The cube theory for 2n-periodic binary sequences
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...
| Main Authors: | , , |
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| Format: | Conference Paper |
| Published: |
2016
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| Online Access: | http://hdl.handle.net/20.500.11937/14042 |
| _version_ | 1848748513862615040 |
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| author | Zhou, J. Liu, Wan-Quan Wang, X. |
| author_facet | Zhou, J. Liu, Wan-Quan Wang, X. |
| author_sort | Zhou, J. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T07:06:15Z |
| format | Conference Paper |
| id | curtin-20.500.11937-14042 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:06:15Z |
| publishDate | 2016 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-140422017-09-13T15:34:02Z The cube theory for 2n-periodic binary sequences Zhou, J. Liu, Wan-Quan Wang, X. 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. 2016 Conference Paper http://hdl.handle.net/20.500.11937/14042 10.1109/FGCN.2015.8 restricted |
| spellingShingle | Zhou, J. Liu, Wan-Quan Wang, X. The cube theory for 2n-periodic binary sequences |
| title | The cube theory for 2n-periodic binary sequences |
| title_full | The cube theory for 2n-periodic binary sequences |
| title_fullStr | The cube theory for 2n-periodic binary sequences |
| title_full_unstemmed | The cube theory for 2n-periodic binary sequences |
| title_short | The cube theory for 2n-periodic binary sequences |
| title_sort | cube theory for 2n-periodic binary sequences |
| url | http://hdl.handle.net/20.500.11937/14042 |