Order within disorder: spectral key generation and distribution in random lasers
Zhijia Hu, Shilong He, Qi, Lianghao, Yalan Li, Siqi Li, Bin Chen, Wenyu Du, Yan Kuai, Zhigang Cao, Min Wang, Kaiming Zhou, Lin Zhang, Qingchuan Guo, Ding, Weimin, Li, Chao, Kang Xie, Anderson S. L. Gomes, Benli Yu
In secure communication, highly random entropy sources are essential for information security. Random lasers (RLs), which arise from multiple scattering in disordered structures, are potentially ideal entropy sources. Traditionally, RLs are viewed as disordered and unpredictable. However, in this work, we present novel evidence that orderly patterns exist beneath the seemingly disordered outputs of RLs. Utilizing deep learning techniques, a variety of advanced neural network models are used to analyze the spectral data in multiple dimensions. The results show that the time series of RLs spectra are unpredictable, but spectral wavelength component intensities can be recovered due to inter-modal correlations. This finding not only breaks through the traditional perception that RLs are unpredictable, but also reveals for the first time that RLs have the dual characteristics of both randomness and determinism. Based on this new characteristic, we further expand the application field of RLs and innovatively design a new type of key generation and distribution scheme. In this scheme, the disordered property of RLs is used for key generation to ensure high randomness, while their ordered property is used for key distribution to guarantee accuracy and reliability. The scheme provides a new strategy for secure communication.
In secure communication, highly random entropy sources are essential for information security. Random lasers (RLs), which arise from multiple scattering in disordered structures, are potentially ideal entropy sources. Traditionally, RLs are viewed as disordered and unpredictable. However, in this work, we present novel evidence that orderly patterns exist beneath the seemingly disordered outputs of RLs. Utilizing deep learning techniques, a variety of advanced neural network models are used to analyze the spectral data in multiple dimensions. The results show that the time series of RLs spectra are unpredictable, but spectral wavelength component intensities can be recovered due to inter-modal correlations. This finding not only breaks through the traditional perception that RLs are unpredictable, but also reveals for the first time that RLs have the dual characteristics of both randomness and determinism. Based on this new characteristic, we further expand the application field of RLs and innovatively design a new type of key generation and distribution scheme. In this scheme, the disordered property of RLs is used for key generation to ensure high randomness, while their ordered property is used for key distribution to guarantee accuracy and reliability. The scheme provides a new strategy for secure communication.
True random numbers with high security originate from non-deterministic physical processes. Random laser with random feedback arising from multiple elastic scattering in a highly disordered structure is an ideal physical entropy source theoretically. In this work, a secure optical ultrafast random number generator based on random laser spectra was demonstrated. Unlike the usual method of recording laser intensity over time, the random laser spectrum under each pump pulse was recorded and converted into random numbers through post-processing. Approaches in three different dimensions—space, spectrum and time were used to increase the rate of random number generation. The randomness of resulting random bit streams was verified by the NIST statistics tests. Experimental results showed that an instantaneous bit rate of 810 terabits per second with off-line post-processing could be theoretically reached with an ideal experimental condition. This novel technique has big advantages in secure communications and promises to further increase the speed of random number generators to the lever of petabits per second or even higher.
The statistical behavior of spectral intensity fluctuations in a Raman gain random fiber laser is investigated for the first time, to the best of our knowledge. Through a fiber Fabry–Perot tunable filter, the intensity of the filtered single wavelength from random laser (RL) spectra is measured at different pump powers. The probability density function (PDF) of spectral intensity values is analyzed. Well below the lasing threshold, the intensity of a single wavelength is stable in the time domain, and the PDF exhibits a typical Gaussian behavior. However, around the threshold, strong fluctuations in intensity emerge. In this case, the statistical distribution is characterized by a power-law-tailed function consistent with a Lévy α-stable distribution. We identify the statistical evolution as the injected pump power increases, from a Gaussian to a Lévy and then back to a Gaussian distribution, which is similar to the case of RLs with a strong disorder due to the presence of photon scatterers and gain related to electronic transitions in the active medium, indicating the universal existence of such statistical properties in random lasing systems.
True random numbers occupy a core role in the field of encryption and security by virtue of their properties such as unpredictability and independence. In this paper, we propose a high-speed physical random number generator based on a dual-emission random fiber laser. The system improves the spectral bandwidth characteristics of the output signals by adjusting the pump power and the feedback length of the single mode fiber. This study effectively suppresses the autocorrelation feature by performing exclusive-OR operations on the forward and backward random laser signals, and obtain the random number sequence with a generation rate of 20 Gbps by post-processing with high-order finite difference and least significant bit extraction. In order to verify the practical application performance, we apply the random sequence as encryption key to digital image encryption, and the experimental results show that the generator has both theoretical security and practical application value.
Correlations existing between spectral components in multi-wavelength lasers have been the key challenge that hinders these laser sources from being developed to chaotic comb entropy sources for parallel random bit generation. Herein, spectrotemporally uncorrelated multi-order Stokes/anti-Stokes emissions are achieved by cooperatively exploiting nonlinear optical processes including cascaded stimulated Brillouin scattering and quasi-phase-matched four-wave mixing in a Brillouin random fiber laser. Chaotic instabilities induced by random mode resonance are enhanced and disorderly redistributed among different lasing lines through complex nonlinear optical interactions, which comprehensively releases the inherent correlation among multiple Stokes/anti-Stokes emission lines, realizing a chaotic frequency comb with multiple spectrotemporally uncorrelated channels. Parallel fast random bit generation is fulfilled with 31 channels, single-channel bit rate of 35-Gbps and total bit rate of 1.085-Tbps. National Institute of Standards and Technology statistic tests verify the randomness of generated bit streams. This work, in a simple and efficient way, breaks the correlation barrier for utilizing multi-wavelength laser to achieve high-quality spectrotemporally uncorrelated chaotic laser source, opening new avenues for achieving greatly accelerated random bit generation through parallelization and potentially revolutionizing the current architecture of secure communication and high-performance computation.
Physical random bit generators (RBGs) that generate unpredictable bits at high speed are now of increasing importance in information science and technology. since they are expected to generate unpredictable random bits with high speed. From the viewpoint of applications for security, it is a crucial issue to be able to give a guarantee of the unpredictability of random bits. In this paper, we review research on physical RBGs, particularly focusing our attention on the studies of the unpredictability of random bits generated by laser systems, which are promising entropy sources for physical RBGs. Finally, we report recent research results on noise-robustness, which could be crucial for reliability of physical RBG.
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.