Due to good pseudorandom properties, generalized cyclotomic sequences have been widely used in simulation, radar systems, cryptography, and so on. In this paper, we consider the k-error linear complexity of Zeng-Cai-T...
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(纸本)9789811330957;9789811330940
Due to good pseudorandom properties, generalized cyclotomic sequences have been widely used in simulation, radar systems, cryptography, and so on. In this paper, we consider the k-error linear complexity of Zeng-Cai-Tang-Yang generalized cyclotomic binary sequences of period p(2), proposed in the recent paper "New generalized cyclotomic binary sequences of period p(2)", by Z. Xiao et al., who calculated the linearcomplexity of the sequence (Designs, Codes and Cryptography, 2018, 86(7): 1483-1497). More exactly, we determine the values of k-error linear complexity over F-2 for f = 2 and almost k > 0 in terms of the theory of Fermat quotients. Results indicate that such sequences have good stability.
The Euler quotient modulo an odd-prime power pr(r > 1) can be uniquely decomposed as a p-adic number of the form(up-1pr-1- 1)/pr≡ a0(u) + a1(u)p + ··· + ar-1(u)pr-1(mod pr), gcd(u, p) = 1, where0≤a...
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The Euler quotient modulo an odd-prime power pr(r > 1) can be uniquely decomposed as a p-adic number of the form(up-1pr-1- 1)/pr≡ a0(u) + a1(u)p + ··· + ar-1(u)pr-1(mod pr), gcd(u, p) = 1, where0≤aj(u) < p for 0≤j≤r- 1 and we set all aj(u) = 0 if gcd(u, p) > 1. We firstly study certain arithmetic properties of the level sequences(aj(u))u≥0over Fp via introducing a new quotient. Then we determine the exact values of linearcomplexity of(aj(u))u≥0 and values of k-error linear complexity for binary sequences defined by(aj(u))u≥0.
complexity measures for sequences, such as the linearcomplexity and the k-error linear complexity, play an important role in stream ciphers. This contribution studies the distribution of 1-errorlinearcomplexity of ...
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complexity measures for sequences, such as the linearcomplexity and the k-error linear complexity, play an important role in stream ciphers. This contribution studies the distribution of 1-errorlinearcomplexity of binary sequences with arbitrary prime period. For any odd prime N, the authors present all possible values of 1-errorlinearcomplexity of N-periodic binary sequences, and derive the exact formulas to count the number of N-periodic binary sequences with any given 1-errorlinearcomplexity.
The linearcomplexity of sequences is an important measure of the cryptographic strength of key streams used in stream ciphers. The instability of linearcomplexity caused by changing a few symbols of sequences can be...
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The linearcomplexity of sequences is an important measure of the cryptographic strength of key streams used in stream ciphers. The instability of linearcomplexity caused by changing a few symbols of sequences can be measured using k-error linear complexity. In their SETA 2006 paper, Fu et al. (SETA, pp. 88-103, 2006) studied the linearcomplexity and the 1-errorlinearcomplexity of 2 (n) -periodic binary sequences to characterize such sequences with fixed 1-errorlinearcomplexity. In this paper we study the linearcomplexity and the k-error linear complexity of 2 (n) -periodic binary sequences in a more general setting using a combination of algebraic, combinatorial, and algorithmic methods. This approach allows us to characterize 2 (n) -periodic binary sequences with fixed 2- or 3-errorlinearcomplexity. Using this characterization we obtain the counting function for the number of 2 (n) -periodic binary sequences with fixed k-error linear complexity for k = 2 and 3.
The k-error linear complexity of periodic binary sequences is defined to be the smallest linearcomplexity that can be obtained by changing k or fewer bits of the sequence per period. For the period length p(n), where...
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The k-error linear complexity of periodic binary sequences is defined to be the smallest linearcomplexity that can be obtained by changing k or fewer bits of the sequence per period. For the period length p(n), where p is an odd prime and 2 is a primitive root modulo p(2), we show a relationship between the linearcomplexity and the minimum value k for which the k-error linear complexity is strictly less than the linearcomplexity. Moreover, we describe an algorithm to determine the k-error linear complexity of a given p(n)-periodic binary sequence.
The errorlinearcomplexity spectrum of a periodic sequence is defined to be the ordered list of -errorlinear complexities of the sequence. In this paper, we present an algorithm which computes the errorlinear compl...
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The errorlinearcomplexity spectrum of a periodic sequence is defined to be the ordered list of -errorlinear complexities of the sequence. In this paper, we present an algorithm which computes the errorlinearcomplexity spectrum for binary sequences with period , where is an odd prime and is a primitive root modulo .
In this paper, we define the linearcomplexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linea...
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In this paper, we define the linearcomplexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linearcomplexity and k-error linear complexity of multidimensional periodic sequences. (C) 2018 Elsevier Inc. All rights reserved.
We consider the k-error linear complexity of a new generalized cyclotomic binary sequence of period p(2) for an odd prime p. The new sequences were introduced recently by Z. Xiao, X. Zeng, C. Li and T. Helleseth by de...
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We consider the k-error linear complexity of a new generalized cyclotomic binary sequence of period p(2) for an odd prime p. The new sequences were introduced recently by Z. Xiao, X. Zeng, C. Li and T. Helleseth by defining a new kind of generalized cyclotomic classes modulo p(2). They proved that the sequences had large linearcomplexity. In this work, we determine the values of the k-error linear complexity in terms of the theory of Fermat quotients. The results indicate that such sequences have good stability, that is, the linearcomplexity does not significantly decrease by changing a few terms. (C) 2019 Elsevier B.V. All rights reserved.
In this article, we present a counterexample to Theorem 4.2 and Theorem 5.2 by kavuluru (Des Codes Cryptogr 53:75-97, 2009). We conclude that the counting functions for the number of 2 (n) -periodic binary sequences w...
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In this article, we present a counterexample to Theorem 4.2 and Theorem 5.2 by kavuluru (Des Codes Cryptogr 53:75-97, 2009). We conclude that the counting functions for the number of 2 (n) -periodic binary sequences with fixed 3-errorlinearcomplexity by kavuluru are not correct.
linearcomplexity and the k-error linear complexity of periodic sequences are the important security indices of stream cipher systems. This paper focuses on the distribution of p-errorlinearcomplexity of p-ary seque...
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linearcomplexity and the k-error linear complexity of periodic sequences are the important security indices of stream cipher systems. This paper focuses on the distribution of p-errorlinearcomplexity of p-ary sequences with period p(n). For p-ary sequences of period p(n) with linearcomplexity p(n) - p + 1, n >= 1, we present all possible values of the p-errorlinearcomplexity, and derive the exact formulas to count the number of the sequences with any given p-errorlinearcomplexity.
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