexing can further increase the speed but previous demonstrations were limited by low intrinsic speed or a small number of channels.
We demonstrate for the first time, to the best of our knowledge, a high-speed physical random bit generator at gigabits/second without the time-delay signature based on chaotic power fluctuations of a random fiber laser. The random fiber laser is configured using a ring structure with semiconductor optical amplifiers as the optical gain and a fiber random grating as the random feedback medium. The long-length ring cavity provides a large number of densely spaced cavity modes that co-exist within the gain bandwidth tailored by the optical filter. Unlike fixed cavity modes in conventional fiber ring lasers, these modes are less phase-correlated due to the random distributed feedback from the fiber random grating fabricated by a plane-by-plane inscription technique without phase control, leading to intensified lasing output fluctuations with high-dimensional chaotic dynamic natures without specific cavity features, when the random fiber laser is operated slightly above the lasing threshold. Random bit generation at a bit rate up to ∼1.6 Gbps is achieved with verified randomness through standard tests. Different from the previously reported schemes requiring offline post-processing procedures, this physical random number generator can function in real time, offering high-quality randomness and security assurance for pertinent applications.
Optoelectronics The security of our digital networks is underpinned by the ability to generate streams of random numbers or bits. As networks expand in an ever-connected way, the challenge is to increase the generation rate of the random numbers to keep pace with demand. Kim et al. designed a chip-scale laser diode that generates random bits at an ultrahigh rate (see the Perspective by Fischer and Gauthier). By tailoring the geometry of the cavity, they were able to exploit the spatiotemporal interference of many lasing modes to generate picosecond-scale emission intensity fluctuations in space and time, producing ultrafast random bit streams in parallel. Such a device will find a wide range of applications requiring an ultrafast, compact, robust, and energy-efficient random bit generator. Science , this issue p. [948][1]; see also p. [889][2] [1]: /lookup/doi/10.1126/science.abc2666 [2]: /lookup/doi/10.1126/science.abg5445