| Cryptography is the core of network information security.Cryptographic algorithms and cryptographic protocols are widely used to ensure the security of network information.In these cryptographic algorithms and protocols,random number is an indispensable part,and the performance of random number directly affects the performance of the cryptographic system.Devices that generate random numbers are known as random number generators.Generally speaking,random number generator includes pseudorandom number generator and physical random number generator.Using seeds and deterministic algorithms,pseudo-random number generator can generate high speed random numbers quickly and conveniently,with a rate up to dozens of Gbit/s.Pseudo-random number generator can generate the key quickly,easily and conveniently,and distributing pseudo-random keys is simple.Thus,pseudorandom number generator is widely used in the present encryption system.But pseudo-random number generator has some fatal defects:(1)once the seeds and algorithms are cracked by attacker,the attacker will be able to predict and even copy the keys,then the security of the encryption system will be completely lost.(2)Since the length of the seeds is limited and the algorithm is determined,the keys generated by the pseudorandom number generator will be periodic.With the rapid improvement of computer performance,the use of pseudorandom number encryption for information security is become more and more danger.In order to improve the security of encryption using pseudo-random number,some researches focus on developing more complex pseudo-random number algorithms to enhance the difficulty of key cracking,but these methods cannot change the deterministic nature of pseudo-random number.With the development of computer technology,pseudo-random number generator using deterministic algorithm is no longer applicable in many occasions.Instead,it is the physical random number generator using unpredictable and non-repeatable physical phenomena to generate random numbers.Physical random number generator extracts unpredictable random numbers from the physical random process,which can guarantee the absolute security of information in principle.Electronic noise of the circuit is an ideal entropy source for physical random number generator due to its natural unpredictability.In circuit,physical random number generator ever used amplifier to amplify the circuit noise directly or used ring oscillator to amplify the jitter caused by the noise in the circuit to generate random numbers.However,the rates of these physical random number generators are generally not high enough to meet the requirement of high-speed secure communication.Shannon’s “one secret at a time” encryption principle can guarantee the absolute security of information,but it needs a large number of physical random numbers in real time as the encryption key.The above physical random number generators generally produce random numbers tens of megabits per second,which is difficult to meet the security encryption requirements of high-speed information.Therefore,researching high-speed physical random number generator becomes one of the key problems to solve secure communication.Because of high bandwidth and large fluctuation characteristics,chaos has enormous potential in high-speed physical random number generator.In recent years,it has received widespread attention that using Boolean chaos generates high-speed physical random number.The reasons are that the autonomous Boolean network circuit that generates Boolean chaos has the advantages of simple structure,strong portability,and easy chip integration.It can be convenient embedded in information security devices.Additionally,because the method can obtain high-speed physical random numbers on the order of hundreds of megabits per second in practice,it can meet the security encryption requirements of massive information.However,the current research on Boolean chaos and autonomous Boolean networks exists some shortcomings,and the following work needs to be completed: 1)The dynamic model of the autonomous Boolean network needs to be further improved and perfected to make the simulation calculation results more consistent with the experimental observation data;2)The security of using Boolean chaos to generate physical random numbers(That is,the unpredictability of random numbers)requires further theoretical and experimental proof.In order to better reveal the mechanism of Boolean chaos in autonomous Boolean networks and the process of unpredictable physical random numbers,this thesis mainly carried out the following research.(1)The equivalent circuit model of XOR logic gate is established.Furthermore,an autonomous Boolean network model using piecewise linear delay differential equation is established,and the influence factors of model parameters are studied.The propagation delay of XOR logic gate is measured,and then the filter coefficient of autonomous Boolean network is determined.It is shown that the autonomous Boolean network model using piecewise linear delay differential equation can overcome the problem of infinite frequency growth of the Boolean delay equation model,and the piecewise linear delay differential equation is closer to the actual operation.(2)Delay parameters,filter coefficient and coupling relation between nodes impacts on dynamic characteristics of autonomous Boolean network are analyzed theoretically and experimentally.Experimental and theoretical results demonstrate that the transition between stable state and chaos can be realized by adjusting delay parameters,filter coefficient and coupling relation between nodes of the autonomous Boolean network.Larger standard deviation of delay parameters,smaller filter coefficient,and autonomous Boolean network is easier to generate chaos.(3)The unpredictability of Boolean chaos is studied.The relationship between phase noise and propagation delay jitter in autonomous Boolean network is studied and the jitter strength is measured.Amplification effect of Boolean chaos on phase noise is proved using numerical simulation,and the unpredictability of Boolean chaos is proved using Shannon entropy evaluation.The unpredictability of Boolean chaos is further studied experimentally,and simulation results is proved,which lays a foundation for autonomous Boolean network generating unpredictable random numbers.(4)The topology of autonomous Boolean network for physical random number generator is optimized.Firstly,the structure of chaos for autonomous Boolean network is selected using theoretical analysis,then the improvement effect of XOR on Shannon entropy is proved.Theoretical analysis and FPGA experimental results show that the topology of 18-node autonomous Boolean network is the optimal structure to meet the performance requirements,and the time interval distribution of the adjacent rising edge of the output signal of the18-node autonomous Boolean network is given.FPGA experiment results show that the bandwidth of 18-node autonomous Boolean network signal-10 dB can reach up to 760 MHz,and the time interval of the output signal adjacent to the rising edge approximately obeys Poisson distribution.The wide signal bandwidth and Poisson distribution of the time interval between adjacent rising edges indicate that Boolean network is expected to produce high-speed physical random numbers.(5)It is determined that the structure of physical random number generator using autonomous Boolean network.Then waveform of random bits,eye map and lattice map generated by physical random number generator demonstrate that random number generation rate can reach to 100 Mbit/s.Furthermore,the random numbers are tested by the detailed international industry test standards.The performance of random numbers is evaluated using ENT,NIST and Diehard international industry testing standards.The test results show that the random numbers using autonomous Boolean network can pass ENT,NIST and Diehard statistical tests successfully,indicating that the generated random numbers have good performance. |
