The linearcomplexity and the -errorlinearcomplexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method o...
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The linearcomplexity and the -errorlinearcomplexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, we investigate the -errorlinearcomplexity distribution of -periodic binary sequences in this paper based on Games-Chan algorithm. First, for , the complete counting functions for the -errorlinearcomplexity of -periodic binary sequences (with linearcomplexity less than ) are characterized. Second, for , the complete counting functions for the -errorlinearcomplexity of -periodic binary sequences with linearcomplexity are presented. Third, as a consequence of these results, the counting functions for the number of -periodic binary sequences with the -errorlinearcomplexity for and are obtained.
In the present paper, by making use of some special properties of the Hermitian function fields, we construct multisequences with both large linearcomplexity and k-error linear complexity. Moreover, these sequences c...
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In the present paper, by making use of some special properties of the Hermitian function fields, we construct multisequences with both large linearcomplexity and k-error linear complexity. Moreover, these sequences can be explicitly constructed.
linearcomplexity and k-error linear complexity are the important measures for sequences in stream ciphers. This paper discusses the asymptotic behavior of the normalized k-error linear complexity L-n,L-k(s)/n of rand...
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linearcomplexity and k-error linear complexity are the important measures for sequences in stream ciphers. This paper discusses the asymptotic behavior of the normalized k-error linear complexity L-n,L-k(s)/n of random binary sequences s, which is based on one of Niederreiter's open problems. For k = n theta, where 0 <= theta <= 1/2 is a fixed ratio, the lower and upper bounds on accumulation points of L-n,L-k((s)under bar)/n are derived, which holds with probability 1. On the other hand, for any fixed k it is shown that lim(n ->infinity) Ln, k ((s)under bar)/n = 1/2 holds with probability 1. The asymptotic bounds on the expected value of normalized k-error linear complexity of binary sequences are also presented.
In this paper, we first optimize the structure of the Wei-Xiao-Chen algorithm for the linearcomplexity of sequences over GF(q) with period N = 2p (n) , where p and q are odd primes, and q is a primitive root modulo p...
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In this paper, we first optimize the structure of the Wei-Xiao-Chen algorithm for the linearcomplexity of sequences over GF(q) with period N = 2p (n) , where p and q are odd primes, and q is a primitive root modulo p (2). The second, an union cost is proposed, so that an efficient algorithm for computing the k-error linear complexity of a sequence with period 2p (n) over GF(q) is derived, where p and q are odd primes, and q is a primitive root modulo p (2). The third, we give a validity of the proposed algorithm, and also prove that there exists an error sequence e (N) , where the Hamming weight of e (N) is not greater than k, such that the linearcomplexity of (s + e) (N) reaches the k-error linear complexity c. We also present a numerical example to illustrate the algorithm. Finally, we present the minimum value k for which the k-error linear complexity is strictly less than the linearcomplexity.
Pseudorandom sequences play an important role in communication and stream ciphers. In recent years, the method of generating pseudorandom sequences based on arithmetical functions has attracted increasing attention. k...
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Pseudorandom sequences play an important role in communication and stream ciphers. In recent years, the method of generating pseudorandom sequences based on arithmetical functions has attracted increasing attention. k-error linear complexity is an important index to evaluate the stability of a sequence. Recently, J. Zhang and C. Zhao introduced binary sequences derived from Euler quotients modulo 2p (where p > 3 is an odd prime). In this paper, the k-error linear complexity of such sequences over F-2 was considered with the condition that 2 is a primitive root modulo p(2). Certain decimal sequences were used to determine the values of k-error linear complexity for all k > 0. The results showed that such sequences have good stability in terms of cryptography.
We establish the existence of periodic sequences over a finite field which simultaneously achieve the maximum value (for the given period length) of the linearcomplexity and of the k-error linear complexity for small...
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We establish the existence of periodic sequences over a finite field which simultaneously achieve the maximum value (for the given period length) of the linearcomplexity and of the k-error linear complexity for small values of k. This disproves a conjecture of Ding, Xiao, and Shan. The result is of relevance for the theory of stream ciphers.
The linearcomplexity and its stability of periodic sequences are of fundamental importance as measure indexes on the security of stream ciphers and the k-error linear complexity reveals the stability of the linear co...
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The linearcomplexity and its stability of periodic sequences are of fundamental importance as measure indexes on the security of stream ciphers and the k-error linear complexity reveals the stability of the linearcomplexity properly. Recently, Zhou designed an algorithm for computing the k-error linear complexity of 2p(n) periodic sequences over GF(q). In this paper, we develop a genetic algorithm to confirm that one can't get the real k-error linear complexity for some sequenes by the Zhou's algorithm. Analysis indicates that the Zhou's algorithm is unreasonable in some steps. The corrected algorithm is presented. Such algorithm will increase the amount of computation, but is necessary to get the real k-error linear complexity. Here p and q are odd prime, and q is a primitive root (mod p(2)).
Recently the first author presented exact formulas for the number of 2(n)-periodic binary sequences with given 1-errorlinearcomplexity, and an exact formula for the expected 1-errorlinearcomplexity and upper and l...
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Recently the first author presented exact formulas for the number of 2(n)-periodic binary sequences with given 1-errorlinearcomplexity, and an exact formula for the expected 1-errorlinearcomplexity and upper and lower bounds for the expected k-error linear complexity, k >= 2, of a random 2(n)-periodic binary sequence. A crucial role for the analysis played the Chan-Games algorithm. We use a more sophisticated generalization of the Chan-Games algorithm by Ding et al. to obtain exact formulas for the counting function and the expected value for the 1-errorlinearcomplexity for p(n)-periodic sequences over F-p,p prime. Additionally we discuss the calculation of lower and upper bounds on the k-error linear complexity of p(n)-periodic sequences over F-p.
The linearcomplexity and k-error linear complexity of a sequence have been used as important measures for keystream strength. In order to study k-error linear complexity of binary sequences with period 2(n), a new to...
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The linearcomplexity and k-error linear complexity of a sequence have been used as important measures for keystream strength. In order to study k-error linear complexity of binary sequences with period 2(n), a new tool called cube theory is developed. In this paper, we first give a general decomposition approach to decompose a binary sequence with period 2(n) into some disjoint cubes. Second, a counting formula for m-cubes with the same linearcomplexity is derived, which is equivalent to the counting formula for k-error vectors. The counting formula of 2(n)-periodic binary sequences which can be decomposed into more than one cube is also investigated, which extends an important result by Etzion et al.. Finally, we study 2(n)-periodic binary sequences with the given k-error linear complexity profile. Consequently, the complete counting formula of 2(n)-periodic binary sequences with given k-error linear complexity profile of descent points 2, 4 and 6 is derived. The periodic sequences having the prescribed k-error linear complexity profile with descent points 1, 3, 5 and 7 are also briefly discussed.
We study the k-error linear complexity of subsequences of the d-ary Sidel'nikov sequences over the prime field F-d. A general lower bound for the k-error linear complexity is given. For several special periods, we...
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We study the k-error linear complexity of subsequences of the d-ary Sidel'nikov sequences over the prime field F-d. A general lower bound for the k-error linear complexity is given. For several special periods, we show that these sequences have large k-error linear complexity.
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