The linear complexity of binary sequences plays a fundamental part in cryptography. In the paper, we construct more general forms of generalized cyclotomic binary sequences with period 2p(m+1)q(n+1). Furthermore, we e...
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The linear complexity of binary sequences plays a fundamental part in cryptography. In the paper, we construct more general forms of generalized cyclotomic binary sequences with period 2p(m+1)q(n+1). Furthermore, we establish the formula of the linear complexity of proposed sequences. The results reveal that such sequences with period 2p(m+1)q(n+1) have a good balance property and high linear complexity.
Let r be an odd prime, such that r >= 5 and r not equal p, m be the order of r modulo p. Then, there exists a 2pth root of unity in the extension field F(r)m. Let G(x) be the generating polynomial of the considered...
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Let r be an odd prime, such that r >= 5 and r not equal p, m be the order of r modulo p. Then, there exists a 2pth root of unity in the extension field F(r)m. Let G(x) be the generating polynomial of the considered quaternary sequences over F-q[x] with q = r(m). By explicitly computing the number of zeros of the generating polynomial G(x) over F(r)m, we can determine the degree of the minimal polynomial, of the quaternary sequences which in turn represents the linear complexity. In this paper, we show that the minimal value of the linear complexity is equal to 1/2(3p - 1) which is more than p, the half of the period 2p. According to Berlekamp-Massey algorithm, these sequences viewed as enough good for the use in cryptography.
linear complexity is a measure of how complex a one dimensional sequence can be. In this paper we extend the concept of linear complexity to multiple dimensions and present a definition that is invariant under well-or...
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ISBN:
(纸本)9781467377041
linear complexity is a measure of how complex a one dimensional sequence can be. In this paper we extend the concept of linear complexity to multiple dimensions and present a definition that is invariant under well-orderings of the arrays. As a result we find that our new definition for the process introduced in the patent titled "Digital Watermarking" produces arrays with good asymptotic properties.
The k-error linear complexity is an important cryptographic measure of pseudorandom sequences in stream ciphers. In this paper, we investigate the k-error linear complexity of p2-periodic binary sequences defined from...
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The k-error linear complexity is an important cryptographic measure of pseudorandom sequences in stream ciphers. In this paper, we investigate the k-error linear complexity of p2-periodic binary sequences defined from the polynomial quotients modulo p, which are the generalizations of the well-studied Fermat ***, first we determine exact values of the k-error linear complexity over the finite field F2 for these binary sequences under the assumption of 2 being a primitive root modulo p2, and then we determine their k-error linear complexity over the finite field Fp. Theoretical results obtained indicate that such sequences possess‘good’ error linear complexity.
In this paper, a constructive approach for determining CELCS（critical error linear complexity spectrum） for the kerror linear complexity distribution of 2~n-periodic binary sequences is developed via the sieve metho...
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ISBN:
(纸本)9781510830981
In this paper, a constructive approach for determining CELCS（critical error linear complexity spectrum） for the kerror linear complexity distribution of 2~n-periodic binary sequences is developed via the sieve method and Games-Chan algorithm. Accordingly, the second descent point（critical point） distribution of the k-error linear complexity for 2~n-periodic binary sequences is characterized. As a by product, it is proved that the maximum k-error linear complexity is 2~n-(2) over all 2~n-periodic binary sequences, where 2<=k < 2 and l < n. With these results, some work by Niu et al. are proved to be incorrect.
linear complexity is an important cryptographic index of sequences. We study the linear complexity of -periodic Legendre-Sidelnikov sequences, which combine the concepts of Legendre sequences and Sidelnikov sequences....
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linear complexity is an important cryptographic index of sequences. We study the linear complexity of -periodic Legendre-Sidelnikov sequences, which combine the concepts of Legendre sequences and Sidelnikov sequences. We get lower and upper bounds on the linear complexity in different cases, and experiments show that the upper bounds can be attained. Remarkably, we associate the linear complexity of Legendre-Sidelnikov sequences with some famous primes including safe prime and Fermat prime. If is a primitive root modulo , and is a safe prime greater than 7, the linear complexity is the period if;if , and if . If is a Fermat prime, the linear complexity is the period if , and if . It is very interesting that the Legendre-Sidelnikov sequence has maximal linear complexity and is balanced if we choose to be some safe prime.
Tang et al. and Lim et al. presented ways to construct balanced quaternary sequences with even period and optimal autocorrelation value by inverse Gray-mapping of binary sequences with optimal autocorrelation value. I...
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Tang et al. and Lim et al. presented ways to construct balanced quaternary sequences with even period and optimal autocorrelation value by inverse Gray-mapping of binary sequences with optimal autocorrelation value. In this article, we consider quaternary sequences constructed from binary Legendre or Hall's sextic sequence by these methods. We derive the linear complexity of series of balanced quaternary sequences with optimal autocorrelation value over the finite ring of four elements.
In this paper, we determine the linear complexity and minimal polynomial of a class of binary sequences with period constructed by Ding et al. (IEEE Trans Inform Theory 47(1):428-433, 2001). Our results show that this...
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In this paper, we determine the linear complexity and minimal polynomial of a class of binary sequences with period constructed by Ding et al. (IEEE Trans Inform Theory 47(1):428-433, 2001). Our results show that this class of sequences have high linear complexity.
Multidimensional arrays have proven to be useful in watermarking, therefore interest in this subject has increased in the previous years along with the number of publications. For one dimensional arrays (sequences), l...
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ISBN:
(纸本)9781467383080
Multidimensional arrays have proven to be useful in watermarking, therefore interest in this subject has increased in the previous years along with the number of publications. For one dimensional arrays (sequences), linear complexity is regarded as standard measure of complexity. Although linear complexity of sequences has been widely studied, only recently, we have extended it to the study of multidimensional arrays. In this paper, we show that the concept of multidimensional linear complexity is a powerful tool, by examining the results for selected constructs. We have obtained the linear complexity of logartihmic Moreno-Tirkel arrays and we show that they show high multidimensional linear complexity. Finally, we explicitly provide the minimal generators for quadratic Moreno-Tirkel arrays. The results show that these techniques are effective in finding the multidimensional linear complexity of the constructions, representing only a small fraction of the applicability of multidimensional linear complexity. The study of multidimensional arrays provides new ways to understand sequences and set the basis for forthcoming proof of the three years old conjectures related with CDMA sequences.
The set of constant-weight sequences over GF(q) from the cyclic difference set generalized by the authors are considered. For the linear complexity(LC) of infinite sequences with their one period as an element in the ...
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ISBN:
(纸本)9781467383080
The set of constant-weight sequences over GF(q) from the cyclic difference set generalized by the authors are considered. For the linear complexity(LC) of infinite sequences with their one period as an element in the set, we give a conjecture that LCs of all sequences except two in the set are the maximum as same as their period and LCs of remaining two sequences are the maximum value minus one. Five numerical examples over two prime fields and three non-prime(extension) fields are shown for evidences of main conjecture in this paper.
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