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THE 2-ERROR LINEAR COMPLEXITY OF 2~n-PERIODIC BINARY SEQUENCES WITH LINEAR COMPLEXITY 2~n-1 被引量:21
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作者 Zhu Fengxiang Qi Wenfeng 《Journal of Electronics(China)》 2007年第3期390-395,共6页
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
关键词 linear complexity k-error linear complexity Periodic binary sequences Chan-Games algorithm
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The k-Error Linear Complexity and the Linear Complexity for pq^n-Periodic Binary Sequences 被引量:1
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作者 ZHU Fengxiang QI Wenfeng 《Wuhan University Journal of Natural Sciences》 CAS 2006年第6期1549-1553,共5页
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
关键词 k-error linear complexity linear complexity pq^n-periodic binary sequences
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Linear Complexity of Some Binary Sequences Derived from Fermat Quotients 被引量:8
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作者 Chen Zhixiong Hu Lei, Du Xiaoni 《China Communications》 SCIE CSCD 2012年第2期105-108,共4页
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
关键词 CRYPTOGRAPHY pseudorandom binary sequences fermat quotients finite fields linear complexity
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ON THE LINEAR COMPLEXITY OF FCSR SEQUENCES 被引量:2
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作者 Qi Wenfeng Xu HongDept of Appl.Math,Zhengzhou Information Engineering Univ., Zhengzhou 450002,China 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2003年第3期318-324,共7页
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
关键词 linear recurring sequence feedback with carry shift register l-sequences linear complexity
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Linear complexity of Ding generalized cyclotomic sequences 被引量:2
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作者 闫统江 陈智雄 肖国镇 《Journal of Shanghai University(English Edition)》 CAS 2007年第1期22-26,共5页
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
关键词 stream cipher generalized cyclotomic sequence linear complexity minimal polynomial
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On k-Error Linear Complexity of Some Explicit Nonlinear Pseudorandom Sequences
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作者 CHEN Zhixiong WU Chenhuang 《Wuhan University Journal of Natural Sciences》 CAS 2008年第5期577-581,共5页
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
关键词 stream ciphers k-error linear complexity explicitinversive generators explicit nonlinear generators
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Linear Complexity of New Generalized Cyclotomic Sequences of Length 2pq
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作者 王宏伟 葛武 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2014年第6期710-716,共7页
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
关键词 generalized cyclotomic sequence linear complexity minimal polynomial
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THE DISTRIBUTION FUNCTIONS FOR THE LINEAR COMPLEXITY OF PERIODIC SEQUENCES
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作者 Yang Minghui Zhu Shixin 《Journal of Electronics(China)》 2012年第3期211-214,共4页
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
关键词 linear complexity Periodic sequences Discrete Fourier Transform (DFT)
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Some Algorithms for the Error Linear Complexity of Binary 2^n-Periodic Sequences
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作者 CHANG Zuling WANG Xueyuan DUAN Li 《Wuhan University Journal of Natural Sciences》 CAS 2013年第1期42-48,共7页
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
关键词 SEQUENCE linear complexity error linear complexity error linear complexity spectrum
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Computing the k-error joint linear complexity of binary periodic multisequences
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作者 LI Fu-lin ZHU Shi-xin 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2013年第6期96-101,共6页
Complexity measures for multisequences over finite fields, such as the joint linear complexity and the k-error joint linear complexity, play an important role in cryptology. In this paper we study a fast algorithm, pr... Complexity measures for multisequences over finite fields, such as the joint linear complexity and the k-error joint linear complexity, play an important role in cryptology. In this paper we study a fast algorithm, presented by Venkateswarlu A, to computer the k-error joint linear complexity of a binary periodic multisequence. In this paper, the aim is mainly to complement the theoretical derivation and proof of the existing algorithm. Moreover, our algorithm reduces computation. 展开更多
关键词 CRYPTOLOGY multisequence algorithm joint linear complexity k-error joint linear complexity
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DISTRIBUTION OF ONE-ERROR LINEAR COMPLEXITY OF BINARY SEQUENCES FOR ARBITRARY PRIME PERIOD
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作者 Lin TAN Wenfeng QI Hong XU 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2012年第6期1223-1233,共11页
Complexity measures for sequences, such as the linear complexity and the k-error linear complexity, play an important role in stream ciphers. This contribution studies the distribution of 1-error linear complexity of ... Complexity measures for sequences, such as the linear complexity and the k-error linear complexity, play an important role in stream ciphers. This contribution studies the distribution of 1-error linear complexity of binary sequences with arbitrary prime period. For any odd prime N, the authors present all possible values of 1-error linear complexity of N-periodic binary sequences, and derive the exact formulas to count the number of N-periodic binary sequences with any given 1-error linear complexity. 展开更多
关键词 k-error linear complexity linear complexity periodic sequences stream ciphers.
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Linear Complexity Problem of Binary Jacobi Sequence
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作者 YAN Tongjiang SUN Yuhua 《Wuhan University Journal of Natural Sciences》 CAS 2012年第6期481-484,共4页
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
关键词 CRYPTOGRAPHY Jacobi sequence linear complexity stability of linear complexity
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On the Linear Complexity of New Generalized Cyclotomic Binary Sequences of Order Two and Period pqr 被引量:4
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作者 Longfei Liu Xiaoyuan Yang +1 位作者 Xiaoni Du Bin Wei 《Tsinghua Science and Technology》 SCIE EI CAS CSCD 2016年第3期295-301,共7页
Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties. The linear complexity of a period sequence plays a fundamental ... Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. Let p, q, and r be distinct odd primes with gcd(p-1, q-1 )=gcd(p- 1, r-1)=gcd(q-1, r-1)=2. In this paper, a new class of generalized cyclotomic sequence with respect to pqr over GF(2) is constructed by finding a special characteristic set. In addition, we determine its linear complexity using cyclotomic theory. Our results show that these sequences have high linear complexity, which means they can resist linear attacks. 展开更多
关键词 stream cipher pseudorandom sequence generalized cyclotomy linear complexity
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Linear complexity of quaternary sequences with odd period and low autocorrelation 被引量:3
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作者 KE Pin-hui LIN Chang-lu ZHANG Sheng-yuan 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2014年第5期89-93,共5页
Equivalence between two classes of quaternary sequences with odd period and best known autocorrelation are proved. A lower bound on the linear complexity of these sequences is presented. It is shown that the quaternar... Equivalence between two classes of quaternary sequences with odd period and best known autocorrelation are proved. A lower bound on the linear complexity of these sequences is presented. It is shown that the quaternary sequences have large linear complexity to resist Reeds and Sloane algorithm attack effectively. 展开更多
关键词 quaternary sequences linear complexity CYCLOTOMY
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A fast algorithm for determining the linear complexity of a binary sequence with period 2~np^m 被引量:3
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作者 魏仕民 肖国镇 陈钟 《Science in China(Series F)》 2001年第6期453-460,共8页
An efficient algorithm for determining the linear complexity and the minimal polynomial of a binary sequence with period 2npm is proposed and proved, where 2 is a primitive root modulo p2. The new algorithm generalize... An efficient algorithm for determining the linear complexity and the minimal polynomial of a binary sequence with period 2npm is proposed and proved, where 2 is a primitive root modulo p2. The new algorithm generalizes the algorithm for computing the linear complexity of a binary sequence with period 2' and the algorithm for computing the linear complexity of a binary sequence with period pn, where 2 is a primitive root modulo p2. 展开更多
关键词 CRYPTOGRAPHY periodic sequence linear complexity minimal polynomial fast algorithm.
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FAMILIES OF p-ARY SEQUENCES WITH LOW CORRELATION AND LARGE LINEAR COMPLEXITY
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作者 CAI Han ZENG Xiangyong HU Lei 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2014年第6期1305-1319,共15页
This paper generalizes a method of generating shift sequences in the interleaved construction proposed by Gong.With the new shift sequences,some new families of p-ary sequences with desired properties can be obtained.... This paper generalizes a method of generating shift sequences in the interleaved construction proposed by Gong.With the new shift sequences,some new families of p-ary sequences with desired properties can be obtained.A lower bound on the number of new families of binary sequences is also established. 展开更多
关键词 Auto-correlation CROSS-CORRELATION linear complexity low correlation p-ary sequence.
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Linear complexity of sequences produced by single cycle T-function
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作者 WANG Yan HU Yu-pu +1 位作者 LI Shun-bo YANG Yang 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2011年第4期123-128,共6页
Four kinds of sequences generated by single cycle triangular function (T-function) are investigated to check the possibility for a single cycle T-function to be a cryptographic component in stream ciphers. Based on ... Four kinds of sequences generated by single cycle triangular function (T-function) are investigated to check the possibility for a single cycle T-function to be a cryptographic component in stream ciphers. Based on the special properties of single cycle T-function and an algorithm due to Wei, linear complexities of these four kinds of sequence are all acquired. The results show that single cycle T-function sequences have high linear complexity. Therefore, T-function satisfies the essential requirements being a basic component of stream cipher. 展开更多
关键词 stream cipher single cycle T-function linear complexity
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On the GF(p) Linear Complexity of Hall's Sextic Sequences and Some Cyclotomic-Set-Based Sequences
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作者 Xianmang HE Liqin HU Dong LI 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2016年第4期515-522,共8页
Klapper(1994) showed that there exists a class of geometric sequences with the maximal possible linear complexity when considered as sequences over GF(2), but these sequences have very low linear complexities when con... Klapper(1994) showed that there exists a class of geometric sequences with the maximal possible linear complexity when considered as sequences over GF(2), but these sequences have very low linear complexities when considered as sequences over GF(p)(p is an odd prime). This linear complexity of a binary sequence when considered as a sequence over GF(p) is called GF(p) complexity. This indicates that the binary sequences with high GF(2) linear complexities are inadequate for security in the practical application, while,their GF(p) linear complexities are also equally important, even when the only concern is with attacks using the Berlekamp-Massey algorithm [Massey, J. L., Shift-register synthesis and bch decoding, IEEE Transactions on Information Theory, 15(1), 1969, 122–127]. From this perspective, in this paper the authors study the GF(p) linear complexity of Hall's sextic residue sequences and some known cyclotomic-set-based sequences. 展开更多
关键词 linear complexity Hall's sextic residues sequence Cyclotomic set
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ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR
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作者 陈洁玲 刘名生 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期295-310,共16页
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
关键词 Bloch-Landau type theorem Bloch constant linear complex operator harmonic mapping biharmonic mapping UNIVALENT
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Statistical Characteristics of the Complexity for Prime-Periodic Sequences
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作者 NIUZhi-hua LINai-cheng XIAOGuo-zhen 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第1期211-213,共3页
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
关键词 stream ciphers periodic sequences linear complexity k-error linearcomplexity
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