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Decomposing Approach for Error Vectors of kError Linear Complexity of Certain Periodic Sequences
Ming SU
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E97A
No.7
pp.15421555 Publication Date: 2014/07/01
Online ISSN: 17451337 Type of Manuscript: PAPER Category: Cryptography and Information Security Keyword: (kerror) linear complexity, error vector, counting functions, expectation, stream cipher,
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Summary:
The kerror linear complexity of periodic sequences is an important security index of stream cipher systems. By using an interesting decomposing approach, we investigate the intrinsic structure for the set of 2^{n}periodic binary sequences with fixed complexity measures. For k ≤ 4, we construct the complete set of error vectors that give the kerror linear complexity. As auxiliary results we obtain the counting functions of the kerror linear complexity of 2^{n}periodic binary sequences for k ≤ 4, as well as the expectations of the kerror linear complexity of a random sequence for k ≤ 3. Moreover, we study the 2^{t}error linear complexity of the set of 2^{n}periodic binary sequences with some fixed linear complexity L, where t < n1 and the Hamming weight of the binary representation of 2^{n}L is t. Also, we extend some results to p^{n}periodic sequences over F_{p}. Finally, we discuss some potential applications.

