Strong linear dependence and unbiased distribution of non-propagative vectors

Yuliang Zheng; Xian Mo Zhang

Strong linear dependence and unbiased distribution of non-propagative vectors

Yuliang Zheng, Xian Mo Zhang

School of Computing

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

2 Citations (Scopus)

Abstract

This paper proves (i) in any (n − 1)-dimensional linear subspace, the non-propagative vectors of a function with n variables are linearly dependent, (ii) for this function, there exists a non-propagative vector in any (n − 2)-dimensional linear subspace and there exist three non-propagative vectors in any (n − 1)-dimensional linear subspace, except for those functions whose nonlinearity takes special values.

Original language	English
Title of host publication	Selected Areas in Cryptography - 6th Annual International Workshop, SAC 1999, Proceedings
Publisher	Springer, Springer Nature
Pages	92-105
Number of pages	14
Volume	1758
ISBN (Print)	3540671854
Publication status	Published - 2000
Event	6th Annual International Workshop on Selected Areas in Cryptography, SAC 1999 - Kingston, Canada Duration: 9 Aug 1999 → 10 Aug 1999

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1758
ISSN (Print)	03029743
ISSN (Electronic)	16113349

Other

Other	6th Annual International Workshop on Selected Areas in Cryptography, SAC 1999
Country/Territory	Canada
City	Kingston
Period	9/08/99 → 10/08/99

Keywords

Boolean function
Cryptography
Nonlinearity
Propagation

Cite this

Zheng, Y., & Zhang, X. M. (2000). Strong linear dependence and unbiased distribution of non-propagative vectors. In Selected Areas in Cryptography - 6th Annual International Workshop, SAC 1999, Proceedings (Vol. 1758, pp. 92-105). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1758). Springer, Springer Nature.

Zheng, Yuliang ; Zhang, Xian Mo. / Strong linear dependence and unbiased distribution of non-propagative vectors. Selected Areas in Cryptography - 6th Annual International Workshop, SAC 1999, Proceedings. Vol. 1758 Springer, Springer Nature, 2000. pp. 92-105 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Strong linear dependence and unbiased distribution of non-propagative vectors",

abstract = "This paper proves (i) in any (n − 1)-dimensional linear subspace, the non-propagative vectors of a function with n variables are linearly dependent, (ii) for this function, there exists a non-propagative vector in any (n − 2)-dimensional linear subspace and there exist three non-propagative vectors in any (n − 1)-dimensional linear subspace, except for those functions whose nonlinearity takes special values.",

keywords = "Boolean function, Cryptography, Nonlinearity, Propagation",

author = "Yuliang Zheng and Zhang, {Xian Mo}",

year = "2000",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer, Springer Nature",

pages = "92--105",

booktitle = "Selected Areas in Cryptography - 6th Annual International Workshop, SAC 1999, Proceedings",

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note = "6th Annual International Workshop on Selected Areas in Cryptography, SAC 1999 ; Conference date: 09-08-1999 Through 10-08-1999",

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Zheng, Y & Zhang, XM 2000, Strong linear dependence and unbiased distribution of non-propagative vectors. in Selected Areas in Cryptography - 6th Annual International Workshop, SAC 1999, Proceedings. vol. 1758, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1758, Springer, Springer Nature, pp. 92-105, 6th Annual International Workshop on Selected Areas in Cryptography, SAC 1999, Kingston, Canada, 9/08/99.

Strong linear dependence and unbiased distribution of non-propagative vectors. / Zheng, Yuliang; Zhang, Xian Mo.
Selected Areas in Cryptography - 6th Annual International Workshop, SAC 1999, Proceedings. Vol. 1758 Springer, Springer Nature, 2000. p. 92-105 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1758).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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AU - Zhang, Xian Mo

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N2 - This paper proves (i) in any (n − 1)-dimensional linear subspace, the non-propagative vectors of a function with n variables are linearly dependent, (ii) for this function, there exists a non-propagative vector in any (n − 2)-dimensional linear subspace and there exist three non-propagative vectors in any (n − 1)-dimensional linear subspace, except for those functions whose nonlinearity takes special values.

AB - This paper proves (i) in any (n − 1)-dimensional linear subspace, the non-propagative vectors of a function with n variables are linearly dependent, (ii) for this function, there exists a non-propagative vector in any (n − 2)-dimensional linear subspace and there exist three non-propagative vectors in any (n − 1)-dimensional linear subspace, except for those functions whose nonlinearity takes special values.

KW - Boolean function

KW - Cryptography

KW - Nonlinearity

KW - Propagation

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VL - 1758

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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EP - 105

BT - Selected Areas in Cryptography - 6th Annual International Workshop, SAC 1999, Proceedings

PB - Springer, Springer Nature

T2 - 6th Annual International Workshop on Selected Areas in Cryptography, SAC 1999

Y2 - 9 August 1999 through 10 August 1999

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Zheng Y, Zhang XM. Strong linear dependence and unbiased distribution of non-propagative vectors. In Selected Areas in Cryptography - 6th Annual International Workshop, SAC 1999, Proceedings. Vol. 1758. Springer, Springer Nature. 2000. p. 92-105. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

Strong linear dependence and unbiased distribution of non-propagative vectors

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