Motivated by representing multidimensional periodic nonlinear and non-stationary signals(functions),we study a class of orthonormal exponential basis for L2(Id)with I:=[0,1),whose exponential parts are piecewise linea...Motivated by representing multidimensional periodic nonlinear and non-stationary signals(functions),we study a class of orthonormal exponential basis for L2(Id)with I:=[0,1),whose exponential parts are piecewise linear spectral sequences with p-knots.It is widely applied in time-frequency analysis.展开更多
For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characteri...For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characterize the Kondratiev space of random test function, in which space it is convenient to study random distribution,random partial differential equation and other problems.展开更多
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 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 presents modified version of a realistic test tool suitable to Design For Testability （DFT） and Built-ln Self Test （BIST） environments. A comprehensive tool is developed in the form of a test simulator....This paper presents modified version of a realistic test tool suitable to Design For Testability （DFT） and Built-ln Self Test （BIST） environments. A comprehensive tool is developed in the form of a test simulator. The simulator is capable of providing a required goal of test for the Circuit Under Test （CUT）. The simulator uses the approach of fault diagnostics with fault grading procedures to provide the optimum tests. The current version of the simulator embeds features of exhaustive and pseudo-random test generation schemes along with the search solutions of cost effective test goals. The simulator provides facilities of realizing all possible pseudo-random sequence generators with all possible combinations of seeds. The tool is developed on a common Personal Computer （PC） platform and hence no special software is required. Thereby, it is a low cost tool hence economical. The tool is very much suitable for determining realistic test sequences for a targeted goal of testing for any CUT. The developed tool incorporates flexible Graphical User Interface （GUI） procedures and can be operated without any special programming skill. The tool is debugged and tested with the results of many bench mark circuits. Further, this developed tool can be utilized for educational purposes for many courses such as fault-tolerant computing, fault diagnosis, digital electronics, and safe-reliable-testable digital logic designs.展开更多
This paper presents the definition of perfect punctured binary sequence pair and the combinatorial admissible conditions for searching the perfect punctured binary sequence pairs and proves that all of the pseudo-rand...This paper presents the definition of perfect punctured binary sequence pair and the combinatorial admissible conditions for searching the perfect punctured binary sequence pairs and proves that all of the pseudo-random binary sequences satisfy these conditions. Computer calculation verifies that the pseudo-random binary sequences with length up to N=127 can be easily turned into perfect punctured binary sequence pairs.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
Cryptographic properties of the single cycle T-function's output sequences are investigated.Bounds of autocorrelation functions of the kth coordinate sequence and bounds of state output sequence are calculated res...Cryptographic properties of the single cycle T-function's output sequences are investigated.Bounds of autocorrelation functions of the kth coordinate sequence and bounds of state output sequence are calculated respectively.The Maximum Sidelobe Ratio(MSR) of the kth coordinate sequence and the MSR of state output sequence are given respectively.The bounds of autocorrelation functions show that the values of autocorrelation functions are large when shifts are small.Comparisons of the autocorrelations between the state output sequence and coordinate output sequence are illustrated.The autocorrelation properties demonstrate that T-functions have cryptographic weaknesses and the illustration result shows coordinate output sequences have better autocorrelation than that of state output sequences.展开更多
A family of binary sequences were constructed by using an elliptic curve and its twisted curves over finite fields. It was shown that these sequences possess ＂good＂ cryptographie properties of 0-1 distribution, long...A family of binary sequences were constructed by using an elliptic curve and its twisted curves over finite fields. It was shown that these sequences possess ＂good＂ cryptographie properties of 0-1 distribution, long period and large linear complexity. The results indicate that such se quences provide strong potential applications in cryptography.展开更多
Pseudo-random sequences with long period, low correlation, high linear complexity, and uniform distribution of bit patterns are widely used in the field of information security and cryptography. This paper proposes an...Pseudo-random sequences with long period, low correlation, high linear complexity, and uniform distribution of bit patterns are widely used in the field of information security and cryptography. This paper proposes an approach for generating a pseudo-random multi-value sequence (including a binary sequence) by utilizing a primitive polynomial, trace function, and k-th power residue symbol over the sub extension field. All our previous sequences are defined over the prime field, whereas, proposed sequence in this paper is defined over the sub extension field. Thus, it’s a new and innovative perception to consider the sub extension field during the sequence generation procedure. By considering the sub extension field, two notable outcomes are: proposed sequence holds higher linear complexity and more uniform distribution of bit patterns compared to our previous work which defined over the prime field. Additionally, other important properties of the proposed multi-value sequence such as period, autocorrelation, and cross-correlation are theoretically shown along with some experimental results.展开更多
Sequence operation theory (SOT) is a powerful tool for solving complex probabilistic problems in power system. However, the basic single dimension SOT cannot satisfy the requirement of multi-state; multi-attribute ana...Sequence operation theory (SOT) is a powerful tool for solving complex probabilistic problems in power system. However, the basic single dimension SOT cannot satisfy the requirement of multi-state; multi-attribute analysis, which is often the case in actual power system practice. To address this problem, multidimensional sequence operation theory (MSOT) is developed. On the basis of previous research, this paper first categorizes the situations by the number of state variables; the number of attribute values,; defines the multidimensional sequence for single state variable; multiple attribute values, as well as the multidimensional sequence for multiple state variables; multiple attribute values. Corresponding to those definitions, four types of operations between two discrete multidimensional sequences are derived respectively. Therefore, the sequence is extended from single dimensional to multidimensional, establishing an integrated theory of multidimensional sequence operation. In particular, the basic single dimension SOT can be viewed as a special case of MSOT with only one state variable; one attribute value. Finally, the paper demonstrates the effectiveness of MSOT through an example of risk evaluation in power system generation scheduling.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
This paper discusses pseudo-randomness of a periodic sequence, named the fourth class of GSS sequence. We get the following results: ① Its least period always reaches the maximum (that is, 2n-1). ② Its least period ...This paper discusses pseudo-randomness of a periodic sequence, named the fourth class of GSS sequence. We get the following results: ① Its least period always reaches the maximum (that is, 2n-1). ② Its least period and linear complexity keep robust under single-symbol-substitution. ③ It has good low-degree-auto-correlation feature. ④ It has good short-length-run-distribution.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
The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sarkozy and later extended to sequences of k symbols （or k-ary sequences）. Certain constructions of pseudo-random sequences of k sym...The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sarkozy and later extended to sequences of k symbols （or k-ary sequences）. Certain constructions of pseudo-random sequences of k symbols were presented over finite fields in the literature. In this paper, two families of sequences of k symbols are constructed by using the integers modulo pq for distinct odd primes p and q. The upper bounds on the well-distribution measure and the correlation measure of the families sequences are presented in terms of certain character sums over modulo pq residue class rings. And low bounds on the linear complexity profile are also estimated.展开更多
基金Supported in part by the President Fund of GUCASSupported in part by National Natural Foundation of China(Grant No.10631080)National Natural Foundation of Beijing(Grant No.1092004)
文摘Motivated by representing multidimensional periodic nonlinear and non-stationary signals(functions),we study a class of orthonormal exponential basis for L2(Id)with I:=[0,1),whose exponential parts are piecewise linear spectral sequences with p-knots.It is widely applied in time-frequency analysis.
基金Supported by Nature Science Foundation of Hainan Province (Grant No. 118MS040,2018CXTD338)NSF of Higher Education Institutions of Hainan Province (Grant No. Hnky2018ZD-6)National Natural Science Foundation of China (Grant No. 11861029)。
文摘For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characterize the Kondratiev space of random test function, in which space it is convenient to study random distribution,random partial differential equation and other problems.
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 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.
文摘This paper presents modified version of a realistic test tool suitable to Design For Testability （DFT） and Built-ln Self Test （BIST） environments. A comprehensive tool is developed in the form of a test simulator. The simulator is capable of providing a required goal of test for the Circuit Under Test （CUT）. The simulator uses the approach of fault diagnostics with fault grading procedures to provide the optimum tests. The current version of the simulator embeds features of exhaustive and pseudo-random test generation schemes along with the search solutions of cost effective test goals. The simulator provides facilities of realizing all possible pseudo-random sequence generators with all possible combinations of seeds. The tool is developed on a common Personal Computer （PC） platform and hence no special software is required. Thereby, it is a low cost tool hence economical. The tool is very much suitable for determining realistic test sequences for a targeted goal of testing for any CUT. The developed tool incorporates flexible Graphical User Interface （GUI） procedures and can be operated without any special programming skill. The tool is debugged and tested with the results of many bench mark circuits. Further, this developed tool can be utilized for educational purposes for many courses such as fault-tolerant computing, fault diagnosis, digital electronics, and safe-reliable-testable digital logic designs.
基金Supported by the National Natural Science Foundation of China under Grant 69972042
文摘This paper presents the definition of perfect punctured binary sequence pair and the combinatorial admissible conditions for searching the perfect punctured binary sequence pairs and proves that all of the pseudo-random binary sequences satisfy these conditions. Computer calculation verifies that the pseudo-random binary sequences with length up to N=127 can be easily turned into perfect punctured binary sequence pairs.
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supported by National Natural Science Foundation of China under Grant No.60833008,60970119the Scientific Research Foundation of Education of Department of Shaanxi Provincial Government of China under Grant No.11JK0503+1 种基金Youth Science and Technology Foundation of Xi'an University of Architecture and Technology under Grant No.QN0831,QN1024Foundation of Guangxi Key Laboratory of Information and Communications under Grant No.20902
文摘Cryptographic properties of the single cycle T-function's output sequences are investigated.Bounds of autocorrelation functions of the kth coordinate sequence and bounds of state output sequence are calculated respectively.The Maximum Sidelobe Ratio(MSR) of the kth coordinate sequence and the MSR of state output sequence are given respectively.The bounds of autocorrelation functions show that the values of autocorrelation functions are large when shifts are small.Comparisons of the autocorrelations between the state output sequence and coordinate output sequence are illustrated.The autocorrelation properties demonstrate that T-functions have cryptographic weaknesses and the illustration result shows coordinate output sequences have better autocorrelation than that of state output sequences.
基金Supported by the National Natural Science Foun-dation of China (60473028) the Natural Science Foundation of FujianProvince (A0540011) +1 种基金the Science and Technology Foundation of Fu-jian Educational Committee (JA04264) the Science and Technolo-gy Foundation of Putian City (2005S04)
文摘A family of binary sequences were constructed by using an elliptic curve and its twisted curves over finite fields. It was shown that these sequences possess ＂good＂ cryptographie properties of 0-1 distribution, long period and large linear complexity. The results indicate that such se quences provide strong potential applications in cryptography.
文摘Pseudo-random sequences with long period, low correlation, high linear complexity, and uniform distribution of bit patterns are widely used in the field of information security and cryptography. This paper proposes an approach for generating a pseudo-random multi-value sequence (including a binary sequence) by utilizing a primitive polynomial, trace function, and k-th power residue symbol over the sub extension field. All our previous sequences are defined over the prime field, whereas, proposed sequence in this paper is defined over the sub extension field. Thus, it’s a new and innovative perception to consider the sub extension field during the sequence generation procedure. By considering the sub extension field, two notable outcomes are: proposed sequence holds higher linear complexity and more uniform distribution of bit patterns compared to our previous work which defined over the prime field. Additionally, other important properties of the proposed multi-value sequence such as period, autocorrelation, and cross-correlation are theoretically shown along with some experimental results.
基金Supported by the National Natural Science Foundation of China (Grant No. 50777031)Program for New Century Excellent Talents in University (Grant No. NCET-07-0484)the Fok Ying-Tong Education Foundation (Grant No. 104020)
文摘Sequence operation theory (SOT) is a powerful tool for solving complex probabilistic problems in power system. However, the basic single dimension SOT cannot satisfy the requirement of multi-state; multi-attribute analysis, which is often the case in actual power system practice. To address this problem, multidimensional sequence operation theory (MSOT) is developed. On the basis of previous research, this paper first categorizes the situations by the number of state variables; the number of attribute values,; defines the multidimensional sequence for single state variable; multiple attribute values, as well as the multidimensional sequence for multiple state variables; multiple attribute values. Corresponding to those definitions, four types of operations between two discrete multidimensional sequences are derived respectively. Therefore, the sequence is extended from single dimensional to multidimensional, establishing an integrated theory of multidimensional sequence operation. In particular, the basic single dimension SOT can be viewed as a special case of MSOT with only one state variable; one attribute value. Finally, the paper demonstrates the effectiveness of MSOT through an example of risk evaluation in power system generation scheduling.
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.
文摘This paper discusses pseudo-randomness of a periodic sequence, named the fourth class of GSS sequence. We get the following results: ① Its least period always reaches the maximum (that is, 2n-1). ② Its least period and linear complexity keep robust under single-symbol-substitution. ③ It has good low-degree-auto-correlation feature. ④ It has good short-length-run-distribution.
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.
基金supported by the National Natural Science Foundation of China under Grant No. 61063041the Program for New Century Excellent Talents of Universities in Fujian Province under Grant No. JK2010047the Funds of the Education Department of Gansu Province under Grant No. 1001-09
文摘The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sarkozy and later extended to sequences of k symbols （or k-ary sequences）. Certain constructions of pseudo-random sequences of k symbols were presented over finite fields in the literature. In this paper, two families of sequences of k symbols are constructed by using the integers modulo pq for distinct odd primes p and q. The upper bounds on the well-distribution measure and the correlation measure of the families sequences are presented in terms of certain character sums over modulo pq residue class rings. And low bounds on the linear complexity profile are also estimated.
