In this paper, the method of calculating the k-variance linear complexity distribution with 2 n -periodical sequences by the Games-Chan algorithm and sieve approach is affirmed for its generality. The main idea of thi...
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In this paper, the method of calculating the k-variance linear complexity distribution with 2 n -periodical sequences by the Games-Chan algorithm and sieve approach is affirmed for its generality. The main idea of this method is to decompose a binary sequence into some subsequences of critical requirements, hence the issue to find k-variance linear complexity distribution with 2 n -periodical sequences becomes a combinatorial problem of these binary subsequences. As a result, we compute the whole calculating formulas on the k-variance linear complexity with 2 n -periodical sequences of linear complexity less than 2 n for k = 4, 5. With combination of results in the whole calculating formulas on the 3-variance linear complexity with 2 n -periodical binary sequences of linear complexity 2 n , we completely solve the problem of the calculating function distributions of 4-variance linear complexity with 2 n -periodical sequences elegantly, which significantly improves the results in the relating references.
Binary sequences with large linear complexity have been found many applications in communication *** determine the linear complexity of a family of p;-periodic binary sequences derived from polynomial quotients modulo...
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Binary sequences with large linear complexity have been found many applications in communication *** determine the linear complexity of a family of p;-periodic binary sequences derived from polynomial quotients modulo an odd prime *** show that these sequences have high linear complexity,which means they can resist the linear attack method.
We define a family of quaternary sequences over the residue class ring modulo 4 of length pq, a product of two distinct odd primes, using the generalized cyclotomic classes modulo pq and calculate the discrete Fourier...
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We define a family of quaternary sequences over the residue class ring modulo 4 of length pq, a product of two distinct odd primes, using the generalized cyclotomic classes modulo pq and calculate the discrete Fourier transform (DFT) of the sequences. The DFT helps us to determine the exact values of linear complexity and the trace representation of the sequences.
In this work, we present a method of computing the linear complexity of the sequences produced by the cryptographic sequence generator known as generalized self-shrinking generator. This approach is based on the compa...
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ISBN:
(纸本)9783319951621;9783319951614
In this work, we present a method of computing the linear complexity of the sequences produced by the cryptographic sequence generator known as generalized self-shrinking generator. This approach is based on the comparison of different shifted versions of a single PN-sequence. Just the analysis of binary digits in these shifted sequences allows one to determine the linear complexity of those generalized sequences. The method is simple, direct and efficient. Furthermore, the concept of linear recurrence relationship and the rows of the Sierpinski's triangle are the basic tools in this computation.
A method of analyzing the root presence test for Nonlinear Filter Generator is presented. We have proved that the Key's upper bound on linear complexity hold for 2nd order product sequence with addition of single ...
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A method of analyzing the root presence test for Nonlinear Filter Generator is presented. We have proved that the Key's upper bound on linear complexity hold for 2nd order product sequence with addition of single order sequence and also for a non-zero linear combination of such sequences under some conditions. Some of these sequences are balanced sequences and satisfy statistical randomness property than the Key's and Groth's sequences. The analysis can also be extended to Word-Oriented Nonlinearly Filtered Primitive Transformation Shift Registers.
Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudo-random properties. The linear complexity of a period sequence plays a fundamental...
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Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudo-random properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. In this paper, we construct a new family of quaternary generalized cyclotomic sequences with order 2d and length 2p(m), which generalize the sequences constructed by Ke et al. in 2012. In addition, we determine its linear complexity using cyclotomic theory. The conclusions reveal that these sequences have high linear complexity, which means they can resist linear attacks.
In this paper, we derive the linear complexity of Hall's sextic residue sequences over the finite field of odd prime order. The order of the field is not equal to a period of the sequence. Our results show that Ha...
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In this paper, we derive the linear complexity of Hall's sextic residue sequences over the finite field of odd prime order. The order of the field is not equal to a period of the sequence. Our results show that Hall's sextic residue sequences have high linear complexity over the finite field of odd order. Also we estimate the linear complexity of series of generalized sextic cyclotomic sequences. The linear complexity of these sequences is larger than half of the period.
The authors have proposed an approach for generating a pseudo random binary sequence by using primitive polynomial, trace function, and Legendre symbol over the proper sub extension field. There are many uses of pseud...
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ISBN:
(纸本)9781509065332
The authors have proposed an approach for generating a pseudo random binary sequence by using primitive polynomial, trace function, and Legendre symbol over the proper sub extension field. There are many uses of pseudo random binary sequence in security applications. The linear complexity of a sequence is considered as the most important property to be analyzed in these types of applications. In this paper, the authors have restricted the discussion on the linear complexity and linear complexity profile properties of the proposed sequence based on some experimental results. According to the results, the proposed sequence always holds a maximum value of the linear complexity.
The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences ca...
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The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. We study the relationship between linear complexity and expansion complexity. In particular, we show that for purely periodic sequences both figures of merit provide essentially the same quality test for a sufficiently long part of the sequence. However, if we study shorter parts of the period or nonperiodic sequences, then we can show, roughly speaking, that the expansion complexity provides a stronger test. We demonstrate this by analyzing a sequence of binomial coefficients modulo p. Finally, we establish a probabilistic result on the behavior of the expansion complexity of random sequences over a finite field.
Pseudorandom number generators are required to generate pseudorandom numbers which have not only good statistical properties but also unpredictability in cryptography. A geometric sequence is a sequence given by apply...
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ISBN:
(纸本)9781509065332
Pseudorandom number generators are required to generate pseudorandom numbers which have not only good statistical properties but also unpredictability in cryptography. A geometric sequence is a sequence given by applying a nonlinear feedforward function to an m-sequence. Nogami, Tada and Uehara proposed a geometric sequence whose nonlinear feedforward function is given by the Legendre symbol, and showed the period, periodic autocorrelation and linear complexity of the sequence. Furthermore, Nogami et al. proposed a generalization of the sequence (this sequence is referred to as the generalized NTU sequence), and showed the period and periodic autocorrelation. In this paper, we investigate the linear complexity of the generalized NTU sequences. Under some conditions, we can ensure that generalized NTU sequences have large linear complexity from the results on linear complexity of Sidel'nikov sequences.
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