In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the br...In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process.Here,we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion(SSE)algorithm.To quantitatively compare them,we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms.After testing several representative observables of the Heisenberg model in one and two dimensions,we recommend the linear congruential generator as the best choice of PRNG.Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.展开更多
Primitive elements play important roles in the Diffie-Hellman protocol for establishment of secret communication keys, in the design of the ElGamal cryptographic system and as generators of pseudo-random numbers. In g...Primitive elements play important roles in the Diffie-Hellman protocol for establishment of secret communication keys, in the design of the ElGamal cryptographic system and as generators of pseudo-random numbers. In general, a deterministic algorithm that searches for primitive elements is currently unknown. In information-hiding schemes, where a primitive element is the key factor, there is the freedom in selection of a modulus. This paper provides a fast deterministic algorithm, which computes every primitive element in modular arithmetic with special moduli. The algorithm requires at most O(log2p) digital operations for computation of a generator. In addition, the accelerated-descend algorithm that computes small generators is described in this paper. Several numeric examples and tables illustrate the algorithms and their properties.展开更多
In plasmonic systems, the response of nanoobjects under light illumination can produce complex optical maps. Such plasmonic or resonant systems have interesting characteristics such as sensitivity on parameters and in...In plasmonic systems, the response of nanoobjects under light illumination can produce complex optical maps. Such plasmonic or resonant systems have interesting characteristics such as sensitivity on parameters and initial conditions. In this paper, we show how these complex maps can be cryptographically improved and associated in order to design a secure pseudo random number generator.展开更多
By analysis and comparison of several chaotic systems that are applied to generate pseudo-random sequence, the generalized Henon map is proposed as a pseudo-random sequence generator. A new algorithm is created to sol...By analysis and comparison of several chaotic systems that are applied to generate pseudo-random sequence, the generalized Henon map is proposed as a pseudo-random sequence generator. A new algorithm is created to solve the problem of non-uniform distribution of the sequence generated by the generalized Henon map. First, move the decimal point of elements in the sequence to the fight; then, cut off the integer; and finally, quantify it into a binary sequence. Statistical test, security analysis, and the application of image encryption have strongly supported the good random statistical characteristics, high linear complexity, large key space, and great sensitivity of the binary sequence.展开更多
A pseudo-random sequence generator is a basic tool for cryptography. To realize a pseudo-random sequence generator, a new block iterating method using shifter, multiplier, and adder operations has been introduced. By ...A pseudo-random sequence generator is a basic tool for cryptography. To realize a pseudo-random sequence generator, a new block iterating method using shifter, multiplier, and adder operations has been introduced. By increasing the iteration of the counter and by performing calculations based on the initial value, an approximate pseudo-random sequence was obtained after exchanging bits. The algorithm and the complexity of the generator were introduced. The result obtained from the calculation shows that the self-correlation of the ＂m＂ block sequence is two-valued; the block field value is [0, 2^m - 1 ], and the block period is 2^m＋8 - 1.展开更多
In many applications of information processing,such as cryptography,generating random sequences presents many difficulties.In this paper,a new pseudo-random sequence is proposed,based on two chaotic systems,a logistic...In many applications of information processing,such as cryptography,generating random sequences presents many difficulties.In this paper,a new pseudo-random sequence is proposed,based on two chaotic systems,a logistic map and a seven-dimensional(7D)hyperchaotic system.The main process of the proposed generator is that it functions by using the logistic map to control the 7D hyperchaotic system,which exhibits random behavior to produce a pseudo-random sequence.Specifically,the logistic map is used to select one of the variables from the 7D hyperchaotic system.The variable selected at each iteration is used as a controller to fill the pseudo-random sequence,choosing from one of the other variables of the 7D hyperchaotic system.This means that in each iteration,the pseudorandom sequence takes a value from the 7D hyperchaotic system according to the logistic map and the selected variable of the 7D hyperchaotic system.This method allows the creation of a highly efficient pseudo-random generator through simple processes.Experimental and analysis results show that the proposed generator has good random characteristics,making it suitable for cryptography applications such as encryption algorithms.展开更多
Stream cipher, DNA cryptography and DNA analysis are the most important R&D fields in both Cryptography and Bioinformatics. HC-256 is an emerged scheme as the new generation of stream ciphers for advanced network ...Stream cipher, DNA cryptography and DNA analysis are the most important R&D fields in both Cryptography and Bioinformatics. HC-256 is an emerged scheme as the new generation of stream ciphers for advanced network security. From a random sequencing viewpoint, both sequences of HC-256 and real DNA data may have intrinsic pseudo-random properties respectively. In a recent decade, many DNA sequencing projects are developed on cells, plants and animals over the world into huge DNA databases. Researchers notice that mammalian genomes encode thousands of large noncoding RNAs (lncRNAs), interact with chromatin regulatory complexes, and are thought to play a role in localizing these complexes to target loci across the genome. It is a challenge target using higher dimensional visualization tools to organize various complex interactive properties as visual maps. The Variant Map System (VMS) as an emerging scheme is systematically proposed in this paper to apply multiple maps that used four Meta symbols as same as DNA or RNA representations. System architecture of key components and core mechanism on the VMS are described. Key modules, equations and their I/O parameters are discussed. Applying the VM System, two sets of real DNA sequences from both sample human (noncoding DNA) and corn (coding DNA) genomes are collected in comparison with pseudo DNA sequences generated by HC-256 to show their intrinsic properties in higher levels of similar relationships among relevant DNA sequences on 2D maps. Sample 2D maps are listed and their characteristics are illustrated under controllable environment. Visual results are briefly analyzed to explore their intrinsic properties on selected genome sequences.展开更多
Discrete memristor has become a hotspot since it was proposed recently.However,the design of chaotic maps based on discrete memristor is in its early research stage.In this paper,a memristive seed chaotic map is propo...Discrete memristor has become a hotspot since it was proposed recently.However,the design of chaotic maps based on discrete memristor is in its early research stage.In this paper,a memristive seed chaotic map is proposed by combining a quadratic discrete memristor with the sine function.Furthermore,by applying the chaotification method,we obtain a high-dimensional chaotic map.Numerical analysis shows that it can generate hyperchaos.With the increase of cascade times,the generated map has more positive Lyapunov exponents and larger hyperchaotic range.The National Institute of Standards and Technology(NIST)test results show that the chaotic pseudo-random sequence generated by cascading two seed maps has good unpredictability,and it indicates the potential in practical application.展开更多
We introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry, especially in the frame of chaotic attractors for solving practical problems(generating ...We introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry, especially in the frame of chaotic attractors for solving practical problems(generating hyperchaos; developing chaos based pseudo random number generator(CPRNG) and chaotic multistream PRNG; secure communication via synchronization). They can also be used in cryptography, generic algorithms in optimization, control, etc.展开更多
A memristive Hopfield neural network(MHNN)with a special activation gradient is proposed by adding a suitable memristor to the Hopfield neural network(HNN)with a special activation gradient.The MHNN is simulated and d...A memristive Hopfield neural network(MHNN)with a special activation gradient is proposed by adding a suitable memristor to the Hopfield neural network(HNN)with a special activation gradient.The MHNN is simulated and dynamically analyzed,and implemented on FPGA.Then,a new pseudo-random number generator(PRNG)based on MHNN is proposed.The post-processing unit of the PRNG is composed of nonlinear post-processor and XOR calculator,which effectively ensures the randomness of PRNG.The experiments in this paper comply with the IEEE 754-1985 high precision32-bit floating point standard and are done on the Vivado design tool using a Xilinx XC7 Z020 CLG400-2 FPGA chip and the Verilog-HDL hardware programming language.The random sequence generated by the PRNG proposed in this paper has passed the NIST SP800-22 test suite and security analysis,proving its randomness and high performance.Finally,an image encryption system based on PRNG is proposed and implemented on FPGA,which proves the value of the image encryption system in the field of data encryption connected to the Internet of Things(Io T).展开更多
We review the constructions of two main kinds of generalized cyclotomic binary sequences with length pq （the product with two distinct primes）. One is the White-generalized cyclotomic sequences, the other is the Din...We review the constructions of two main kinds of generalized cyclotomic binary sequences with length pq （the product with two distinct primes）. One is the White-generalized cyclotomic sequences, the other is the Ding-Helleseth（DH, for short）-generalized cyclotomic sequences. We present some new pseudo-random properties of DH-generalized cyclotomic sequences using the theory of character sums instead of the theory of cyclotomy, which is a conventional method for investigating generalized cyclotomic sequences.展开更多
<正> The performance of individual pseudo-random sequence, generated by some mechanism, is often not ideal. The asymptotic performance of the addition (in the sense (mod p) of a large number of such individual s...<正> The performance of individual pseudo-random sequence, generated by some mechanism, is often not ideal. The asymptotic performance of the addition (in the sense (mod p) of a large number of such individual sequences is studied and the necessary and sufficient condition under which the resulting sequence may converge to genuine randomness is obtained.展开更多
Sequences with nice pseudo-randomness play an important role in not only communication system but also cryptography system. Based on the Legendre-Sidelnikov sequence, a modified Legendre-Sidelnikov sequence was introd...Sequences with nice pseudo-randomness play an important role in not only communication system but also cryptography system. Based on the Legendre-Sidelnikov sequence, a modified Legendre-Sidelnikov sequence was introduced. The exact value of the autocorrelation function was derived by strict computation. According to the values of the autocorrelation functions of the two Legendre-Sidelnikov sequences, it is proven that both of them have perfect pseudo-randomness. Furthermore, a detailed comparison between autocorrelation functions of the two Legendre-Sidelnikov sequences was deduced. It indicates that no matter which parameters are chosen, the modified sequence has pseudo-randomness as good as the primitive sequence, which is of great significance for applications.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12274046,11874094,and 12147102)Chongqing Natural Science Foundation(Grant No.CSTB2022NSCQ-JQX0018)Fundamental Research Funds for the Central Universities(Grant No.2021CDJZYJH-003).
文摘In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process.Here,we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion(SSE)algorithm.To quantitatively compare them,we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms.After testing several representative observables of the Heisenberg model in one and two dimensions,we recommend the linear congruential generator as the best choice of PRNG.Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.
文摘Primitive elements play important roles in the Diffie-Hellman protocol for establishment of secret communication keys, in the design of the ElGamal cryptographic system and as generators of pseudo-random numbers. In general, a deterministic algorithm that searches for primitive elements is currently unknown. In information-hiding schemes, where a primitive element is the key factor, there is the freedom in selection of a modulus. This paper provides a fast deterministic algorithm, which computes every primitive element in modular arithmetic with special moduli. The algorithm requires at most O(log2p) digital operations for computation of a generator. In addition, the accelerated-descend algorithm that computes small generators is described in this paper. Several numeric examples and tables illustrate the algorithms and their properties.
基金the Region Champagne- Ardennes and the Conseil Regional de l’Aube
文摘In plasmonic systems, the response of nanoobjects under light illumination can produce complex optical maps. Such plasmonic or resonant systems have interesting characteristics such as sensitivity on parameters and initial conditions. In this paper, we show how these complex maps can be cryptographically improved and associated in order to design a secure pseudo random number generator.
基金the National Natural Science Foundation of China (60372061)
文摘By analysis and comparison of several chaotic systems that are applied to generate pseudo-random sequence, the generalized Henon map is proposed as a pseudo-random sequence generator. A new algorithm is created to solve the problem of non-uniform distribution of the sequence generated by the generalized Henon map. First, move the decimal point of elements in the sequence to the fight; then, cut off the integer; and finally, quantify it into a binary sequence. Statistical test, security analysis, and the application of image encryption have strongly supported the good random statistical characteristics, high linear complexity, large key space, and great sensitivity of the binary sequence.
文摘A pseudo-random sequence generator is a basic tool for cryptography. To realize a pseudo-random sequence generator, a new block iterating method using shifter, multiplier, and adder operations has been introduced. By increasing the iteration of the counter and by performing calculations based on the initial value, an approximate pseudo-random sequence was obtained after exchanging bits. The algorithm and the complexity of the generator were introduced. The result obtained from the calculation shows that the self-correlation of the ＂m＂ block sequence is two-valued; the block field value is [0, 2^m - 1 ], and the block period is 2^m＋8 - 1.
文摘In many applications of information processing,such as cryptography,generating random sequences presents many difficulties.In this paper,a new pseudo-random sequence is proposed,based on two chaotic systems,a logistic map and a seven-dimensional(7D)hyperchaotic system.The main process of the proposed generator is that it functions by using the logistic map to control the 7D hyperchaotic system,which exhibits random behavior to produce a pseudo-random sequence.Specifically,the logistic map is used to select one of the variables from the 7D hyperchaotic system.The variable selected at each iteration is used as a controller to fill the pseudo-random sequence,choosing from one of the other variables of the 7D hyperchaotic system.This means that in each iteration,the pseudorandom sequence takes a value from the 7D hyperchaotic system according to the logistic map and the selected variable of the 7D hyperchaotic system.This method allows the creation of a highly efficient pseudo-random generator through simple processes.Experimental and analysis results show that the proposed generator has good random characteristics,making it suitable for cryptography applications such as encryption algorithms.
文摘Stream cipher, DNA cryptography and DNA analysis are the most important R&D fields in both Cryptography and Bioinformatics. HC-256 is an emerged scheme as the new generation of stream ciphers for advanced network security. From a random sequencing viewpoint, both sequences of HC-256 and real DNA data may have intrinsic pseudo-random properties respectively. In a recent decade, many DNA sequencing projects are developed on cells, plants and animals over the world into huge DNA databases. Researchers notice that mammalian genomes encode thousands of large noncoding RNAs (lncRNAs), interact with chromatin regulatory complexes, and are thought to play a role in localizing these complexes to target loci across the genome. It is a challenge target using higher dimensional visualization tools to organize various complex interactive properties as visual maps. The Variant Map System (VMS) as an emerging scheme is systematically proposed in this paper to apply multiple maps that used four Meta symbols as same as DNA or RNA representations. System architecture of key components and core mechanism on the VMS are described. Key modules, equations and their I/O parameters are discussed. Applying the VM System, two sets of real DNA sequences from both sample human (noncoding DNA) and corn (coding DNA) genomes are collected in comparison with pseudo DNA sequences generated by HC-256 to show their intrinsic properties in higher levels of similar relationships among relevant DNA sequences on 2D maps. Sample 2D maps are listed and their characteristics are illustrated under controllable environment. Visual results are briefly analyzed to explore their intrinsic properties on selected genome sequences.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61901530,62071496,and 62061008)
文摘Discrete memristor has become a hotspot since it was proposed recently.However,the design of chaotic maps based on discrete memristor is in its early research stage.In this paper,a memristive seed chaotic map is proposed by combining a quadratic discrete memristor with the sine function.Furthermore,by applying the chaotification method,we obtain a high-dimensional chaotic map.Numerical analysis shows that it can generate hyperchaos.With the increase of cascade times,the generated map has more positive Lyapunov exponents and larger hyperchaotic range.The National Institute of Standards and Technology(NIST)test results show that the chaotic pseudo-random sequence generated by cascading two seed maps has good unpredictability,and it indicates the potential in practical application.
文摘We introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry, especially in the frame of chaotic attractors for solving practical problems(generating hyperchaos; developing chaos based pseudo random number generator(CPRNG) and chaotic multistream PRNG; secure communication via synchronization). They can also be used in cryptography, generic algorithms in optimization, control, etc.
基金supported by the Scientific Research Fund of Hunan Provincial Education Department(Grant No.21B0345)the Postgraduate Scientific Research Innovation Project of Changsha University of Science and Technology(Grant Nos.CX2021SS69 and CX2021SS72)+3 种基金the Postgraduate Scientific Research Innovation Project of Hunan Province,China(Grant No.CX20200884)the Natural Science Foundation of Hunan Province,China(Grant Nos.2019JJ50648,2020JJ4622,and 2020JJ4221)the National Natural Science Foundation of China(Grant No.62172058)the Special Funds for the Construction of Innovative Provinces of Hunan Province,China(Grant Nos.2020JK4046 and 2022SK2007)。
文摘A memristive Hopfield neural network(MHNN)with a special activation gradient is proposed by adding a suitable memristor to the Hopfield neural network(HNN)with a special activation gradient.The MHNN is simulated and dynamically analyzed,and implemented on FPGA.Then,a new pseudo-random number generator(PRNG)based on MHNN is proposed.The post-processing unit of the PRNG is composed of nonlinear post-processor and XOR calculator,which effectively ensures the randomness of PRNG.The experiments in this paper comply with the IEEE 754-1985 high precision32-bit floating point standard and are done on the Vivado design tool using a Xilinx XC7 Z020 CLG400-2 FPGA chip and the Verilog-HDL hardware programming language.The random sequence generated by the PRNG proposed in this paper has passed the NIST SP800-22 test suite and security analysis,proving its randomness and high performance.Finally,an image encryption system based on PRNG is proposed and implemented on FPGA,which proves the value of the image encryption system in the field of data encryption connected to the Internet of Things(Io T).
基金supported in part by the Open Funds of Key Lab of Fujian Province University Network Security and Cryptology(Grant No. 07B005)the Funds of the Education Department of Fujian Province (Grant No. JA07164) the Natural Science Foundation of Fujian Province of China (Grant No. 2007F3086).
文摘We review the constructions of two main kinds of generalized cyclotomic binary sequences with length pq （the product with two distinct primes）. One is the White-generalized cyclotomic sequences, the other is the Ding-Helleseth（DH, for short）-generalized cyclotomic sequences. We present some new pseudo-random properties of DH-generalized cyclotomic sequences using the theory of character sums instead of the theory of cyclotomy, which is a conventional method for investigating generalized cyclotomic sequences.
基金Project supported by the National Natural Science Foundation of China,the UPGC of Hong Kong,Hong Kong Baptist University and SRCU.
文摘<正> The performance of individual pseudo-random sequence, generated by some mechanism, is often not ideal. The asymptotic performance of the addition (in the sense (mod p) of a large number of such individual sequences is studied and the necessary and sufficient condition under which the resulting sequence may converge to genuine randomness is obtained.
基金supported by the National Natural Science Foundation of China (60833008)the Science and Technology on Communication Security Laboratory (9140C110201110C1102)the Fundamental Research Funds for the Central Universities (K5051270003, K50511010007)
文摘Sequences with nice pseudo-randomness play an important role in not only communication system but also cryptography system. Based on the Legendre-Sidelnikov sequence, a modified Legendre-Sidelnikov sequence was introduced. The exact value of the autocorrelation function was derived by strict computation. According to the values of the autocorrelation functions of the two Legendre-Sidelnikov sequences, it is proven that both of them have perfect pseudo-randomness. Furthermore, a detailed comparison between autocorrelation functions of the two Legendre-Sidelnikov sequences was deduced. It indicates that no matter which parameters are chosen, the modified sequence has pseudo-randomness as good as the primitive sequence, which is of great significance for applications.
