The linearcomplexity and the k-error linear complexity are important concepts for the theory of stream ciphers in cryptology. keystreams that are suitable for stream ciphers must have large values of these complexity...
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The linearcomplexity and the k-error linear complexity are important concepts for the theory of stream ciphers in cryptology. keystreams that are suitable for stream ciphers must have large values of these complexity measures. We study periodic sequences over an arbitrary finite field F-q and establish conditions under which there are many periodic sequences over linearcomplexity N, and k-error linear complexity close to N. The existence of many such sequences thwarts attacks against the keystreams by exhaustive search.
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 of sequences is one of the important security measures for stream cipher systems. Recently, using fast algorithms for computing the linearcomplexity and the k-error linear complexity of 2(n)-per...
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ISBN:
(纸本)3540445234
The linearcomplexity of sequences is one of the important security measures for stream cipher systems. Recently, using fast algorithms for computing the linearcomplexity and the k-error linear complexity of 2(n)-periodic binary sequences, Meidl determined the counting function and expected value for the 1-errorlinearcomplexity of 2(n)-periodic binary sequences. In this paper, we study the linearcomplexity and the 1-errorlinearcomplexity of 2(n)-periodic binary sequences. Some interesting properties of the linearcomplexity and the 1-errorlinearcomplexity of 2(n)-periodic binary sequences are obtained. Using these properties, we characterize the 2(n)-periodic binary sequences with fixed 1-errorlinearcomplexity. Along the way, we obtain a new approach to derive the counting function for the 1-errorlinearcomplexity of 2(n)-periodic binary sequences. Finally, we give new fast algorithms for computing the 1-errorlinearcomplexity and locating the error positions for 2(n)-periodic binary sequences.
In his 1986 book, Rueppel conjectured that periodic binary sequences have expected linearcomplexity close to the period length N. In this paper, we determine the expected value of the linearcomplexity of N-periodic ...
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In his 1986 book, Rueppel conjectured that periodic binary sequences have expected linearcomplexity close to the period length N. In this paper, we determine the expected value of the linearcomplexity of N-periodic sequences explicitly and confirm Rueppel's conjecture for arbitrary finite fields. Cryptographically strong sequences should not only have a large linearcomplexity, but also the change of a few terms should not cause a significant decrease of the linearcomplexity. This requirement leads to the concept of the k-error linear complexity of N-periodic sequences. We present a method to establish a lower bound on the expected k-error linear complexity of N-periodic sequences based on the knowledge of the counting function V-N,V- 0 (c), i.e., the number of N-periodic sequences with given linearcomplexity c. For some cases, we give explicit formulas for that lower bound and we also determine N-N,N- 0 (c).
complexity measures for sequences of elements of a finite field play an important role in cryptology. We focus first on the linearcomplexity of periodic sequences. By means of the discrete Fourier transform, we deter...
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complexity measures for sequences of elements of a finite field play an important role in cryptology. We focus first on the linearcomplexity of periodic sequences. By means of the discrete Fourier transform, we determine the number of periodic sequences S with given prime period length N and linearcomplexity L-N, 0 (S) = c as well as the expected value of the linearcomplexity of N-periodic sequences. Cryptographically strong sequences should not only have a large linearcomplexity. but also the change of a few terms should not cause a significant decrease of the linearcomplexity. This requirement leads to the concept of the k-error linear complexity L-N.k(S) of sequences S with period length N, For some k and c we determine the number of periodic sequences S with given period length N and L-N.k(S) = c. For prime N we establish a lower bound on the expected value of the k-error linear complexity. (C) 2002 Elsevier Science (USA).
An efficient algorithm for computing the k-error linear complexity of a sequence over GF(q) with period p(n) is presented, where q is a prime and a primitive root modulo p(2). The new algorithm is a generalization of ...
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An efficient algorithm for computing the k-error linear complexity of a sequence over GF(q) with period p(n) is presented, where q is a prime and a primitive root modulo p(2). The new algorithm is a generalization of an algorithm presented by Xiao, Wei, Lam and Imamura.
Using the fact that the factorization of x - 1 over GF（2） is especially explicit. we completely establish the distributions and the expected values of the linearcomplexity and the k-error linear complexity of the N...
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Using the fact that the factorization of x - 1 over GF（2） is especially explicit. we completely establish the distributions and the expected values of the linearcomplexity and the k-error linear complexity of the N-periodic sequences respectively, where N is an odd prime and 2 is a primitive root modulo N. The results show that there are a large percentageof sequences with both the linearcomplexity and the k-error linear complexity not less than N, quite close to their maximum possible values.
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.
We introduce a fast algorithm for determining the linearcomplexity and the minimal polynomial of a sequence with period p(n) over GF(q), where p is an odd prime, q is a prime and a primitive root modulo p(2);and its ...
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ISBN:
(纸本)3540002634
We introduce a fast algorithm for determining the linearcomplexity and the minimal polynomial of a sequence with period p(n) over GF(q), where p is an odd prime, q is a prime and a primitive root modulo p(2);and its two generalized algorithms. One is the algorithm for determining the linearcomplexity and the minimal polynomial of a sequence with period p(m)q(n) over GF(q), the other is the algorithm for determining the k-error linear complexity of a sequence with period p(n) over GF(q), where p is an odd prime, q is a prime and a primitive root modulo p(2). The algorithm for determining the linearcomplexity and the minimal polynomial of a sequence with period 2p(n) over GF(q) is also introduced. where p and q are odd prime, and q is a primitive root (mod p(2)). These algorithms uses the fact that in these case the factorization of x(N) - 1 is especially simple for N = p(n), 2p(n), p(n)q(m).
An algorithm is given for the k-error linear complexity of sequences over GF(p(m)) with period p(n), p a prime. The algorithm is derived by the generalized Games-Chan algorithm for the linearcomplexity of sequences o...
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An algorithm is given for the k-error linear complexity of sequences over GF(p(m)) with period p(n), p a prime. The algorithm is derived by the generalized Games-Chan algorithm for the linearcomplexity of sequences over GF(p(m)) with period p(n) and by using the modified cost different from that used in the Stamp-Martin algorithm for sequences over GF(2) with period 2(n). A method is also given for computing an error vector which gives the k-error linear complexity. (C) 1999 Academic Press.
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