Study On High-speed Multi-bit Physical Random Number Generation Based On Chaotic Laser

Random numbers are broadly and importantly used in scientific computation,identity authentication,radar ranging,information safety,etc.Particularly,random numbers are employed to encrypt the plain-text as secret keys in secure communication,which have great influence on national security,commercial finance and personal privacy.To guarantee the information be absolutely secure in the current high-speed communication,the random keys should possess a generation speed not less than the encrypted data rate,according to "one-time pad" theory found by Shannon.Generally,random numbers can be divided into pseudo-random numbers and physical random numbers,according to different generation mechanisms.Pseudo-random numbers generated by algorithms may easily get a speed at dozens of Gbps,but their coherent periodicity makes them impossible to meet the requirements of absolutely secure communication that mentioned above.Physical stochastic phenomena have the characteristic of unrepeatability or unpredictability and thus could produce reliable random numbers.Single-photon,thermal noise of resistor,shot noise,chaotic circuit and oscillator jitter have been widely used as the entropies in random number generators(RNGs)already.However,the bandwidths of these entropies are at the level of MHz so that their generation speeds are also limited at Mb/s typically.That is far below than the current high-speed communication rate.Chaotic laser,a complex signal with a broad bandwidth,is suitable for generating random numbers on account of its random fluctuation of amplitude.Regularly,the chaotic laser is converted into an electronic signal by a photoelectric detector(PD)in the first step and then sampled and quantized by an ADC trigged by RF clock in the electronic domain.Further,post-processing methods are frequently introduced to optimize the randomness of raw random numbers.A large number of research works prove that the generation speed of RNGs based on chaotic laser have the possibility to reach Tbps in theory,but the achieved real-time speed in practice is under 5 Gbps owing to the "electrical jitter bottleneck".Aiming at this problem,we propose a new scheme to enhance the real-time speed of an RNG,in which the chaotic laser is sampled in all-optical domain and quantized by a multi-bit comparator.Specifically,a train of optical pulses generated by a mode-locked laser with an ultralow temporal jitter is used as an optical clock to trigger the TOAD sampler,and thus continuous chaotic laser is transform into a train of chaotic pulses with an equal interval.Then,the peak amplitude of each sampled chaotic pulse is quantified to binary numbers by a multi-bit comparator(i.e.,a multi-bit ADC without the S/H circuit).Finally,physical random numbers are directly acquired by optimize the least significant bits(LSBs)without complicated post-processing.The generation speed of random numbers in this scheme equals to the product of optical sampling rate and the selected LSBs.Specifically,the following researches have been done on the main techniques in the scheme:1.In order to obtain random numbers with high-quality,the main parameters that are useful for suppress the time-delay signature of chaotic laser are analyzed experimentally.Furthermore,ultra-broad bandwidth chaotic laser without time-delay signature is obtained by injecting optical feedback chaotic laser into a slave laser diode.2.A TOAD sampler is structured and the optimum range of window width is determined by measuring the states of small and large window in the experiment.Moreover,we sample different wavelengths of optical signal with the TOAD and the results show that the sampler has a good stability and linearity.Finally,5 GSa/s and 10 GSa/s real-time sampling of 6 GHz and 11.9 GHz chaotic laser are realized,respectively.3.Based on the aforementioned study,we integrate two prototypes called as Chaotic Laser Source and All-optical Sampler,respectively.4.We establish a mathematical model based on the central limit theorem and the law of iterated logarithm to analyze the Brownian motion characteristics of random numbers extracted from chaotic laser by means of multi-bit quantization.The test results show that random numbers based on chaotic laser could simulate Brownian motion perfectly,which prove its nondeterministic property.5.For the technique of multi-bit quantization,we explore the effect of selected LSBs on random numbers.In the experiment,a sequence of chaotic laser pulses with 5 GHz repetition frequency is digitized by an 8-bit comparator,and 4 LSBs are optimized.Eventually,we successfully generate 20 Gbps physical random numbers with good randomness.