The cube theory for 2n-periodic binary sequences
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The linear complexity and k-error linear complexity of a sequencehave been used as important measures for keystream strength, hencedesigning a sequence with high linear complexity and k-errorlinear complexity is a popular research topic in cryptography. In order to study k-error linear complexity of binarysequences with period 2n, a new tool called cube theory isdeveloped. In this paper, we first give ageneral decomposition approach to decompose a binary sequence with period 2n into some disjoint cubes. Second, a countingformula for m-cubes with the same linear complexity is derived, which is equivalent to the counting formula for k-error vectors. The counting formulaof 2n-periodic binary sequences which can be decomposedinto more than one cube is also investigated, which extends an important result by Etzion et al.
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Zhou, J.; Liu, Wan-Quan; Wang, X. (2016)© 2016 SERSC. The linear complexity 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 2n, ...
Structure analysis on the k-error linear complexity for 2<sup>n</sup>-periodic binary sequencesZhou, J.; Liu, Wan-Quan; Wang, X. (2017)In this paper, in order to characterize the critical error linear complexity spectrum (CELCS) for 2 n -periodic binary sequences, we first propose a decomposition based on the cube theory. Based on the proposed k-error ...
Zhou, Jianqin (2017)This thesis proposes various novel approaches for studying the k-error linear complexity distribution of periodic binary sequences for k > 2, and the second descent point and beyond of k-error linear complexity critical ...