The $$k$$-error linear complexity distribution for $$2^n$$-periodic binary sequences
Abstract The linear complexity and the $$k$$-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, we investigate the $$k$$-error linear complexity dis...
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Gespeichert in:
| Autor*in: |
Zhou, Jianqin [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Designs, codes and cryptography - Springer US, 1991, 73(2013), 1 vom: 10. März, Seite 55-75 |
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| Übergeordnetes Werk: |
volume:73 ; year:2013 ; number:1 ; day:10 ; month:03 ; pages:55-75 |
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| DOI / URN: |
10.1007/s10623-013-9805-8 |
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| 520 | |a Abstract The linear complexity and the $$k$$-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, we investigate the $$k$$-error linear complexity distribution of $$2^n$$-periodic binary sequences in this paper based on Games–Chan algorithm. First, for $$k=2,3$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences (with linear complexity less than $$2^n$$) are characterized. Second, for $$k=3,4$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences with linear complexity $$2^n$$ are presented. Third, as a consequence of these results, the counting functions for the number of $$2^n$$-periodic binary sequences with the $$k$$-error linear complexity for $$k = 2$$ and $$3$$ are obtained. | ||
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10.1007/s10623-013-9805-8 doi (DE-627)OLC2027294996 (DE-He213)s10623-013-9805-8-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Zhou, Jianqin verfasserin aut The $$k$$-error linear complexity distribution for $$2^n$$-periodic binary sequences 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract The linear complexity and the $$k$$-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, we investigate the $$k$$-error linear complexity distribution of $$2^n$$-periodic binary sequences in this paper based on Games–Chan algorithm. First, for $$k=2,3$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences (with linear complexity less than $$2^n$$) are characterized. Second, for $$k=3,4$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences with linear complexity $$2^n$$ are presented. Third, as a consequence of these results, the counting functions for the number of $$2^n$$-periodic binary sequences with the $$k$$-error linear complexity for $$k = 2$$ and $$3$$ are obtained. Periodic sequence Linear complexity -error linear complexity -error linear complexity distribution Liu, Wanquan aut Enthalten in Designs, codes and cryptography Springer US, 1991 73(2013), 1 vom: 10. März, Seite 55-75 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:73 year:2013 number:1 day:10 month:03 pages:55-75 https://doi.org/10.1007/s10623-013-9805-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 73 2013 1 10 03 55-75 |
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10.1007/s10623-013-9805-8 doi (DE-627)OLC2027294996 (DE-He213)s10623-013-9805-8-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Zhou, Jianqin verfasserin aut The $$k$$-error linear complexity distribution for $$2^n$$-periodic binary sequences 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract The linear complexity and the $$k$$-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, we investigate the $$k$$-error linear complexity distribution of $$2^n$$-periodic binary sequences in this paper based on Games–Chan algorithm. First, for $$k=2,3$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences (with linear complexity less than $$2^n$$) are characterized. Second, for $$k=3,4$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences with linear complexity $$2^n$$ are presented. Third, as a consequence of these results, the counting functions for the number of $$2^n$$-periodic binary sequences with the $$k$$-error linear complexity for $$k = 2$$ and $$3$$ are obtained. Periodic sequence Linear complexity -error linear complexity -error linear complexity distribution Liu, Wanquan aut Enthalten in Designs, codes and cryptography Springer US, 1991 73(2013), 1 vom: 10. März, Seite 55-75 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:73 year:2013 number:1 day:10 month:03 pages:55-75 https://doi.org/10.1007/s10623-013-9805-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 73 2013 1 10 03 55-75 |
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10.1007/s10623-013-9805-8 doi (DE-627)OLC2027294996 (DE-He213)s10623-013-9805-8-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Zhou, Jianqin verfasserin aut The $$k$$-error linear complexity distribution for $$2^n$$-periodic binary sequences 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract The linear complexity and the $$k$$-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, we investigate the $$k$$-error linear complexity distribution of $$2^n$$-periodic binary sequences in this paper based on Games–Chan algorithm. First, for $$k=2,3$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences (with linear complexity less than $$2^n$$) are characterized. Second, for $$k=3,4$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences with linear complexity $$2^n$$ are presented. Third, as a consequence of these results, the counting functions for the number of $$2^n$$-periodic binary sequences with the $$k$$-error linear complexity for $$k = 2$$ and $$3$$ are obtained. Periodic sequence Linear complexity -error linear complexity -error linear complexity distribution Liu, Wanquan aut Enthalten in Designs, codes and cryptography Springer US, 1991 73(2013), 1 vom: 10. März, Seite 55-75 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:73 year:2013 number:1 day:10 month:03 pages:55-75 https://doi.org/10.1007/s10623-013-9805-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 73 2013 1 10 03 55-75 |
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10.1007/s10623-013-9805-8 doi (DE-627)OLC2027294996 (DE-He213)s10623-013-9805-8-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Zhou, Jianqin verfasserin aut The $$k$$-error linear complexity distribution for $$2^n$$-periodic binary sequences 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract The linear complexity and the $$k$$-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, we investigate the $$k$$-error linear complexity distribution of $$2^n$$-periodic binary sequences in this paper based on Games–Chan algorithm. First, for $$k=2,3$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences (with linear complexity less than $$2^n$$) are characterized. Second, for $$k=3,4$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences with linear complexity $$2^n$$ are presented. Third, as a consequence of these results, the counting functions for the number of $$2^n$$-periodic binary sequences with the $$k$$-error linear complexity for $$k = 2$$ and $$3$$ are obtained. Periodic sequence Linear complexity -error linear complexity -error linear complexity distribution Liu, Wanquan aut Enthalten in Designs, codes and cryptography Springer US, 1991 73(2013), 1 vom: 10. März, Seite 55-75 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:73 year:2013 number:1 day:10 month:03 pages:55-75 https://doi.org/10.1007/s10623-013-9805-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 73 2013 1 10 03 55-75 |
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10.1007/s10623-013-9805-8 doi (DE-627)OLC2027294996 (DE-He213)s10623-013-9805-8-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Zhou, Jianqin verfasserin aut The $$k$$-error linear complexity distribution for $$2^n$$-periodic binary sequences 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract The linear complexity and the $$k$$-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, we investigate the $$k$$-error linear complexity distribution of $$2^n$$-periodic binary sequences in this paper based on Games–Chan algorithm. First, for $$k=2,3$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences (with linear complexity less than $$2^n$$) are characterized. Second, for $$k=3,4$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences with linear complexity $$2^n$$ are presented. Third, as a consequence of these results, the counting functions for the number of $$2^n$$-periodic binary sequences with the $$k$$-error linear complexity for $$k = 2$$ and $$3$$ are obtained. Periodic sequence Linear complexity -error linear complexity -error linear complexity distribution Liu, Wanquan aut Enthalten in Designs, codes and cryptography Springer US, 1991 73(2013), 1 vom: 10. März, Seite 55-75 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:73 year:2013 number:1 day:10 month:03 pages:55-75 https://doi.org/10.1007/s10623-013-9805-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 73 2013 1 10 03 55-75 |
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Abstract The linear complexity and the $$k$$-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, we investigate the $$k$$-error linear complexity distribution of $$2^n$$-periodic binary sequences in this paper based on Games–Chan algorithm. First, for $$k=2,3$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences (with linear complexity less than $$2^n$$) are characterized. Second, for $$k=3,4$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences with linear complexity $$2^n$$ are presented. Third, as a consequence of these results, the counting functions for the number of $$2^n$$-periodic binary sequences with the $$k$$-error linear complexity for $$k = 2$$ and $$3$$ are obtained. © Springer Science+Business Media New York 2013 |
| abstractGer |
Abstract The linear complexity and the $$k$$-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, we investigate the $$k$$-error linear complexity distribution of $$2^n$$-periodic binary sequences in this paper based on Games–Chan algorithm. First, for $$k=2,3$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences (with linear complexity less than $$2^n$$) are characterized. Second, for $$k=3,4$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences with linear complexity $$2^n$$ are presented. Third, as a consequence of these results, the counting functions for the number of $$2^n$$-periodic binary sequences with the $$k$$-error linear complexity for $$k = 2$$ and $$3$$ are obtained. © Springer Science+Business Media New York 2013 |
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Abstract The linear complexity and the $$k$$-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, we investigate the $$k$$-error linear complexity distribution of $$2^n$$-periodic binary sequences in this paper based on Games–Chan algorithm. First, for $$k=2,3$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences (with linear complexity less than $$2^n$$) are characterized. Second, for $$k=3,4$$, the complete counting functions for the $$k$$-error linear complexity of $$2^n$$-periodic binary sequences with linear complexity $$2^n$$ are presented. Third, as a consequence of these results, the counting functions for the number of $$2^n$$-periodic binary sequences with the $$k$$-error linear complexity for $$k = 2$$ and $$3$$ are obtained. © Springer Science+Business Media New York 2013 |
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The $$k$$-error linear complexity distribution for $$2^n$$-periodic binary sequences |
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