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Secondary constructions of highly nonlinear Boolean functions and disjoint spectra plateaued functions.

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Title: Secondary constructions of highly nonlinear Boolean functions and disjoint spectra plateaued functions.
Authors: Zhang, Feng-rong1 zhfl203@163.com, Carlet, Claude2 claude.carlet@univ-paris8.fr, Hu, Yu-pu3 yphu@mail.xidian.edu.cn, Cao, Tian-jie1 tjcao@cumt.edu.cn
Source: Information Sciences. Nov2014, Vol. 283, p94-106. 13p.
Subjects: Nonlinear analysis, Boolean functions, Bent functions, Algebraic immunity, Iterative methods (Mathematics)
Abstract: In this paper, we modify a generalized indirect sum construction to construct functions with high nonlinearity. By utilizing the modified construction, highly nonlinear functions in (n + m) variables can be obtained from known bent functions in n variables and highly nonlinear functions in m variables. It is possible to obtain new (n + 15) -variable functions with nonlinearity 2 n + 15 - 1 - 2 (n + 15 - 1) / 2 + 20 × 2 n / 2 and new 12-variable 2-resilient functions with nonlinearity 2000 and algebraic degree 8, which achieve optimal algebraic immunity. Moreover, the modified construction can also be used as an iterative construction of a quadruple of disjoint spectra plateaued functions. In addition, we present sufficient conditions for a quadruple of disjoint spectra plateaued functions to have no nonzero linear structure. [ABSTRACT FROM AUTHOR]
Copyright of Information Sciences is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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An: 97578048
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  Data: Secondary constructions of highly nonlinear Boolean functions and disjoint spectra plateaued functions.
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  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Feng-rong%22">Zhang, Feng-rong</searchLink><relatesTo>1</relatesTo><i> zhfl203@163.com</i><br /><searchLink fieldCode="AR" term="%22Carlet%2C+Claude%22">Carlet, Claude</searchLink><relatesTo>2</relatesTo><i> claude.carlet@univ-paris8.fr</i><br /><searchLink fieldCode="AR" term="%22Hu%2C+Yu-pu%22">Hu, Yu-pu</searchLink><relatesTo>3</relatesTo><i> yphu@mail.xidian.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Cao%2C+Tian-jie%22">Cao, Tian-jie</searchLink><relatesTo>1</relatesTo><i> tjcao@cumt.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Information+Sciences%22">Information Sciences</searchLink>. Nov2014, Vol. 283, p94-106. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Nonlinear+analysis%22">Nonlinear analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Boolean+functions%22">Boolean functions</searchLink><br /><searchLink fieldCode="DE" term="%22Bent+functions%22">Bent functions</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+immunity%22">Algebraic immunity</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink>
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  Data: In this paper, we modify a generalized indirect sum construction to construct functions with high nonlinearity. By utilizing the modified construction, highly nonlinear functions in (n + m) variables can be obtained from known bent functions in n variables and highly nonlinear functions in m variables. It is possible to obtain new (n + 15) -variable functions with nonlinearity 2 n + 15 - 1 - 2 (n + 15 - 1) / 2 + 20 × 2 n / 2 and new 12-variable 2-resilient functions with nonlinearity 2000 and algebraic degree 8, which achieve optimal algebraic immunity. Moreover, the modified construction can also be used as an iterative construction of a quadruple of disjoint spectra plateaued functions. In addition, we present sufficient conditions for a quadruple of disjoint spectra plateaued functions to have no nonzero linear structure. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Information Sciences is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.ins.2014.06.024
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      – Code: eng
        Text: English
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        PageCount: 13
        StartPage: 94
    Subjects:
      – SubjectFull: Nonlinear analysis
        Type: general
      – SubjectFull: Boolean functions
        Type: general
      – SubjectFull: Bent functions
        Type: general
      – SubjectFull: Algebraic immunity
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
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      – TitleFull: Secondary constructions of highly nonlinear Boolean functions and disjoint spectra plateaued functions.
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            NameFull: Carlet, Claude
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            NameFull: Hu, Yu-pu
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            – D: 01
              M: 11
              Text: Nov2014
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              Y: 2014
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