Random numbers play a crucial role in modern security schemes. Couple to the rapid development of cryptography, the strength of security protocols and encryption algorithms consumingly relies on the quality of random ...Random numbers play a crucial role in modern security schemes. Couple to the rapid development of cryptography, the strength of security protocols and encryption algorithms consumingly relies on the quality of random number. With simple architecture and faster speed, linear feedback shift register often is selected in many applications. However, the random sequence generated by LFSR can not meet the demand of unpredictability for secure mechanism. Genetic algorithm improves the linear property of LFSR and constructs a novel random sequence generator with longer period and complex architecture.展开更多
Let （Xn）n∈EN be a sequence of arbitrary continuous random variables, by the notion of relative entropy hμ^μ（w） as a measure of dissimilarity between probability measure # and reference measure μ, the explicit,...Let （Xn）n∈EN be a sequence of arbitrary continuous random variables, by the notion of relative entropy hμ^μ（w） as a measure of dissimilarity between probability measure # and reference measure μ, the explicit, general bounds for the partial sums of arbitrary continuous random variables under suitable conditions are developed. The argument uses the known and elementary lcmma of convergence for likelihood ratio.展开更多
This note is devoted to introduce a new concept of conditionally dominated random variables.Under suitable restrict conditions,a general strong law of large numbers for arbitrary continuous random variables is obtained.
We first design a discrete hyperchaotic system via piece-wise linear state feedback. The states of the closed loop system are locally expanding in two directions but absolutely bounded on the whole, which implies hype...We first design a discrete hyperchaotic system via piece-wise linear state feedback. The states of the closed loop system are locally expanding in two directions but absolutely bounded on the whole, which implies hyperchaos. Then, we use three suchlike hyperchaotic systems with different feedback gain matrices to design a pseudo-random sequence generator (PRSG). Through a threshold function, three sub-sequences generated from the output of piecewise linear functions are changed into 0-1 sequences. Then, followed by XOR operation, an unpredictable pseudo-random sequence (PRS) is ultimately obtained. The analysis and simulation results indicate that the PRS, generated with hyperchaotic systems, has desirable statistical features.展开更多
This paper mainly study extreme values of FGM random sequences.We prove a technique theorem by the dependence structure of FGM sequences,and further obtain the limiting distributions of maxima and k-th largest for sta...This paper mainly study extreme values of FGM random sequences.We prove a technique theorem by the dependence structure of FGM sequences,and further obtain the limiting distributions of maxima and k-th largest for stationary FGM random sequences.展开更多
In this paper,we establish an invariance principle for ρ^--mixing random sequences under some moment condition.The result improve and extend the relevant result of Wu（2003）.
Let {Xn,n ≥ 1} be a sequence of arbitrary continuous random variables,we introduce the notion of limit asymptotic logarithm likelihood ratio r（ω）,as a measure of dissimilarity between probability measure P and ref...Let {Xn,n ≥ 1} be a sequence of arbitrary continuous random variables,we introduce the notion of limit asymptotic logarithm likelihood ratio r（ω）,as a measure of dissimilarity between probability measure P and reference measure Q.We get some strong deviation theorems for the partial sums of arbitrary continuous random variables under Chung-Teicher＇s type conditions[6-7].展开更多
In this paper, a random sequence generator based on chaotic circuits is presented.Fundamental principle and experimental circuit have been carried out in case of Chua's circuit.The statistical results are in good ...In this paper, a random sequence generator based on chaotic circuits is presented.Fundamental principle and experimental circuit have been carried out in case of Chua's circuit.The statistical results are in good agreement with probability characteristics of random sequence.展开更多
This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theor...This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theory and the modern cryptography.展开更多
Randomness number generation plays a key role in network, information security and IT applications. In this paper, a permutation and complementary algorithm is proposed to use vector complementary and permuta-tion ope...Randomness number generation plays a key role in network, information security and IT applications. In this paper, a permutation and complementary algorithm is proposed to use vector complementary and permuta-tion operations to extend n-variable Logic function space from 22n functions to 22n * 2n! configurations for variant logic framework. Each configuration contains 2n functions can be shown in a 22n-1*22n-1 matrix. A set of visual results can be represented by their symmetric properties in W, F and C codes respec-tively to provide the essential support on the variant logic framework.展开更多
This paper proposes new hierarchical structures for generating pseudorandom sequences and arrays. The principle of the structures is based on a new concept-multi-interleaving. It is the generalization of normal sequen...This paper proposes new hierarchical structures for generating pseudorandom sequences and arrays. The principle of the structures is based on a new concept-multi-interleaving. It is the generalization of normal sequence decimation(sampling). The kernal of the structures is a lower speed linear feedback shift register together with several high speed time-division multiplexers arranged hierarchically. These new structures have much higher speed compared with that of other schemes proposed before.展开更多
This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence ...This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.展开更多
This paper introduces a new theory and algorithm that can be used in blind detection of the carrier wave signal and the pseudo-random sequence of the direct sequence spread spectrum （DS/SS） signal with negative SNR....This paper introduces a new theory and algorithm that can be used in blind detection of the carrier wave signal and the pseudo-random sequence of the direct sequence spread spectrum （DS/SS） signal with negative SNR. First, without any a priori knowledge of the DS/SS signal, the carrier wave signal can be detected from DS/SS signal with negative SNR by using stochastic differential equations and energy detection method. Based on this, the pseudo-random sequence can also be blindly detected in DS/SS signal with negative SNR by reducing noise of the nonlinear signal and the algorithm of wavelet multiscale decomposition algorithm. Finally, the computer simulation shows that we can detect the carrier wave signal with SNR=-27 dB and the pseudo-random sequence under error code ratio 10^-4with SNR =-10 dB.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
Let {qn, } be a sequence of positive integers, and In={0,1,..,qn}. The sequence of random variables {Xn, n0} is called a Cantor-like random sequence if for every n,Xn takes on values in In, and p(X0=x0,…Xn=xn)>0,T...Let {qn, } be a sequence of positive integers, and In={0,1,..,qn}. The sequence of random variables {Xn, n0} is called a Cantor-like random sequence if for every n,Xn takes on values in In, and p(X0=x0,…Xn=xn)>0,The purpose of this paper is to give a strong limit theorem for these sequences.展开更多
In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong...In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.展开更多
We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to c...We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.展开更多
We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnum...We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.展开更多
Let （?）=（S,S,…）be a binary random sequence with period N=2<sup>n</sup>,where S=(S<sub>0</sub>,…,S<sub>N-1</sub>)is its one period with N independent and uniformly distributed ...Let （?）=（S,S,…）be a binary random sequence with period N=2<sup>n</sup>,where S=(S<sub>0</sub>,…,S<sub>N-1</sub>)is its one period with N independent and uniformly distributed binary random variables.The main results of this paper are as follows.1)Var c（?）=2-（2N+1）2<sup>-N</sup>-2<sup>-2N</sup>;2)E|c（?）-c（?）|=[2<sup>c（?）+1</sup>-2]2<sup>-N</sup>for any sequence （?） with period 2<sup>n</sup>;3)N-1+2<sup>-N</sup>-(n/2+1-2<sup>-（N-n）</sup>)≤E[（?）c（?）]≤N-1+2<sup>-N</sup>4)2-2<sup>-（N-1）</sup>≤E[（?）|c（?）-c（?）|]≤2-2<sup>-N</sup>+n/2-2<sup>-（N-n）</sup>,where E and Var stand for taking expectation and variance respectively,c（?） is the linearcomplexity of the sequence （?） and W（b） the Hamming weight of one period of the seqnence （?）.展开更多
基金Supported by the National Natural Science Foundation of China (60373087, 90104005 and 60473023)
文摘Random numbers play a crucial role in modern security schemes. Couple to the rapid development of cryptography, the strength of security protocols and encryption algorithms consumingly relies on the quality of random number. With simple architecture and faster speed, linear feedback shift register often is selected in many applications. However, the random sequence generated by LFSR can not meet the demand of unpredictability for secure mechanism. Genetic algorithm improves the linear property of LFSR and constructs a novel random sequence generator with longer period and complex architecture.
基金Supported by the NNSF of China(10571076) Anhui High Education Research Grant( 2006Kj246B).
文摘Let （Xn）n∈EN be a sequence of arbitrary continuous random variables, by the notion of relative entropy hμ^μ（w） as a measure of dissimilarity between probability measure # and reference measure μ, the explicit, general bounds for the partial sums of arbitrary continuous random variables under suitable conditions are developed. The argument uses the known and elementary lcmma of convergence for likelihood ratio.
基金Supported by the National Nature Science Foundation of China（10571076） Supported by Anhui High Education Research（2006Kj246B）
文摘This note is devoted to introduce a new concept of conditionally dominated random variables.Under suitable restrict conditions,a general strong law of large numbers for arbitrary continuous random variables is obtained.
基金This project was supported by the National Natural Science Foundation of China (69874025).
文摘We first design a discrete hyperchaotic system via piece-wise linear state feedback. The states of the closed loop system are locally expanding in two directions but absolutely bounded on the whole, which implies hyperchaos. Then, we use three suchlike hyperchaotic systems with different feedback gain matrices to design a pseudo-random sequence generator (PRSG). Through a threshold function, three sub-sequences generated from the output of piecewise linear functions are changed into 0-1 sequences. Then, followed by XOR operation, an unpredictable pseudo-random sequence (PRS) is ultimately obtained. The analysis and simulation results indicate that the PRS, generated with hyperchaotic systems, has desirable statistical features.
文摘This paper mainly study extreme values of FGM random sequences.We prove a technique theorem by the dependence structure of FGM sequences,and further obtain the limiting distributions of maxima and k-th largest for stationary FGM random sequences.
基金Supported by the National Natural Science Foundation of China（10661006） Supported by the New Century Guangxi Ten-hundred-thousand Talents Project（2005214）
文摘In this paper,we establish an invariance principle for ρ^--mixing random sequences under some moment condition.The result improve and extend the relevant result of Wu（2003）.
基金Supported by Anhui High Education Research(2006Kj246B)
文摘Let {Xn,n ≥ 1} be a sequence of arbitrary continuous random variables,we introduce the notion of limit asymptotic logarithm likelihood ratio r（ω）,as a measure of dissimilarity between probability measure P and reference measure Q.We get some strong deviation theorems for the partial sums of arbitrary continuous random variables under Chung-Teicher＇s type conditions[6-7].
基金Supported by the Doctoral Fund of the State Education Committee of Chinathe Nature Science Foundation of Zhejiang Province
文摘In this paper, a random sequence generator based on chaotic circuits is presented.Fundamental principle and experimental circuit have been carried out in case of Chua's circuit.The statistical results are in good agreement with probability characteristics of random sequence.
基金Supported by Trans-century Training Program Foundation for the Talents by the State Education Commission
文摘This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theory and the modern cryptography.
文摘Randomness number generation plays a key role in network, information security and IT applications. In this paper, a permutation and complementary algorithm is proposed to use vector complementary and permuta-tion operations to extend n-variable Logic function space from 22n functions to 22n * 2n! configurations for variant logic framework. Each configuration contains 2n functions can be shown in a 22n-1*22n-1 matrix. A set of visual results can be represented by their symmetric properties in W, F and C codes respec-tively to provide the essential support on the variant logic framework.
文摘This paper proposes new hierarchical structures for generating pseudorandom sequences and arrays. The principle of the structures is based on a new concept-multi-interleaving. It is the generalization of normal sequence decimation(sampling). The kernal of the structures is a lower speed linear feedback shift register together with several high speed time-division multiplexers arranged hierarchically. These new structures have much higher speed compared with that of other schemes proposed before.
基金Supported by the National Natural Science Foundation of China（11061012） Supported by the Natural Science Foundation of Guangxi（2010GXNSFA013121）
文摘This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.
基金the National Defence Key Foundation of China (Grant No. 614144)
文摘This paper introduces a new theory and algorithm that can be used in blind detection of the carrier wave signal and the pseudo-random sequence of the direct sequence spread spectrum （DS/SS） signal with negative SNR. First, without any a priori knowledge of the DS/SS signal, the carrier wave signal can be detected from DS/SS signal with negative SNR by using stochastic differential equations and energy detection method. Based on this, the pseudo-random sequence can also be blindly detected in DS/SS signal with negative SNR by reducing noise of the nonlinear signal and the algorithm of wavelet multiscale decomposition algorithm. Finally, the computer simulation shows that we can detect the carrier wave signal with SNR=-27 dB and the pseudo-random sequence under error code ratio 10^-4with SNR =-10 dB.
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Let {qn, } be a sequence of positive integers, and In={0,1,..,qn}. The sequence of random variables {Xn, n0} is called a Cantor-like random sequence if for every n,Xn takes on values in In, and p(X0=x0,…Xn=xn)>0,The purpose of this paper is to give a strong limit theorem for these sequences.
基金the National Natural Science Foundation of China(10671149)
文摘In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.
基金Supported by the National Natural Science Foundation of China (10671149)
文摘We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.
基金Supported by the National Natural Science Foundation of China (10671149)
文摘We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.
基金This project was supported by National Natural Science Foundation of China
文摘Let （?）=（S,S,…）be a binary random sequence with period N=2<sup>n</sup>,where S=(S<sub>0</sub>,…,S<sub>N-1</sub>)is its one period with N independent and uniformly distributed binary random variables.The main results of this paper are as follows.1)Var c（?）=2-（2N+1）2<sup>-N</sup>-2<sup>-2N</sup>;2)E|c（?）-c（?）|=[2<sup>c（?）+1</sup>-2]2<sup>-N</sup>for any sequence （?） with period 2<sup>n</sup>;3)N-1+2<sup>-N</sup>-(n/2+1-2<sup>-（N-n）</sup>)≤E[（?）c（?）]≤N-1+2<sup>-N</sup>4)2-2<sup>-（N-1）</sup>≤E[（?）|c（?）-c（?）|]≤2-2<sup>-N</sup>+n/2-2<sup>-（N-n）</sup>,where E and Var stand for taking expectation and variance respectively,c（?） is the linearcomplexity of the sequence （?） and W（b） the Hamming weight of one period of the seqnence （?）.
