The error linear complexity spectrum constitutes a well-known cryptographic criterion for sequences, indicating how the linearcomplexity of the sequence decreases as the number of bits allowed to be modified per peri...
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The error linear complexity spectrum constitutes a well-known cryptographic criterion for sequences, indicating how the linearcomplexity of the sequence decreases as the number of bits allowed to be modified per period increases. In this paper, via defining an association between 2(n)-periodic binary sequences and Boolean functions on n variables, it is shown that the error linear complexity spectrum also provides useful cryptographic information for the corresponding Boolean function f - namely, it yields an upper bound on the minimum Hamming distance between f and the set of functions depending on fewer number of variables. Therefore, the prominent Lauder-Paterson algorithm for computing the error linear complexity spectrum of a sequence may also be used for efficiently determining approximations of a Boolean function that depend on fewer number of variables. Moreover, it is also shown that, through this approach, low-degree approximations of a Boolean function can be also obtained in an efficient way.
The error linear complexity 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 error linear complexity 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 error linear complexity spectrum for binary sequences with period , where is an odd prime and is a primitive root modulo .
The properties of errorlinearcomplexity of binary sequences with period 2n are studied in this *** Games-Chan algorithm as main tool,accurate formulas of the minimum value k for which the k-errorlinearcomplexity i...
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The properties of errorlinearcomplexity of binary sequences with period 2n are studied in this *** Games-Chan algorithm as main tool,accurate formulas of the minimum value k for which the k-errorlinearcomplexity is strictly less than the first and second errorlinearcomplexity are provided respectively.
This paper studies some enumeration problems of binary sequences with period 2(n) based on the Games-Chan algorithm and a modified Stamp-Martin algorithm. We provide the exact number of critical error sequences of bin...
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This paper studies some enumeration problems of binary sequences with period 2(n) based on the Games-Chan algorithm and a modified Stamp-Martin algorithm. We provide the exact number of critical error sequences of binary 2(n)-periodic sequences corresponding to the second critical point. The exact formula for the number of binary 2(n)-periodic sequences with exactly three critical points is also derived.
Based on the Games-Chan algorithm and StampMartin algorithm, this paper provides some new algorithms to compute the error linear complexity spectrum of binary 2n-periodic se- quences. These new algorithms are clearer ...
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Based on the Games-Chan algorithm and StampMartin algorithm, this paper provides some new algorithms to compute the error linear complexity spectrum of binary 2n-periodic se- quences. These new algorithms are clearer and simpler than old algorithms, and they can quickly compute the errorlinear com- plexity spectrum of sequences according to different situations. We also discuss such algorithms and give some new results about linearcomplexity and errorlinearcomplexity of sequences.
Binary sequences with high linearcomplexity are of interest in cryptography. The linearcomplexity should remain high even when a small number of changes are made to the sequence. The error linear complexity spectrum...
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Binary sequences with high linearcomplexity are of interest in cryptography. The linearcomplexity should remain high even when a small number of changes are made to the sequence. The error linear complexity spectrum of a sequence reveals how the linearcomplexity of the sequence varies as an increasing number of the bits of the sequence are changed. We present an algorithm which computes the errorlinearcomplexity for binary sequences of period l = 2(n) using O(l(log l)(2)) bit operations. The algorithm generalizes both the Games-Chan and Stamp-Martin algorithms, which compute the linearcomplexity and the k-errorlinearcomplexity of a binary sequence of period f = 2(n), respectively. We also discuss an application of an extension of our algorithm to decoding a class of linear subcodes of Reed-Muller codes.
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