A fast algorithm for determining the complexity of a binary sequence with period&amp;lt;tex&amp;gt;2^n&amp;lt;/tex&amp;gt;(Corresp.)

Games, Richard A.; Chan, Agnes Hui

doi:10.1109/tit.1983.1056619

Cited by 148 publications

(108 citation statements)

References 3 publications

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“…The Games-Chan algorithm, [3], computes the linear complexity for any binary sequence with period a power of two, i.e. for any s ∈ P 2 n it computes c(s).…”

Section: A Infinite Sequencesmentioning

confidence: 99%

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On the Computation of the Linear Complexity and the k-Error Linear Complexity of Binary Sequences with Period a Power of Two

Sălăgean

2005

Sequences and Their Applications - SETA 2004

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On the computation of the linear complexity and the k-error linear complexity of binary sequences with period a power of two On the computation of the linear complexity and the k-error linear complexity of binary sequences with period a power of two Ana SȃlȃgeanAbstract-The linear Games-Chan algorithm for computing the linear complexity c(s) of a binary sequence s of period = 2 n requires the knowledge of the full sequence, while the quadratic Berlekamp-Massey algorithm only requires knowledge of 2c(s) terms. We show that we can modify the Games-Chan algorithm so that it computes the complexity in linear time knowing only 2c(s) terms. The algorithms of Stamp-Martin and Lauder-Paterson can also be modified, without loss of efficiency, to compute analogues of the k-error linear complexity for finite binary sequences viewed as initial segments of infinite sequences with period a power of two.We also develop an algorithm which, given a constant c and an infinite binary sequence s with period = 2 n , computes the minimum number k of errors (and the associated error sequence) needed over a period of s for bringing the linear complexity of s below c. The algorithm has a time and space bit complexity of O( ). We apply our algorithm to decoding and encoding binary repeated-root cyclic codes of length in linear, O( ), time and space. A previous decoding algorithm proposed by Lauder and Paterson has O( (log ) 2 ) complexity.

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“…The Games-Chan algorithm, [3], computes the linear complexity for any binary sequence with period a power of two, i.e. for any s ∈ P 2 n it computes c(s).…”

Section: A Infinite Sequencesmentioning

confidence: 99%

“…For the particular case of binary sequences with period a power of two, Games and Chan devised an algorithm with linear time and space bit complexity, [3].…”

Section: Introductionmentioning

confidence: 99%

On the Computation of the Linear Complexity and the k-Error Linear Complexity of Binary Sequences with Period a Power of Two

Sălăgean

2005

Sequences and Their Applications - SETA 2004

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“…A further enhancement is the notion of a linear complexity profile, which measures the linear complexity of the sequence as it gets longer and longer [1357,1168,411,1582]. Another algorithm for computing linear complexity is useful only in very specialized circumstances [597,595,596,1333]. A generalization of linear complexity is in [776].…”

Section: Linear Complexitymentioning

confidence: 99%

Applied cryptography: Protocols, algorithms, and source code in C

1994

Computer Law & Security Review

771

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“…Applying Property 1 in Section 2 and using the fact that L w H (s) (s) = 0 the full approximate k-error linear complexity profile is found: {(0, 8), (1,8), (2,7), (3,5), (4,5), (5, 2), (6, 2), (7, 2), (8, 2), (9, 2), (10, 2), (11, 0)}. The exact k-error linear complexity profile obtained by an exhaustive search algorithm is: (2,6), (3,4), (4, 2), (5, 1), (6, 1), (7,1), (8,1), (9, 1), (10, 1), (11, 0)}. : n ← 0 10: while sn = 0 and n < t − 1 do go over the initial zeros 11:…”

Section: The Modified Berlekamp-massey Algorithmmentioning

confidence: 99%

“…These algorithms are based on the algorithms of Games and Chan [3] and Ding, Xiao, Shan [2] for computing the linear complexity of such sequences, and they work only when a full period of the sequence is known, i.e. the whole sequence is known, which is not the case in cryptanalysis applications.…”

Section: Introductionmentioning

confidence: 99%

Modified Berlekamp-Massey Algorithm for Approximating the k-Error Linear Complexity of Binary Sequences

Alecu

Sălăgean

Cryptography and Coding

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Abstract. Some cryptographical applications use pseudorandom sequences and require that the sequences are secure in the sense that they cannot be recovered by only knowing a small amount of consecutive terms. Such sequences should therefore have a large linear complexity and also a large k-error linear complexity. Efficient algorithms for computing the k-error linear complexity of a sequence only exist for sequences of period equal to a power of the characteristic of the field. It is therefore useful to find a general and efficient algorithm to compute a good approximation of the k-error linear complexity. We show that the Berlekamp-Massey Algorithm, which computes the linear complexity of a sequence, can be adapted to approximate the k-error linear complexity profile for a general sequence over a finite field. While the complexity of this algorithm is still exponential, it is considerably more efficient than the exhaustive search.

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A fast algorithm for determining the complexity of a binary sequence with period<tex>2^n</tex>(Corresp.)

Cited by 148 publications

References 3 publications

On the Computation of the Linear Complexity and the k-Error Linear Complexity of Binary Sequences with Period a Power of Two

On the Computation of the Linear Complexity and the k-Error Linear Complexity of Binary Sequences with Period a Power of Two

Applied cryptography: Protocols, algorithms, and source code in C

Modified Berlekamp-Massey Algorithm for Approximating the k-Error Linear Complexity of Binary Sequences

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