| Random numbers play an important role in daily life,statistical simulation,cryptography and other fields,and the tools that generate random numbers are called random number generators.According to the different principles of generating random numbers,random number generators are generally divided into pseudo random number generators(PRNG)and true random number generators(TRNG).PRNG generates pseudo-random sequences based on complex mathematical algorithms,which usually have good statistical properties,but also have long periodicity and predictability.These shortcomings make the pseudo-random sequence unable to be used in areas with high security requirements,such as secure communications.In secure communication,a cryptographic system based on algorithm complexity is the current mainstream method.However,with the continuous development of quantum computers,cryptosystems based on algorithm complexity are facing the risk of being cracked,and More secure and reliable secure communication methods are urgently needed.With the proposed of quantum secure communication,The "one-time pad" encryption method combined with the Quantum Key Distribution(QKD)system can theoretically realize an absolutely secure cryptographic system.In the QKD system,the preparation of the quantum state and the modulation of the decoy state are the guarantee of the security of the system,and the quality of the true random numbers used in these two processes determines whether the system is safe and reliable.With the rapid development of the QKD system,the real-time generation rate of true random numbers has become a key factor restricting the key generation rate of the QKD system.In addition,due to the hardware complexity of the QKD system,the high integration requirements for TRNG are also aspects that need to be considered.This paper focuses on this,and conducts a systematic and in-depth study on the key count of the design of highly integrated and high-speed TRNG.The thesis first analyzes and discusses various TRNG implementation schemes at home and abroad,and concludes that the TRNG design process generally includes:the selection or construction of entropy sources,randomness extraction methods,postprocessing of random numbers,and statistical testing of random sequences.Through these four key steps,a comprehensive comparison of various TRNGs shows that TRNGs based on a single FPGA have obvious advantages in terms of complexity,ease of integration,and low cost.But so far,the low TRNG rate based on a single FPGA is still a problem that needs to be solved urgently.For this reason,the paper analyzes the entropy source characteristics of high-speed TRNG in detail,and concludes that the entropy source should meet the requirements of high frequency,high randomness,and easy extraction as much as possible,and the entropy source should be screened and constructed through these characteristics.Through the "3D-charlie model",the self-time ring(STR)oscillation mode is studied in detail,and the conditions for the STR to enter the uniform oscillation mode are derived,and the STR in this mode is used to have high resolution and high time accuracy.Features.Two STR-based TRNGs,a single-clock sampling scheme and a multi-clock sampling scheme,are implemented in the FPGA.And set up a mathematical model to evaluate the random number entropy.The two schemes realize the true random number generation rate of single channel 625 Mbps and 2.5 Gbps respectively.Through the multi-channel layout of the multi-clock sampling scheme,a true random number generation rate of 60 Gbps in all 24 channels is finally realized.In order to pursue a higher rate of true random number generation,the thesis conducted a detailed study on the structure and oscillation principle of Galois ring oscillator(GARO).The oscillation frequency of the GARO signal is extremely high,and the shortest period can reach the order of sub-nanosecond.The existing FPGA TDC cannot continuously measure such a short time interval.Therefore,the paper designs and implements the FPGA-based ultra-short dead time TDC and GARO’s cycle for precise measurement.The TDC can measure pulse signals with the shortest cycle of 341 ps and the measurement accuracy reaches 13.5ps.By analyzing and summarizing the periodic distribution of GARO of various structures,two oscillation modes of GARO are proposed,namely chaotic oscillation mode and long-period oscillation mode,and the correctness of the oscillation mode is proved through theoretical establishment of a mathematical model.Then the paper puts forward guiding suggestions on the selection of GARO feedback coefficient polynomials through the state sampling method and the period digitization method,so that it can enter the long period oscillation mode or the stable chaotic oscillation mode.Using the long-period oscillation mode,a sample TRNG with minimal resource consumption is realized inside the FPGA,and the singlechannel true random number generation rate is 280 Mbps.Using the chaotic oscillation mode,the simple state sampling TRNG and the ultra-high-rate periodic digital TRNG are implemented in the FPGA.The single-channel true random number generation rates are 500 Mbps and 4.42 Gbps.Finally,consider the alternative TRNG scheme when the TRNG based on FPGA entropy source is attacked.The realization of entropy sources requires diversification.In the QKD system,single-photon detection equipment is necessary.Therefore,this paper uses a representative silicon photomultiplier(SiPM)as an example to study in detail the nature of the SiPM dark count,and use the dark count generation time interval and generation channel information is used as the entropy source to design TRNG.The paper proposes a cumulative distribution function(CDF)post-processing method to uniformize the dark count time interval,and a simplified linear feedback shift register(LFSR)method to correct the channel information.In addition,a dark count rate monitoring module is also designed to make the CDF post-processing module robust and able to resist the influence of environmental factors.Sampling a dark count can generate 17bit time interval random numbers and 2-bit channel information random numbers.The final 4-channel SiPM random number generation rate is 63.54 Mbps.SiPM or singlephoton avalanche diode(SPAD)and the corresponding readout circuit are integrated in systems such as QKD,and the rest of the data acquisition and processing modules are implemented by a single-chip FPGA,so the TRNG solution will not increase the complexity of the QKD system.In the future,in practical applications,more SiPM channels can be read in parallel or a laser source can be added to form a hybrid entropy source to achieve a higher random number generation rate.The innovation of this paper is:systematic analysis summarizes the general structure and development process of single-chip TRNG;deep analysis of the requirements of high-speed TRNG for entropy source characteristics,through which three suitable entropy sources are found,and their In-depth research on characteristics;design and implementation of ultra-short dead time FPGA TDC;design and implementation of a TRNG based on STR,two TRNGs based on GARO,and a TRNG based on SiPM dark count. |
