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IEEE Journal of Selected Topics in Quantum Electronics

Performance of Random Number Generators Using Noise-Based Superluminescent Diode and Chaos-Based Semiconductor Lasers

T. Yamazaki, Atsushi Uchida

Published Feb 12, 2013• 65 citations
Publisher

Abstract

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.

DOI
10.1109/jstqe.2013.2246777

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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.
Abstract We experimentally demonstrate a 12.5 Gb s −1 random number generator based on measuring the spontaneous emission noise of a single-mode semiconductor laser. The spontaneous emission of light is quantum mechanical in nature and is an inborn physical entropy source of true randomness. By combining a high-speed analog-to-digital converter and off-line processing, random numbers are extracted from the spontaneous emission with the verified randomness. The generator is simple, robust, and with no need of accurately tuning the comparison threshold. The use of semiconductor lasers makes it particularly compatible with the delivery of random numbers in optical networks.
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.
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 demonstrate robust, high-speed random number generation using interference of the steady-state emission of guaranteed random phases, obtained through gain-switching a semiconductor laser diode. Steady-state emission tolerates large temporal pulse misalignments and therefore significantly improves the interference quality. Using an 8-bit digitizer followed by a finite-impulse-response unbiasing algorithm, we achieve random number generation rates of 8 and 20 Gb/s, for laser repetition rates of 1 and 2.5 GHz, respectively, with a ±20% tolerance in the interferometer differential delay. We also report a generation rate of 80 Gb/s using partially phase-correlated short pulses. In relation to the field of quantum key distribution, our results confirm the gain-switched laser diode as a suitable light source, capable of providing phase-randomized coherent pulses at a clock rate of up to 2.5 GHz.
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.
Abstract Diode Lasers (DLs) are influenced by fast frequency noise stemming from fluctuations in spontaneous emissions, a phenomenon that is of great use when generating fast physical-random numbers. This paper describes a physical-random number generator that uses a DLs frequency noise and rubidium (Rb) absorption lines as frequency noise sources and frequency discriminators. This device actually produced physical-random numbers at a rate of 500 megabits per second, but it depends on the relation between the DL frequency noise and frequency discriminator characteristics. This relation is investigated and the conditions for physical-random number generation are explained.