Minimal polynomials and linear complexity of binary Ding generalized cyclotomic sequences of order 2 with the two-prime residue ring Zpq are obtained by Bai in 2005. In this paper, we obtain linear complexity and mini...Minimal polynomials and linear complexity of binary Ding generalized cyclotomic sequences of order 2 with the two-prime residue ring Zpq are obtained by Bai in 2005. In this paper, we obtain linear complexity and minimal polynomials of all Ding generalized cyclotomic sequences. Our result shows that linear complexity of these sequences takes on the values pq and pq-1 on our necessary and sufficient condition with probability 1/4 and the lower bound （pq - 1）/2 with probability 1/8. This shows that most of these sequences are good. We also obtained that linear complexity and minimal polynomials of these sequences are independent of their orders. This makes it no more difficult in choosing proper p and q.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
Using the fact that the factorization of x^N — 1 over GF(2) is especiallyexplicit, we completely establish the distributions and the expected values of the lineal complexityand the k-error linear complexity of the N-...Using the fact that the factorization of x^N — 1 over GF(2) is especiallyexplicit, we completely establish the distributions and the expected values of the lineal complexityand the k-error linear complexity of the N-periodic sequences respectively,where N is an odd primeand 2 is a primitive root modulo N. The results show that there are a large percentage of sequenceswith both the linear complexity and the k-enor linear complexity not less than N, quite close totheir maximum possible values.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
Two new families of finite binary sequences are constructed using multiplicative inverse. The sequences are shown to have strong pseudorandom properties by using some estimates of certain exponential sums over finite ...Two new families of finite binary sequences are constructed using multiplicative inverse. The sequences are shown to have strong pseudorandom properties by using some estimates of certain exponential sums over finite fields. The constructions can be implemented fast since multiplicative inverse over finite fields can be computed in polynomial time.展开更多
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 encoding thousands of large noncoding RNAs ...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 encoding 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 tools to organize various complex interactive properties as visual maps. In this paper, a Pseudo DNA Variant MapPDVM is proposed following Cellular Automata to represent multiple maps that use four Meta symbols as well as DNA or RNA representations. The system architecture of key components and the core mechanism on the PDVM are described. Key modules, equations and their I/O parameters are discussed. Applying the PDVM, two sets of real DNA sequences from both the sample human (noncoding DNA) and corn (coding DNA) genomes are collected in comparison with two sets of pseudo DNA sequences generated by a stream cipher HC-256 under different modes 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 a controllable environment. Various distributions can be observed on both noncoding and coding conditions from their symmetric properties on 2D maps.展开更多
Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functi...Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.展开更多
Generalized self-shrinking sequences, simply named the GSS sequences, are novel periodic sequences that have many advantages in cryptography. In this paper, we give several results about GSS sequence's application...Generalized self-shrinking sequences, simply named the GSS sequences, are novel periodic sequences that have many advantages in cryptography. In this paper, we give several results about GSS sequence's application to cryptography. First, we give a simple method for selecting those GSS sequences whose least periods reach the maximum. Second, we give a method for describing and computing the auto-correlation coefficients of GSS sequences. Finally, we point out that some GSS sequences, when used as stream ciphers, have a security weakness.展开更多
A novel family of frequency-hopping(FH)se-quences based on iterated block cipher is proposed for frequencyhopping multiple-access(FHMA)communica-tions.The design offers a class of nonlinear FH codes with high security...A novel family of frequency-hopping(FH)se-quences based on iterated block cipher is proposed for frequencyhopping multiple-access(FHMA)communica-tions.The design offers a class of nonlinear FH codes with high security,large linear span and a uniform spread over the entire frequency bandwidth.Moreover,FH sequences among the family are independent from each other and they perform as well as random patterns in terms of multi-ple access interference in anti-jamming applications.With the performance of packet error and throughput for FHMA network being derived in theory,many numerical results of the 3DES sequences are presented,comparing with those of shift register sequences and chaotic FH sequences.Effi-ciently implemented in field programmable gate arrays(FPGA),the generator prototype of the proposed sequence has been realized and incorporated into fast FH radio.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.60473028)the Natural Science Foundation of Fujian Province(Grant No.A0540011)the Science and Technology Fund of Educational Committee of Fujian Province(Grant No.JA04264)
文摘Minimal polynomials and linear complexity of binary Ding generalized cyclotomic sequences of order 2 with the two-prime residue ring Zpq are obtained by Bai in 2005. In this paper, we obtain linear complexity and minimal polynomials of all Ding generalized cyclotomic sequences. Our result shows that linear complexity of these sequences takes on the values pq and pq-1 on our necessary and sufficient condition with probability 1/4 and the lower bound （pq - 1）/2 with probability 1/8. This shows that most of these sequences are good. We also obtained that linear complexity and minimal polynomials of these sequences are independent of their orders. This makes it no more difficult in choosing proper p and q.
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.
文摘Using the fact that the factorization of x^N — 1 over GF(2) is especiallyexplicit, we completely establish the distributions and the expected values of the lineal complexityand the k-error linear complexity of the N-periodic sequences respectively,where N is an odd primeand 2 is a primitive root modulo N. The results show that there are a large percentage of sequenceswith both the linear complexity and the k-enor linear complexity not less than N, quite close totheir maximum possible values.
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.
基金Supported by the Open Funds of Key Lab of Fujian Province University Network Security and Cryptology (07B005)the Funds of the Education Department of Fujian Province (JA07164)the Natural Science Foundation of Fujian Province of China (2007F3086)
文摘Two new families of finite binary sequences are constructed using multiplicative inverse. The sequences are shown to have strong pseudorandom properties by using some estimates of certain exponential sums over finite fields. The constructions can be implemented fast since multiplicative inverse over finite fields can be computed in polynomial time.
文摘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 encoding 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 tools to organize various complex interactive properties as visual maps. In this paper, a Pseudo DNA Variant MapPDVM is proposed following Cellular Automata to represent multiple maps that use four Meta symbols as well as DNA or RNA representations. The system architecture of key components and the core mechanism on the PDVM are described. Key modules, equations and their I/O parameters are discussed. Applying the PDVM, two sets of real DNA sequences from both the sample human (noncoding DNA) and corn (coding DNA) genomes are collected in comparison with two sets of pseudo DNA sequences generated by a stream cipher HC-256 under different modes 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 a controllable environment. Various distributions can be observed on both noncoding and coding conditions from their symmetric properties on 2D maps.
文摘Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.
文摘Generalized self-shrinking sequences, simply named the GSS sequences, are novel periodic sequences that have many advantages in cryptography. In this paper, we give several results about GSS sequence's application to cryptography. First, we give a simple method for selecting those GSS sequences whose least periods reach the maximum. Second, we give a method for describing and computing the auto-correlation coefficients of GSS sequences. Finally, we point out that some GSS sequences, when used as stream ciphers, have a security weakness.
基金supported by the National Natural Science Foundation of China(No.60402040)Natural Sci-ence Foundation of Shaanxi Province(No.2005F29)the 10th Fok Ying Tong Education Foundation for Young Teacher(No.101065),China.
文摘A novel family of frequency-hopping(FH)se-quences based on iterated block cipher is proposed for frequencyhopping multiple-access(FHMA)communica-tions.The design offers a class of nonlinear FH codes with high security,large linear span and a uniform spread over the entire frequency bandwidth.Moreover,FH sequences among the family are independent from each other and they perform as well as random patterns in terms of multi-ple access interference in anti-jamming applications.With the performance of packet error and throughput for FHMA network being derived in theory,many numerical results of the 3DES sequences are presented,comparing with those of shift register sequences and chaotic FH sequences.Effi-ciently implemented in field programmable gate arrays(FPGA),the generator prototype of the proposed sequence has been realized and incorporated into fast FH radio.
