Several geometric sequences have very low linear complexities when considered as sequences over GF（p）, such as the binary sequences of period q^n - 1 constructed by Chan and Games [1-2] （q is a prime power p^m, p i...Several geometric sequences have very low linear complexities when considered as sequences over GF（p）, such as the binary sequences of period q^n - 1 constructed by Chan and Games [1-2] （q is a prime power p^m, p is an odd prime） with the maximal possible linear complexity q^n-1 when considered as sequences over GF（2）. This indicates that binary sequences with high GF（2） linear complexities LC2 and low GF（p）-linear complexities LCp are not secure for use in stream ciphers. In this article, several lower bounds on the GF（p）-linear complexities of binary sequences is proved and the results are applied to the GF（p）-linear complexities of Blum-Blum-Shub, self-shrinking, and de Bruijn sequences. A lower bound on the number of the binary sequences with LC2 〉 LCD is also presented.展开更多
A new family of GMW sequences over an arbitrary Galois ring was defined by using the trace functions and permutations.This generalizes the concept of GMW sequences over finite fields.Utilizing the Fourier representati...A new family of GMW sequences over an arbitrary Galois ring was defined by using the trace functions and permutations.This generalizes the concept of GMW sequences over finite fields.Utilizing the Fourier representation,we derived an estimate of the linear complexities of this family of GMW sequences.And the result shows that such sequences have large linear complexities.展开更多
Recently,inspired by a modified generalized shift-splitting iteration method for complex symmetric linear systems,we propose two variants of the modified generalized shift-splitting iteration(MGSS)methods for solving ...Recently,inspired by a modified generalized shift-splitting iteration method for complex symmetric linear systems,we propose two variants of the modified generalized shift-splitting iteration(MGSS)methods for solving com-plex symmetric linear systems.One is a parameterized MGSS iteration method and the other is a modified parameterized MGSS iteration method.We prove that the proposed methods are convergent under appropriate constraints on the parameters.In addition,we also give the eigenvalue distributions of differ-ent preconditioned matrices to verify the effectiveness of the preconditioners proposed in this paper.展开更多
Linear complexity and k-error linear complexity of the stream cipher are two important standards to scale the randomicity of keystreams. For the 2n -periodicperiodic binary sequence with linear complexity 2n 1and k = ...Linear complexity and k-error linear complexity of the stream cipher are two important standards to scale the randomicity of keystreams. For the 2n -periodicperiodic binary sequence with linear complexity 2n 1and k = 2,3,the number of sequences with given k-error linear complexity and the expected k-error linear complexity are provided. Moreover,the proportion of the sequences whose k-error linear complexity is bigger than the expected value is analyzed.展开更多
We determined the linear complexity of a family of p2-periodic binary threshold sequences and a family of p2-periodic binary sequences constructed using the Legendre symbol,both of which are derived from Fermat quotie...We determined the linear complexity of a family of p2-periodic binary threshold sequences and a family of p2-periodic binary sequences constructed using the Legendre symbol,both of which are derived from Fermat quotients modulo an odd prime p.If 2 is a primitive element modulo p2,the linear complexity equals to p2-p or p2-1,which is very close to the period and it is large enough for cryptographic purpose.展开更多
The linear complexity of a new kind of keystream sequences.FCSR sequences,is discussed by use of the properties of cyclotomic polynomials.Based on the results of C.Seo's,an upper bound and a lower bound on the li...The linear complexity of a new kind of keystream sequences.FCSR sequences,is discussed by use of the properties of cyclotomic polynomials.Based on the results of C.Seo's,an upper bound and a lower bound on the linear complexity of a significant kind of FCSR sequences—l-sequences are presented.展开更多
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
The k-error linear complexity and the linear complexity of the keystream of a stream cipher are two important standards to scale the randomness of the key stream. For a pq^n-periodic binary sequences where p, q are tw...The k-error linear complexity and the linear complexity of the keystream of a stream cipher are two important standards to scale the randomness of the key stream. For a pq^n-periodic binary sequences where p, q are two odd primes satisfying that 2 is a primitive root module p and q^2 and gcd（p-1, q-1） = 2, we analyze the relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity.展开更多
Based on the Games-Chan algorithm and StampMartin algorithm, this paper provides some new algorithms to compute the error linear complexity spectrum of binary 2n-periodic se- quences. These new algorithms are clearer ...Based on the Games-Chan algorithm and StampMartin algorithm, this paper provides some new algorithms to compute the error linear complexity spectrum of binary 2n-periodic se- quences. These new algorithms are clearer and simpler than old algorithms, and they can quickly compute the error linear com- plexity spectrum of sequences according to different situations. We also discuss such algorithms and give some new results about linear complexity and error linear complexity of sequences.展开更多
Combining with the research on the linear complexity of explicit nonlinear generators of pseudorandom sequences, we study the stability on linear complexity of two classes of explicit inversive generators and two clas...Combining with the research on the linear complexity of explicit nonlinear generators of pseudorandom sequences, we study the stability on linear complexity of two classes of explicit inversive generators and two classes of explicit nonlinear generators. We present some lower bounds in theory on the k-error linear complexity of these explicit generatol＇s, which further improve the cryptographic properties of the corresponding number generators and provide very useful information when they are applied to cryptography.展开更多
This paper contributes to the stability of linear complexity of a binary periodic Jacobi sequence.By employing a pair of reference sequences,we prove that the linear complexity of a binary Jacobi sequence is unstable,...This paper contributes to the stability of linear complexity of a binary periodic Jacobi sequence.By employing a pair of reference sequences,we prove that the linear complexity of a binary Jacobi sequence is unstable,namely,by changing its few bits in one-period length,the linear complexity of the modified sequences will become far less than the required value.展开更多
The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+1.The results show ...The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+1.The results show that this sequence has high linear complexity.展开更多
Linear complexity is an important standard to scale the randomicity of stream ciphers. The distribution function of a sequence complexity measure gives the function expression for the number of sequences with a given ...Linear complexity is an important standard to scale the randomicity of stream ciphers. The distribution function of a sequence complexity measure gives the function expression for the number of sequences with a given complexity measure value. In this paper, we mainly determine the distribution function of sequences with period over using Discrete Fourier Transform (DFT), where and the characteristics of are odd primes, gcd and is a primitive root modulo The results presented can be used to study the randomness of periodic sequences and the analysis and design of stream cipher.展开更多
New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations a...New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.展开更多
Achieving linear complexity is crucial for demonstrating optimal convergence rates in adaptive refinement.It has been shown that the existing linear complexity local refinement algorithm for T-splines generally produc...Achieving linear complexity is crucial for demonstrating optimal convergence rates in adaptive refinement.It has been shown that the existing linear complexity local refinement algorithm for T-splines generally produces more degrees of freedom than the existing greedy refinement,which lacks linear complexity.This paper introduces a novel greedy local refinement algorithm for analysis-suitable T-splines,which achieves linear complexity and requires fewer control points than existing algorithms with linear complexity.Our approach is based on the observation that confining refinements around each T-junction to a preestablished feasible region ensures the algorithm’s linear complexity.Building on this constraint,we propose a greedy optimization local refinement algorithm that upholds linear complexity while significantly reducing the degrees of freedom relative to previous linear complexity local refinement methods.展开更多
A fast algorithm for determining the minimal polynomial and linear complexity of a upn-periodic sequence over a finite field Fq is given.Let p,q,and u be distinct primes,q a primitive root modulo p2,m the smallest pos...A fast algorithm for determining the minimal polynomial and linear complexity of a upn-periodic sequence over a finite field Fq is given.Let p,q,and u be distinct primes,q a primitive root modulo p2,m the smallest positive integer such that qm≡1 mod u,and gcd（m,p（p-1））=1.An algorithm is used to reduce a periodic upn sequence over Fq to several pn-periodic sequences over Fq（ζ）,where ζ is a u-th primitive root of unity,and an algorithm proposed by Xiao et al.is employed to obtain the minimal polynomial of each pn-periodic sequence.展开更多
The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled...The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled kinematic screw and parallel mechanism in singularity. A 3UPS-S parallel mechanism is presented which fulfils 3-DOF in rotation. The regularity of nutation angle singularity is analyzed based on the Jacobian matrix, and the singularity surface of 3UPS-S parallel mechanisms is obtained. By applying the concept of reciprocal product in screw theory, the singular kinematic screw is derived when 3UPS-S parallel mechanism is in singularity. The geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism is investigated by using programs in MATLAB. It is revealed that there are two kinds of situation. Firstly, the three limbs of 3UPS-S parallel mechanism intersect the singular kinematic screw in space simultaneously; Secondly, two limbs cross the singular kinematic screw while the third limb parallels with that screw. It is concluded that the nutation angle singularity of 3UPS-S parallel mechanism belongs to the singular linear complexes. This paper sheds light into and clarifies the geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism.展开更多
In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,...In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.展开更多
To resist the fast algebraic attack and fast selective discrete Fourier transform attacks,spectral immunity of a sequence or a Boolean function was proposed.At the same time,an algorithm to compute the spectral immuni...To resist the fast algebraic attack and fast selective discrete Fourier transform attacks,spectral immunity of a sequence or a Boolean function was proposed.At the same time,an algorithm to compute the spectral immunity of the binary sequence with odd period N was presented,here N is a factor of 2^n-1,where n is an integer.The case is more complicated when the period is even.In this paper,we compute linear complexity of every orthogonal sequence of a given sequence using Chan-Games algorithm and k-error linear complexity algorithm.Then,an algorithm for spectral immunity of binary sequence with period N=2^n is obtained.Furthermore,the time complexity of this algorithm is proved to be O（n）.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
基金supported by the National Natural Science Foundation of China (10871068)
文摘Several geometric sequences have very low linear complexities when considered as sequences over GF（p）, such as the binary sequences of period q^n - 1 constructed by Chan and Games [1-2] （q is a prime power p^m, p is an odd prime） with the maximal possible linear complexity q^n-1 when considered as sequences over GF（2）. This indicates that binary sequences with high GF（2） linear complexities LC2 and low GF（p）-linear complexities LCp are not secure for use in stream ciphers. In this article, several lower bounds on the GF（p）-linear complexities of binary sequences is proved and the results are applied to the GF（p）-linear complexities of Blum-Blum-Shub, self-shrinking, and de Bruijn sequences. A lower bound on the number of the binary sequences with LC2 〉 LCD is also presented.
文摘A new family of GMW sequences over an arbitrary Galois ring was defined by using the trace functions and permutations.This generalizes the concept of GMW sequences over finite fields.Utilizing the Fourier representation,we derived an estimate of the linear complexities of this family of GMW sequences.And the result shows that such sequences have large linear complexities.
基金supported by the National Natural Science Foundation of China(Grant No.12371378)by the Natural Science Foundation of Fujian Province(Grant Nos.2024J01980,2024J08242).
文摘Recently,inspired by a modified generalized shift-splitting iteration method for complex symmetric linear systems,we propose two variants of the modified generalized shift-splitting iteration(MGSS)methods for solving com-plex symmetric linear systems.One is a parameterized MGSS iteration method and the other is a modified parameterized MGSS iteration method.We prove that the proposed methods are convergent under appropriate constraints on the parameters.In addition,we also give the eigenvalue distributions of differ-ent preconditioned matrices to verify the effectiveness of the preconditioners proposed in this paper.
基金the National Natural Science Foundation of China (No.60373092).
文摘Linear complexity and k-error linear complexity of the stream cipher are two important standards to scale the randomicity of keystreams. For the 2n -periodicperiodic binary sequence with linear complexity 2n 1and k = 2,3,the number of sequences with given k-error linear complexity and the expected k-error linear complexity are provided. Moreover,the proportion of the sequences whose k-error linear complexity is bigger than the expected value is analyzed.
基金the National Natural Science Foundation of China，the Open Funds of State Key Laboratory of Information Security (Chinese Academy of Sciences)，the Program for New Century Excellent Talents in Fujian Province University
文摘We determined the linear complexity of a family of p2-periodic binary threshold sequences and a family of p2-periodic binary sequences constructed using the Legendre symbol,both of which are derived from Fermat quotients modulo an odd prime p.If 2 is a primitive element modulo p2,the linear complexity equals to p2-p or p2-1,which is very close to the period and it is large enough for cryptographic purpose.
基金The work is supported by the Special Fund of National Excellently Doctoral Paper and HAIPURT.
文摘The linear complexity of a new kind of keystream sequences.FCSR sequences,is discussed by use of the properties of cyclotomic polynomials.Based on the results of C.Seo's,an upper bound and a lower bound on the linear complexity of a significant kind of FCSR sequences—l-sequences are presented.
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.
基金Supported by the National Natural Science Foun-dation of China (60373092)
文摘The k-error linear complexity and the linear complexity of the keystream of a stream cipher are two important standards to scale the randomness of the key stream. For a pq^n-periodic binary sequences where p, q are two odd primes satisfying that 2 is a primitive root module p and q^2 and gcd（p-1, q-1） = 2, we analyze the relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity.
基金Supported by the National Natural Science Foundation of China (61174085, 61170270, 61121061)
文摘Based on the Games-Chan algorithm and StampMartin algorithm, this paper provides some new algorithms to compute the error linear complexity spectrum of binary 2n-periodic se- quences. These new algorithms are clearer and simpler than old algorithms, and they can quickly compute the error linear com- plexity spectrum of sequences according to different situations. We also discuss such algorithms and give some new results about linear complexity and error linear complexity of sequences.
基金the Natural Science Foundation of Fujian Province (2007F3086)the Funds of the Education Department of Fujian Prov-ince (JA07164)the Open Funds of Key Laboratory of Fujian Province University Network Security and Cryptology (07B005)
文摘Combining with the research on the linear complexity of explicit nonlinear generators of pseudorandom sequences, we study the stability on linear complexity of two classes of explicit inversive generators and two classes of explicit nonlinear generators. We present some lower bounds in theory on the k-error linear complexity of these explicit generatol＇s, which further improve the cryptographic properties of the corresponding number generators and provide very useful information when they are applied to cryptography.
基金Supported by the National Natural Science Foundation of China (61170319,61063041)the Natural Science Fund of Shandong Province (ZR2010FM017)+1 种基金the China Postdoctoral Science Foundation Funded Project(119103S148)the Fundamental Research Funds for the Central Universities(11CX04056A,10CX04038A)
文摘This paper contributes to the stability of linear complexity of a binary periodic Jacobi sequence.By employing a pair of reference sequences,we prove that the linear complexity of a binary Jacobi sequence is unstable,namely,by changing its few bits in one-period length,the linear complexity of the modified sequences will become far less than the required value.
基金Supported by the Natural Science Foundation of Hubei Province(2009CDZ004)the Scientific Research Fund of Hubei Provincial Education Department(B20104403)
文摘The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+1.The results show that this sequence has high linear complexity.
基金Supported by the National Natural Science Foundation of China (No. 60973125)
文摘Linear complexity is an important standard to scale the randomicity of stream ciphers. The distribution function of a sequence complexity measure gives the function expression for the number of sequences with a given complexity measure value. In this paper, we mainly determine the distribution function of sequences with period over using Discrete Fourier Transform (DFT), where and the characteristics of are odd primes, gcd and is a primitive root modulo The results presented can be used to study the randomness of periodic sequences and the analysis and design of stream cipher.
文摘New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB0640000)the Key Grant Project of the NSF of China(Grant No.12494552)the NSF of China(Grant No.12471360).
文摘Achieving linear complexity is crucial for demonstrating optimal convergence rates in adaptive refinement.It has been shown that the existing linear complexity local refinement algorithm for T-splines generally produces more degrees of freedom than the existing greedy refinement,which lacks linear complexity.This paper introduces a novel greedy local refinement algorithm for analysis-suitable T-splines,which achieves linear complexity and requires fewer control points than existing algorithms with linear complexity.Our approach is based on the observation that confining refinements around each T-junction to a preestablished feasible region ensures the algorithm’s linear complexity.Building on this constraint,we propose a greedy optimization local refinement algorithm that upholds linear complexity while significantly reducing the degrees of freedom relative to previous linear complexity local refinement methods.
基金The National Natural Science Foundation of China (No.10971250,11171150)
文摘A fast algorithm for determining the minimal polynomial and linear complexity of a upn-periodic sequence over a finite field Fq is given.Let p,q,and u be distinct primes,q a primitive root modulo p2,m the smallest positive integer such that qm≡1 mod u,and gcd（m,p（p-1））=1.An algorithm is used to reduce a periodic upn sequence over Fq to several pn-periodic sequences over Fq（ζ）,where ζ is a u-th primitive root of unity,and an algorithm proposed by Xiao et al.is employed to obtain the minimal polynomial of each pn-periodic sequence.
基金supported by Aeronautical Science Foundation of China(Grant No.20081651025)
文摘The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled kinematic screw and parallel mechanism in singularity. A 3UPS-S parallel mechanism is presented which fulfils 3-DOF in rotation. The regularity of nutation angle singularity is analyzed based on the Jacobian matrix, and the singularity surface of 3UPS-S parallel mechanisms is obtained. By applying the concept of reciprocal product in screw theory, the singular kinematic screw is derived when 3UPS-S parallel mechanism is in singularity. The geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism is investigated by using programs in MATLAB. It is revealed that there are two kinds of situation. Firstly, the three limbs of 3UPS-S parallel mechanism intersect the singular kinematic screw in space simultaneously; Secondly, two limbs cross the singular kinematic screw while the third limb parallels with that screw. It is concluded that the nutation angle singularity of 3UPS-S parallel mechanism belongs to the singular linear complexes. This paper sheds light into and clarifies the geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism.
基金supported by the Natural Science Foundation of Guangdong Province(2021A1515010058)。
文摘In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.
基金Supported by the National Natural Science Foundation of China(61300181,61272057,61202434,61170270,61100203,61121061)
文摘To resist the fast algebraic attack and fast selective discrete Fourier transform attacks,spectral immunity of a sequence or a Boolean function was proposed.At the same time,an algorithm to compute the spectral immunity of the binary sequence with odd period N was presented,here N is a factor of 2^n-1,where n is an integer.The case is more complicated when the period is even.In this paper,we compute linear complexity of every orthogonal sequence of a given sequence using Chan-Games algorithm and k-error linear complexity algorithm.Then,an algorithm for spectral immunity of binary sequence with period N=2^n is obtained.Furthermore,the time complexity of this algorithm is proved to be O（n）.
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.
